Information entropy calculation method and device for wafer processing machine stability evaluation

Abstract

The application provides an information entropy calculation method and device for wafer processing machine stability evaluation. The method comprises the following steps: obtaining full high-dimensional data set collected by FDC system, each data point in the full high-dimensional data set corresponding to a set of process parameter values, and having multiple dimension characteristic information; performing normalization preprocessing on the full high-dimensional data set to eliminate the dimensional difference between parameters; traversing the full high-dimensional data set, taking each data point as a target data point, calculating the distance between the target data point and the remaining data points, and selecting the K nearest data points to form a neighbor set of the target data point; and calculating the information entropy value of the full high-dimensional data set based on the neighbor set of all target data points. The application uses information entropy as a measurement index, converts the complex high-dimensional parameter running state into a single comparable numerical value, and can intuitively and quantitatively represent the wafer processing machine running stability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of semiconductor technology, in particular to an information entropy calculation method and device for stability evaluation of a wafer processing machine. BACKGROUND

[0002] In the process of semiconductor wafer processing, in order to ensure product yield and process stability, a fault detection and classification system (FDC) is usually used to monitor the running state of the equipment in real time. The FDC system collects process parameters including temperature, pressure, flow, voltage, etc. through multiple sensors deployed at key positions of the machine, and judges the abnormality by setting the threshold range of the parameters.

[0003] In the prior art, the key parameters in the set threshold range are mainly monitored to evaluate the running stability of the machine. However, due to the complexity of the wafer manufacturing process, a large amount of multi-dimensional process parameter data will be generated during the processing of the equipment, and many of these parameters, although not set to be monitored, actually have a potential impact on the running stability of the machine. Limited by the high dependence of traditional analysis methods on manual experience and computing power, it is difficult to achieve comprehensive processing and real-time evaluation of high-dimensional and multi-parameter data, thereby affecting the comprehensiveness and accuracy of abnormal detection.

[0004] Therefore, how to automatically process the full amount of multi-dimensional parameters collected by the FDC system without a large amount of manual intervention, and build an evaluation method that can reflect the overall running state of the machine, has become a technical problem that needs to be solved in the field. SUMMARY

[0005] In view of the deficiencies in the prior art, the present application provides an information entropy calculation method and device for stability evaluation of a wafer processing machine, to at least solve the problem that the prior art relies on manual setting of thresholds to monitor a small number of key parameters, and cannot accurately measure the overall running state of the wafer processing machine.

[0006] To achieve the above-mentioned purposes and other advantages, the present application adopts the following technical solutions:

[0007] In a first aspect, the present application provides an information entropy calculation method for stability evaluation of a wafer processing machine, comprising:

[0008] obtaining a full amount of high-dimensional data set collected by the FDC system, each data point in the full amount of high-dimensional data set corresponding to a set of process parameter values, having a plurality of dimensional characteristic information;

[0009] normalizing the full amount of high-dimensional data set to eliminate the dimensional differences between parameters;

[0010] Traverse the full amount of high-dimensional data set, take each data point as a target data point, calculate the distance between the target data point and the remaining data points, and select the nearest K data points to form the neighbor set of the target data point;

[0011] Based on all the neighbor sets of the target data points, the information entropy value of the full amount of high-dimensional data set is calculated, which is used as a quantitative index for evaluating the stability of the wafer processing machine.

[0012] According to the information entropy calculation method for wafer processing machine stability evaluation provided by the present application, the step of calculating the information entropy value of the full amount of high-dimensional data set based on all the neighbor sets of the target data points includes:

[0013] In the neighbor set, sort the distance from the target data point in ascending order, and take the distance corresponding to the Kth neighbor data point as the neighbor distance;

[0014] A high-dimensional hypersphere is constructed with the target data point as the center and the neighbor distance as the radius, and the volume of the high-dimensional hypersphere is calculated;

[0015] Based on the volume of the high-dimensional hypersphere, the neighbor distance, the data space dimension and the total amount of data samples, an information entropy estimation model is constructed, and the information entropy value reflecting the overall uncertainty of the full amount of high-dimensional data set is calculated.

