Information entropy calculation method and equipment for stability evaluation of wafer processing machine

Abstract

The invention provides an information entropy calculation method and equipment for stability evaluation of a wafer processing machine, and the method comprises the steps: obtaining a full-amount high-dimensional data set collected by an FDC system, and enabling each data point in the full-amount high-dimensional data set to correspond to a group of technological parameter values, and to have feature information of multiple dimensions; performing normalization preprocessing on the full-amount high-dimensional data set to eliminate dimensional differences among parameters; traversing the full-amount high-dimensional data set, taking each data point as a target data point, calculating the distance between the target data point and other data points, and selecting K nearest data points to form a neighbor set of the target data points; and calculating an information entropy value of the full-amount high-dimensional data set based on the neighbor set of all the target data points. According to the method, the information entropy is used as a measurement index, the complex high-dimensional parameter operation state is converted into a single comparable numerical value, and the operation stability of the wafer processing machine can be visually and quantitatively represented.

Description

Technical Field

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

[0002] To ensure product yield and process stability during semiconductor wafer processing, a fault detection and classification (FDC) system is often relied upon to monitor equipment operating status in real time. FDC systems utilize multiple sensors deployed at key locations on the machine to collect process parameters such as temperature, pressure, flow rate, and voltage, and identify anomalies based on set parameter thresholds.

[0003] Existing technologies primarily monitor key parameters within set thresholds to assess tool operational stability. However, due to the complexity of wafer manufacturing processes, equipment generates a large amount of multi-dimensional process parameter data during processing. Many of these parameters, while not subject to specific monitoring specifications, nonetheless have a potential impact on tool operational stability. Traditional analytical methods, limited by their heavy reliance on human experience and computing power, struggle to fully process and evaluate high-dimensional, multi-parameter data in real time, hindering the comprehensiveness and accuracy of anomaly detection.

[0004] Therefore, how to automatically process the full range 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 operating status of the machine has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] In response to the shortcomings of the existing technology, the present application provides an information entropy calculation method and equipment for wafer processing machine stability evaluation, so as to at least solve the problem that the existing technology relies on manually set thresholds to monitor a small number of key parameters and cannot accurately measure the overall operating status of the wafer processing machine.

[0006] In order to achieve the above objectives 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 wafer processing tool stability assessment, comprising:

[0008] Obtaining a full high-dimensional data set collected by the FDC system, where each data point in the full high-dimensional data set corresponds to a set of process parameter values ​​and has feature information in multiple dimensions;

[0009] Performing normalization preprocessing on the full high-dimensional data set to eliminate 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, is the information entropy of the full high-dimensional data set, N is the total number of data samples, D is the data space dimension, is the distance between the i-th data point and the K-th neighboring 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, As a deviation correction term between the number of samples and the number of neighbors, is a constant term used to correct the estimation bias, is the volume of a high-dimensional hypersphere with unit radius, , is the gamma function.

[0023] According to an information entropy calculation method for wafer processing machine stability evaluation provided in the present application, the full high-dimensional data set is processed using a 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 distance between data points is calculated using 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, 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 graphically output and displayed in the FDC system.

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

[0027] One or more processors; and a memory storing computer program instructions, wherein when the computer program instructions are executed, the processor executes the information entropy calculation method for wafer processing tool stability assessment as described above.

[0028] In a third aspect, the present application provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements an information entropy calculation method for wafer processing tool stability evaluation as described in any one of the above.

[0029] In a fourth aspect, the present application provides a computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the information entropy calculation method for wafer processing tool stability assessment as described in any one of the above.