[0016] According to the information entropy calculation method for wafer processing machine stability evaluation provided by the present application, the information entropy estimation model is constructed by the following steps:

[0017] Take the natural logarithm of the neighbor distance of each target data point to obtain the logarithmic distance value as the density estimation index of the target data point in the high-dimensional hypersphere;

[0018] Add up all the logarithmic distance values of the target data points and divide by the total amount of data samples to obtain the average logarithmic neighbor distance;

[0019] Multiply the average logarithmic neighbor distance by the data space dimension, and combine it with the volume of the high-dimensional hypersphere and a statistical correction term to form the variable term of the information entropy estimation model.

[0020] According to the information entropy calculation method for wafer processing machine stability evaluation provided by the present application, the calculation formula of the information entropy estimation model is:

[0021]

[0022] Wherein, H (X) = -∑p (x) logp (x), where N is the total number of data samples, D is the dimension of data space, is the distance between the i-th data point and the k-th nearest neighbor data point, is the value of Digamma function at the total number of samples N, is the value of Digamma function at the number of nearest neighbors k, is the bias correction term between the number of samples and the number of nearest neighbors, is a constant term to correct the estimation bias, is the volume of a high-dimensional hyper-sphere with unit radius, , is the Gamma function.

[0023] According to the information entropy calculation method for wafer processing machine stability evaluation provided in the present application, the total high-dimensional data set is processed by using the minimum-maximum normalization method to scale each process parameter value to a predetermined range.

[0024] According to the information entropy calculation method for wafer processing machine stability evaluation provided in the present application, the calculation method of the distance between data points includes any one of Euclidean distance, Manhattan distance or Chebyshev distance.

[0025] According to the information entropy calculation method for wafer processing machine stability evaluation provided in the present application, the information entropy value is correlated with the wafer yield data of the corresponding batch to construct a prediction model based on the correlation between information entropy and yield, and the prediction model is used to predict the wafer yield trend of future batches and is graphically output in the FDC system.

[0026] In a second aspect, the present application provides an electronic device, which comprises:

[0027] one or more processors; and a memory storing computer program instructions which, when executed, cause the processor to perform the information entropy calculation method for wafer processing machine stability evaluation as described above.

[0028] In a third aspect, the present application provides a computer-readable storage medium having stored thereon computer program / instructions which, when executed by a processor, implement the information entropy calculation method for wafer processing machine stability evaluation as described above.

[0029] In a fourth aspect, the present application provides a computer program product comprising computer program / instructions which, when executed by a processor, implement the information entropy calculation method for wafer processing machine stability evaluation as described above.

[0030] The application provides an information entropy calculation method and device for wafer processing machine stability evaluation. The method comprises the following steps: acquiring full-dimensional data set collected by FDC system, each data point in the full-dimensional data set corresponding to a set of process parameter values, and having multiple dimension characteristic information; performing normalization preprocessing on the full-dimensional data set to eliminate the dimensional difference between parameters; traversing the full-dimensional data set, taking each data point as a target data point, calculating the distance between the target data point and the remaining data points, and selecting the K nearest data points to form a neighbor set of the target data point; and calculating the information entropy value of the full-dimensional data set based on the neighbor set of all target data points, and the information entropy value is used as a quantitative index for evaluating the running stability of the wafer processing machine. The application uses the massive data of the FDC system and uses information entropy as a measurement index to convert the complex high-dimensional parameter running state into a single comparable value, which can intuitively and quantitatively represent the running stability of the wafer processing machine. Compared with the prior art which relies on physical modeling of each machine or setting of parameter threshold by experts, the application does not rely on the type of equipment, and even if the types of parameters corresponding to different machines are different, as long as the vector can be formed, the entropy information can be calculated. The application can be applied to any type of wafer processing machine and has strong engineering applicability and popularization value. The automatic stability evaluation is realized by the algorithm, which replaces the manual parameter judgment mode, significantly reduces the workload of engineers, and improves the response speed and intelligent level of the production line. BRIEF DESCRIPTION OF DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the application, and other embodiments can be obtained by those skilled in the art without creative labor.

[0032] Figure 1 is one of the flowcharts of the information entropy calculation method for wafer processing machine stability evaluation provided by the embodiments of the application;

[0033] Figure 2 is the second flowchart of the information entropy calculation method for wafer processing machine stability evaluation provided by the embodiments of the application;

[0034] Figure 3 is a legend of the desensitized partial process parameter data provided by the embodiments of the application;

[0035] Figure 4 is a legend of the partial data index table for constructing the neighbor set provided by the embodiments of the application;

[0036] Figure 5 is a structural schematic diagram of an electronic device provided by the embodiments of the application. Detailed Implementation

[0037] The above description is merely an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings.

[0038] It should be noted that those skilled in the art will understand, explicitly and implicitly, that the embodiments described in this application can be combined with other embodiments without conflict. Unless otherwise defined, the technical or scientific terms used in this application should have the ordinary meaning understood by those skilled in the art. The terms "a," "an," "an," "the," and similar words used in this application do not indicate quantity limitation and can represent singular or plural. The terms "comprising," "including," "having," and any variations thereof used in this application are intended to cover non-exclusive inclusion; the terms "first," "second," "third," etc., used in this application are merely to distinguish similar objects and do not represent a specific ordering of objects.

[0039] Fault Detection and Classification (FDC) systems are crucial for real-time monitoring, detection, and classification of process faults in semiconductor manufacturing. FDC systems continuously monitor the production process by collecting process parameters, equipment status, and environmental data in real time through various sensors installed on production equipment.

[0040] Information entropy is a core statistic in information theory, used to quantify the degree of uncertainty in a probability distribution. During semiconductor wafer fabrication, various sensors on the equipment continuously collect a large amount of process-related parameter data, such as temperature, pressure, gas flow rate, current, and voltage. The amount of data generated after each wafer is processed is extremely large, forming a typical high-dimensional, diverse process dataset.

[0041] When the machine is operating stably and the process parameters are well controlled, the parameter data exhibits strong regularity and a relatively concentrated distribution structure, resulting in a low information entropy value and indicating minimal uncertainty. Conversely, when the machine experiences operational anomalies or potential deviations (such as sudden temperature changes or pressure fluctuations), the volatility of the process parameters increases, and the data distribution tends to become discrete or irregular, leading to a significant increase in the information entropy value.

[0042] Therefore, the information entropy can be used as a quantitative index for measuring the uncertainty of the distribution of process parameters in the wafer processing process, and thus reflects the stability level of the machine operation. Based on this, the present application provides an information entropy calculation method and device for wafer processing machine stability evaluation, which processes the collected full-dimensional high-dimensional parameter data, constructs an information entropy estimation model, and realizes automatic and quantitative stability evaluation of the wafer processing machine operation state.

[0043] Referring to Figure 1 , Figure 2 As shown in the figure, the present application provides an information entropy calculation method for wafer processing machine stability evaluation, which includes:

[0044] Step S1: Obtain the full-dimensional high-dimensional data set collected by the FDC system. Each data point in the full-dimensional high-dimensional data set corresponds to a set of process parameter values, and has multiple dimensional characteristic information.

[0045] It should be noted that the FDC system is a key online monitoring system in the semiconductor manufacturing process, which can collect and record various process parameters of the machine in the wafer processing process in real time, such as temperature, air pressure, flow, voltage, current, radio frequency power, cavity vacuum degree, reaction time, etc. These parameters are collected by sensors distributed in each module of the processing equipment and uploaded to the central data platform, and are stored in a structured manner according to the wafer batch or processing time period.

[0046] The full-dimensional high-dimensional data set refers to all valid process parameter data extracted from the FDC system within the target analysis period (for example, a wafer batch, a time period or a process section), which covers all available sensor channels and characteristic items. The full-dimensional high-dimensional data set is composed of multiple data points, each data point corresponding to a wafer, a processing step or a time snapshot. Each data point is composed of multiple dimensional process parameter values, forming a vector representation in high-dimensional space.

[0047] Exemplarily, the process parameter data can be historical operation data or real-time collected data from multiple sensors in the semiconductor wafer processing equipment.

[0048] For example, in a certain processing process, if 589 sensor parameters are collected in the wafer processing process, and the process section involves 1568 wafers, the final data set contains 1568 data points, each point has 589 dimensions, corresponding to a complete structured process parameter data matrix (matrix size is 1568x589). An example of desensitized part of the process parameter data is as follows: Figure 3Each row in the table corresponds to a data point, representing a certain wafer or a certain process state at a certain time; each column corresponds to a specific process parameter variable value, such as temperature, voltage, flow rate, radio frequency power, gas pressure, reaction time, etc. With such structured process data as a starting point, normalization preprocessing, neighbor relationship construction and information entropy estimation analysis are performed in subsequent steps to realize quantitative evaluation of the stability of the machine.

[0049] Step S2: Normalization preprocessing is performed on the full high-dimensional data set to eliminate the dimensional differences between parameters. The minimum-maximum normalization method is used to process the full high-dimensional data set to scale the process parameter values to a predetermined range.

[0050] It should be noted that if the distance between sample data points is calculated directly without normalization preprocessing, the parameters with larger scales will dominate the distance calculation, thereby masking the influence of other dimensions and affecting the accuracy of local density estimation. Therefore, in order to ensure the accuracy and stability of subsequent distance calculation and information entropy estimation, normalization preprocessing needs to be performed on the process parameter values in the full high-dimensional data set. The numerical dominance bias caused by the differences in physical dimensions and value ranges between different parameter dimensions is eliminated, so that the characteristics of each dimension have the same scale in the high-dimensional space, and the calculation efficiency and robustness of the subsequent information entropy estimation model are improved.

[0051] Specifically, in this embodiment, the minimum-maximum normalization method is used to process each dimension parameter, and the specific steps are as follows:

[0052] Each process parameter dimension of the full high-dimensional data set is traversed to obtain the minimum value and the maximum value of the parameter in this process parameter dimension.

[0053] For a parameter value in any data point, the following normalization formula is used for conversion:

[0054]

[0055] wherein, is the normalized value of the data, X is the original parameter value, and are the minimum value and the maximum value of the process parameter dimension in the full high-dimensional data set, respectively.

[0056] After normalization processing, all parameter values are scaled to between 0 and 1, or between -1 and 1, with a uniform scale, eliminating the dimensional influence between different parameter dimensions.

[0057] Step S3: The full high-dimensional data set is traversed, each data point is taken as a target data point, the distance between the target data point and the remaining data points is calculated, and the K nearest neighbors of the target data point are selected to form the neighbor set of the target data point.

[0058] Specifically, the entire full-volume high-dimensional data set can be defined as: wherein, represents a sensor data set of the i-th wafer or the i-th processing cycle, and N is the total amount of data samples. Each data point is an n-dimensional vector, represents the j-th parameter value of the i-th data point.

[0059] The current data point is taken as a target data point, and the distance between the target data point and all other data points (j ≠ i) is sequentially calculated. The first K data points with the smallest distance from the target data point are selected, and are recorded as the neighbor set of the target data point.

[0060] The parameter K is a preset constant, and is used to specify the number of nearest neighbor data points required for each data point. The value of K is selected according to experience or data set characteristics. In actual application, a smaller K value can reflect the sensitivity of local structure, and is suitable for capturing minor abnormal changes; and a larger K value has stronger anti-noise ability and statistical stability, and is suitable for overall trend evaluation. In the embodiment, the value of K is set to 5, and part of the data of the generated K-neighbor index matrix is shown as shown in Figure 4 .

[0061] The relative distance relationship between the target data point and the most similar sample data point in the high-dimensional space is calculated, so as to measure the relative distance and distribution characteristics between the data point and the surrounding data points in the feature space, and to depict the local space structure characteristics of the point. The neighbor set can reflect the probability density of each data point in the local space neighborhood. In this way, minor disturbances or abnormal changes in data distribution can be captured, and the sensitivity to machine operation abnormalities can be improved.

[0062] In the embodiment, the distance calculation method between data points includes any one of Euclidean distance, Manhattan distance or Chebyshev distance.

[0063] Euclidean distance is the most commonly used distance measurement method, and is used to calculate the straight-line distance between two points in high-dimensional space. For two data points , the Euclidean distance between the two data points is defined as:

[0064]

[0065] Euclidean distance is suitable for scenarios where parameter values are continuous, scales are uniform, and geometric space intuition is met, and is the preferred distance measurement method in the embodiment.

[0066] The Manhattan distance is used to calculate the total distance of two points in a standard coordinate system along the coordinate axis direction (the sum of the absolute axis distance). The Manhattan distance of two points is defined as:

[0067]

[0068] The Chebyshev distance is used to calculate the maximum value of the difference between two points in each coordinate dimension, that is, the maximum difference in any dimension. The Chebyshev distance of two points is defined as:

[0069]

[0070] Step S4: Based on the near-neighbor set of all target data points, the information entropy value of the full high-dimensional data set is calculated, and the information entropy value is used as a quantitative index for evaluating the stability of the wafer processing machine.

[0071] In this embodiment, step S4 specifically includes:

[0072] Step S401: In the near-neighbor set, sort the distances from the target data point in ascending order, and take the distance corresponding to the Kth nearest neighbor data point as the near-neighbor distance.

[0073] According to the constructed near-neighbor set, the distance values are sorted from small to large. The distance corresponding to the Kth nearest neighbor point in the sorting result is selected as the near-neighbor distance ε of the target data point, which is used to represent the local density of the data point in the high-dimensional space. The near-neighbor distance is not only the local boundary of the target data point, but also a key variable for constructing high-dimensional hyperspheres and estimating density, which directly affects the accuracy and stability of the entropy value.

[0074] Step S402: Construct a high-dimensional hypersphere with the target data point as the center and the near-neighbor distance as the radius, and calculate the volume of the high-dimensional hypersphere;

[0075] After obtaining the near-neighbor distance, a high-dimensional hypersphere is constructed in the D-dimensional data space with the target data point as the center and the near-neighbor distance ε as the radius. The high-dimensional hypersphere represents the local neighborhood range containing the K nearest neighbor sample data points centered on the target data point.

[0076] The volume of the high-dimensional hypersphere is calculated by the following formula:

[0077]

[0078] wherein, is the volume of the high-dimensional hypersphere with a unit radius, D is the dimension of the data space, is the gamma function.

[0079] Step S403: Based on the volume of the high-dimensional hypersphere, combined with the near neighbor distance, data space dimension and total amount of data samples, an information entropy estimation model is constructed, and the information entropy value reflecting the overall uncertainty of the whole high-dimensional data set is calculated.

[0080] Combined with the near neighbor distance of the target data point obtained in steps S401 and S402 and the volume parameter of the high-dimensional hypersphere, an information entropy estimation model is constructed based on a non-parametric information entropy estimation method, and the statistical information entropy value of the whole data set is calculated.

[0081] The information entropy estimation model is constructed by the following method:

[0082] The near neighbor distance of each target data point is Take the natural logarithm to get the logarithmic distance value , which is used as the density estimation index of the target data point in its high-dimensional hypersphere. The logarithmic distance value is used to reflect the spatial density of the target point in its local high-dimensional hypersphere neighborhood, and indirectly represents the reciprocal of its local probability density estimation value, so it can be used as an uncertainty evaluation index of the point.

[0083] The logarithmic distance values of all N target data points are accumulated and divided by the total amount of data samples N to get the logarithmic near neighbor distance mean , which is used to represent the average local density level of the sample data points in the whole data set.

[0084] The logarithmic near neighbor distance mean is multiplied by the data space dimension , which is used to quantify the local density fluctuation in high-dimensional space. And together with the volume of the high-dimensional hypersphere and the statistical correction term, it constitutes the variable term of the information entropy estimation model. The statistical correction term includes: Digamma function , used for bias correction under limited samples, and adjustment term , used for consistency improvement of entropy estimation.

[0085] The finally constructed information entropy estimation model is as follows:

[0086]

[0087] Where, is the information entropy of the whole high-dimensional data set, N is the total amount of data samples, D is the data space dimension, is the distance between the i-th data point and the K-th near neighbor data point, is the value of the Digamma function at the sample total number N, is the value of the Digamma function at the near neighbor number k, is the bias correction term between the sample number and the near neighbor number, is a constant term used to correct the estimation bias, Volume of a hyper-sphere with unit radius.

[0088] The information entropy value is used to measure the overall distribution uncertainty of the data set. The larger the value, the more dispersed and unstable the data is. The smaller the value, the more concentrated the data distribution is, and the more stable the machine is running.

[0089] The information entropy estimation model measures the overall uncertainty of high-dimensional data sets by using the spatial neighborhood structure of sample data points without distribution assumption. Since it does not depend on labels or yield labels, it is suitable for online machine stability detection. Moreover, it does not require data to follow a specific distribution such as Gaussian, and has good versatility, suitable for multiple types of wafer processing equipment. The information entropy estimation model can be deployed in the existing FDC system as an anomaly detection module, used for quantitative evaluation of machine stability, and auxiliary functions such as early warning, root cause analysis and yield prediction.

[0090] In this embodiment, the information entropy value and the wafer yield data of the corresponding batch are analyzed for correlation, and a prediction model based on the correlation between information entropy and yield is constructed. The prediction model is used to predict the wafer yield trend of future batches and is displayed graphically in the FDC system.

[0091] Specifically, the information entropy value comes from the information entropy estimation model and corresponds to the process parameters collected for the wafer batch. The yield is the actual output statistical value of the wafer batch. By jointly analyzing the correlation between the two, the correlation trend between entropy value fluctuation and yield change can be revealed. For example, using the Pearson correlation coefficient, assuming the result range is [-1, 1], the closer to -1 or +1, the stronger the correlation. If the entropy value is higher and the yield is lower, there is a negative correlation.

[0092] The prediction model based on the correlation between information entropy and yield can be constructed using regression analysis, machine learning or time series modeling, etc. A mapping model of entropy value to yield is constructed to evaluate the prediction ability of entropy value on yield. After the model training is completed, it can be used to input the current or predicted period entropy value, and output the yield prediction value or trend change direction of future batches.

[0093] The prediction results are displayed graphically through the FDC system interface, and engineers can quickly identify potential quality problems based on the graph, implement a pre-quality warning mechanism based on stability evaluation, and thus reduce the yield loss caused by sudden abnormalities.

[0094] In summary, the application provides a method for calculating information entropy for evaluating the stability of a wafer processing machine. The method includes obtaining a full high-dimensional data set collected by an FDC system, each data point in the full high-dimensional data set corresponding to a set of process parameter values and having multiple dimensions of feature information; performing normalization preprocessing on the full high-dimensional data set to eliminate dimensional differences between the parameters; traversing the full high-dimensional data set, taking each data point as a target data point, calculating the distance between the target data point and the remaining data points, and selecting the K nearest data points to form a neighbor set of the target data point; and calculating the information entropy value of the full high-dimensional data set based on the neighbor sets of all target data points, the information entropy value being used as a quantitative index for evaluating the running stability of the wafer processing machine. The application uses the massive data of the FDC system and uses information entropy as a measurement index to convert the complex high-dimensional parameter running state into a single comparable numerical value, which can intuitively and quantitatively represent the running stability of the wafer processing machine. Compared with the prior art which relies on physical modeling of each machine or setting of parameter threshold values by experts, the application does not rely on the type of equipment. Even if the types of parameters corresponding to different machines are different, as long as a vector can be formed, the entropy information can be calculated. The application can be applied to any type of wafer processing machine and has strong engineering applicability and promotional value. The algorithm realizes automatic stability evaluation, replacing the manual parameter-by-parameter judgment mode, significantly reducing the workload of engineers, and improving the response speed and intelligent level of the production line.

[0095] Those skilled in the art can understand that, in the above method of the specific implementation, the writing order of each step does not mean a strict execution order and does not constitute any limitation on the implementation process. The specific execution order of each step should be determined by its function and possible internal logic.

[0096] In addition, some embodiments of the application also provide an electronic device. The electronic device can be various forms of digital computers, such as laptops, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and the like. The electronic device can also be various forms of mobile devices, such as personal digital assistants, cellular phones, smart phones, wearable devices, and other similar computing devices.

[0097] The electronic device includes one or more processors and a memory storing computer program instructions that, when executed, cause the processor to perform the method for calculating information entropy for evaluating the stability of a wafer processing machine provided by any one or more of the above embodiments. Figure 5 An exemplary structure diagram of the electronic device is disclosed. As shown in FIG. 1, the electronic device includes a processor 100 and a memory 200. Figure 5As shown, the electronic device includes one or more processors 1101, a memory 1102, and interfaces for connecting various components, including high-speed interfaces and low-speed interfaces. The various components are interconnected by different buses, and can be mounted on a common main board or otherwise installed as appropriate. The processor can process instructions executed within the electronic device, including instructions stored in the memory or on the memory to display graphical information of a GUI on an external input / output device such as a display device coupled to the interface. In some other embodiments, a plurality of processors and / or buses can be used with a plurality of memories and a plurality of memory, if necessary. Also, a plurality of electronic devices can be connected, each device providing part of the necessary operations (for example, as a server array, a set of blade servers, or a multi-processor system). Among them, the components shown herein, their connections and relationships, and their functions are only examples, and are not intended to limit the implementation of the present application described and / or claimed herein.

[0098] The electronic device can also include an input device 1103 and an output device 1104. The processor 1101, the memory 1102, the input device 1103, and the output device 1104 can be connected by a bus or otherwise, Figure 5 The bus connection is taken as an example.

[0099] The input device 1103 can receive input digital or character information, and generate key signal input related to user settings and function control of the electronic device, such as touch screen, keypad, mouse, trackpad, touchpad, pointing stick, one or more mouse buttons, trackball, joystick, etc. The output device 1104 can include a display device, an auxiliary lighting device (e.g., LED), and a tactile feedback device (e.g., a vibration motor), etc. The display device can include but is not limited to a liquid crystal display (LCD), a light-emitting diode (LED) display, and a plasma display. In some embodiments, the display device can be a touch screen.

[0100] To provide for interaction with a user, the electronic device can be a computer. The computer has a display device (e.g., a cathode ray tube (CRT) or liquid crystal display (LCD) monitor) for displaying information to the user and a keyboard and a pointing device (e.g., a mouse or a trackball) by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form, including acoustic, speech, or tactile input.

[0101] In the embodiments of the present application, the computer program / instruction is stored on the computer readable medium, and the computer program / instruction is executed by the processor to implement the information entropy calculation method for wafer processing machine stability evaluation provided by any one or more of the above embodiments. The computer readable medium can be included in the electronic device described in the above embodiments, or can exist separately and not be assembled into the device. The computer readable medium carries one or more computer readable instructions.

[0102] The memory 1102 can be used as a non-transitory computer readable storage medium to store non-transitory software programs, non-transitory computer executable programs and modules. The processor 1101 executes various functions and data processing of the server by running the non-transitory software programs, instructions and modules stored in the memory 1102, so as to implement the program instructions / modules corresponding to the method provided by any one or more of the above embodiments in the embodiments of the present application.

[0103] The memory 1102 can include a program storage area and a data storage area. The program storage area can store an operating system and at least one application required by a function. The data storage area can store data created according to the use of the electronic device, etc. In addition, the memory 1102 can include a high-speed random access memory, and can also include a non-transitory memory, such as at least one magnetic disk storage device, a flash memory device, or other non-transitory solid-state memory device. In some embodiments, the memory 1102 can optionally include a memory disposed remotely with respect to the processor 1101, and these remote memories can be connected to the electronic device through a network. Examples of the above network include but are not limited to the Internet, an intranet, a local area network, a mobile communication network, and a combination thereof.

[0104] Note that more specific examples of the computer-readable storage medium can include but are not limited to an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the present application, the computer-readable storage medium can be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.

[0105] Computer-readable storage media include permanent and non-permanent, removable and non-removable media implemented in any method or technology for information storage. Information can be computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, read-only compact disc (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette, magnetic disk storage or other magnetic storage device, or any other non-transmission medium that can be used to store information accessible by a computing device.

[0106] Computer program code for carrying out operations of the present application can be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0107] In the above-described embodiments, all or part of the embodiments can be implemented by software, hardware, firmware, or any combination thereof. For example, application specific integrated circuits (ASICs), general purpose computers or any other similar devices can be used. In some embodiments, software programs of the present application can be executed by a processor to implement the above steps or functions. Also, software programs of the present application (including related data structures) can be stored in a computer-readable recording medium, such as a RAM memory, a magnetic or optical drive or diskette, and the like. In addition, some steps or functions of the present application can be implemented by hardware, such as a circuit that cooperates with a processor to perform the respective steps or functions.

[0108] The computer program product provided by the embodiments of the present application includes one or more computer programs / instructions, which, when executed by a processor, generate all or part of the processes or functions described in the embodiments of the present application. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions can be transmitted from one website, computer, server or data center to another website, computer, server or data center through wired (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.) mode. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. integrated with one or more available media. The available media can be magnetic media (such as floppy disk, hard disk, magnetic tape), optical media (such as DVD), or semiconductor media (such as solid state disk, SSD, solid state disk), etc.

[0109] The flowcharts or block diagrams in the drawings illustrate the architecture, functionality, and operation of possible implementations of devices, methods, and computer program products according to various embodiments of the present application. In this regard, each block in the flowcharts or block diagrams can represent a module, a segment, or a portion of code, which contains one or more executable instructions for implementing the specified logical functions. It should also be noted that in some alternative implementations, the functions noted in the blocks can occur in a different order than that shown in the figures. For example, two blocks noted in succession can actually be executed substantially concurrently, or they can sometimes be executed in reverse order, depending on the functionality involved. It should also be noted that each block in the block diagrams and / or flowcharts, as well as combinations of blocks in the block diagrams and / or flowcharts, can be implemented by dedicated hardware-based systems that perform specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0110] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any skilled person in the art can easily make changes or replacements within the technical range disclosed in the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be limited by the protection scope of the claims, and the above-mentioned embodiments should be regarded as exemplary and non-limiting.

Claims

1. An information entropy calculation method for wafer processing machine stability evaluation, characterized in that, The method comprises: acquiring a full-volume high-dimensional data set collected by an FDC system, each data point in the full-volume high-dimensional data set corresponding to a set of process parameter values, and having multiple dimensions of feature information; performing normalization preprocessing on the full-volume high-dimensional data set to eliminate dimensional differences between parameters; traversing the full-volume high-dimensional data set, taking each data point as a target data point, calculating distances between the target data point and the remaining data points, and selecting K nearest data points to form a neighbor set of the target data point; based on the neighbor sets of all target data points, calculating an information entropy value of the full-volume high-dimensional data set, comprising: in the neighbor set, sorting the neighbor set in ascending order of distance from the target data point, and taking the distance corresponding to the Kth neighbor data point as a neighbor distance; constructing a high-dimensional hypersphere with the target data point as the center and the neighbor distance as the radius, and calculating a volume of the high-dimensional hypersphere; based on the volume of the high-dimensional hypersphere, combining the neighbor distance, the data space dimension, and the total amount of data samples to construct an information entropy estimation model, and calculating an information entropy value reflecting the overall uncertainty of the full-volume high-dimensional data set, wherein the information entropy value is used as a quantitative index for evaluating the running stability of a wafer processing machine.

2. The information entropy calculation method for wafer processing machine stability evaluation according to claim 1, wherein, The information entropy estimation model is constructed by the following steps: taking the natural logarithm of the neighbor distance of each target data point to obtain a logarithmic distance value as a density estimation index of the target data point in the high-dimensional hypersphere thereof; accumulating the logarithmic distance values of all target data points and dividing by the total amount of data samples to obtain a logarithmic neighbor distance mean value; multiplying the logarithmic neighbor distance mean value by the data space dimension, and combining the volume of the high-dimensional hypersphere and a statistical correction term to form a variable term of the information entropy estimation model.

3. The information entropy calculation method for wafer processing machine stability evaluation according to claim 2, wherein, The calculation formula of the information entropy estimation model is: ； where, is the information entropy of the full high-dimensional data set, N is the total number of data samples, and D is the data space dimension, is the distance between the i-th data point and the k-th nearest neighbor data point, is the value of the Digamma function at the total number of samples N, is the value of the Digamma function at the number of neighbors k, is a bias correction term between the number of samples and the number of neighbors, is a constant term to correct the estimation bias, is the volume of a high-dimensional hypersphere with unit radius, , is the Gamma function.

4. The information entropy calculation method for wafer processing machine stability evaluation according to claim 1, wherein, The full-volume high-dimensional data set is processed by a min-max normalization method to scale each process parameter value to a predetermined range.

5. The information entropy calculation method for wafer processing machine stability evaluation according to claim 1, wherein, The distance between data points can be calculated in any one of the Euclidean distance, Manhattan distance, or Chebyshev distance.

6. The information entropy calculation method for wafer processing machine stability evaluation according to claim 1, wherein, Correlation analysis is performed between the information entropy value and wafer yield data of a corresponding batch to construct a prediction model based on the correlation between information entropy and yield, the prediction model being used to predict the yield trend of future batches and being displayed graphically in the FDC system.

7. An electronic device, comprising: The electronic device comprises: one or more processors; and a memory storing computer program instructions that, when executed, cause the processors to perform the information entropy calculation method for wafer processing machine stability evaluation according to any one of claims 1-6.

8. A computer readable storage medium having stored thereon a computer program and / or instructions, characterized in that, The computer program and / or instructions, when executed by a processor, implement the information entropy calculation method for wafer processing machine stability evaluation according to any one of claims 1-6.

9. A computer program product comprising computer programs and / or instructions, characterized in that, The computer program and / or instructions, when executed by a processor, implement the information entropy calculation method for wafer processing machine stability evaluation according to any one of claims 1-6.

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