[0030] This application provides a method and device for calculating information entropy for wafer processing tool stability assessment. The method obtains a full high-dimensional dataset collected by an FDC system, where each data point corresponds to a set of process parameter values ​​and has multi-dimensional feature information. The method then performs normalization preprocessing on the full high-dimensional dataset to eliminate dimensional differences between the parameters. The method then traverses the full high-dimensional dataset, taking each data point as a target data point, calculates the distance between the target data point and the remaining data points, and selects the K closest data points to form a neighbor set for the target data point. Based on the neighbor sets of all target data points, the method calculates the information entropy value of the full high-dimensional dataset. The information entropy value is used to quantitatively assess the operational stability of the wafer processing tool. This application utilizes the massive data from the FDC system and uses information entropy as a metric to convert the complex high-dimensional parameter operating status into a single, comparable value, enabling intuitive and quantitative characterization of the operational stability of the wafer processing tool. Compared to existing technologies that rely on physical modeling of each tool or expert-set parameter thresholds, this method is independent of the type of equipment. Even if different tools correspond to different parameter types, entropy information can be calculated as long as a vector can be formed. It can be applied to any type of wafer processing machine, demonstrating strong engineering applicability and promotional value. The algorithm implements automated stability assessment, replacing manual parameter-by-parameter judgment, significantly reducing the manual analysis workload for engineers and improving the response speed and intelligence level of the production line. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other implementation methods can be obtained based on these drawings without paying any creative work.

[0032] Figure 1 This is one of the flow charts of the information entropy calculation method for wafer processing tool stability evaluation provided in an embodiment of the present application;

[0033] Figure 2 This is the second flow chart of the information entropy calculation method for wafer processing tool stability evaluation provided in an embodiment of the present application;

[0034] Figure 3 This is a diagram of some process parameter data after desensitization provided in the examples of this application;

[0035] Figure 4 This is a diagram of a partial data index table for constructing a neighbor set provided in an embodiment of the present application;

[0036] Figure 5 It is a structural diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0037] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present application more obvious and easy to understand, the following specifically cites a preferred embodiment and describes it in detail with reference to the accompanying drawings.

[0038] It should be noted that, it is explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments in the absence of conflict. Unless otherwise defined, the technical terms or scientific terms involved in this application should be the usual meanings understood by people with ordinary skills in the technical field to which this application belongs. The words "one", "a", "a", "the" and similar words involved in this application do not indicate a quantitative limit and can represent the singular or plural. The terms "include", "comprise", "have" and any variations thereof involved in this application are intended to cover non-exclusive inclusions; the terms "first", "second", "third" and the like involved 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 utilize various sensors installed on production equipment to collect real-time data on process parameters, equipment status, and environmental conditions, enabling continuous monitoring of the production process.

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

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

[0042] Therefore, information entropy can be used as a quantitative indicator to measure the uncertainty of process parameter distribution during wafer processing, thereby reflecting 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 assessment. By processing the full amount of collected high-dimensional parameter data, an information entropy estimation model is constructed to achieve automated and quantitative stability assessment of the operating status of the wafer processing machine.

[0043] Reference Figure 1 、 Figure 2 As shown, the embodiment of the present application provides an information entropy calculation method for wafer processing tool stability evaluation, including:

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

[0045] It's important to note that the FDC system, a critical online monitoring system in semiconductor manufacturing, collects and records various process parameters in real time during wafer processing, such as temperature, pressure, flow, voltage, current, RF power, chamber vacuum, and response time. These parameters are collected by sensors distributed throughout the processing equipment and uploaded to a central data platform for structured storage based on wafer batches or processing time periods.

[0046] A full, high-dimensional dataset refers to all valid process parameter data extracted from the FDC system during the target analysis period (e.g., a wafer batch, a time period, or a process step), encompassing all available sensor channels and features. This full, high-dimensional dataset consists of multiple data points, each corresponding to a wafer, a processing step, or a snapshot in time. Each data point consists of process parameter values ​​across multiple dimensions, forming a vector representation in a high-dimensional space.

[0047] For example, the process parameter data may be historical operating data or real-time collected data from a plurality of sensors in semiconductor wafer processing equipment.

[0048] For example, in a certain process, if 589 sensor parameters are collected during the wafer processing, and the process involves a total of 1568 wafers, the final data set contains 1568 data points, each with 589 dimensions, corresponding to a complete structured process parameter data matrix (matrix size is 1568×589). An example of some process parameter data after desensitization 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 high-dimensional dataset can be defined as: ,in, , represents the sensor data set of the i-th wafer or the i-th processing cycle, and N is the total number of data samples. Each data point , is an n-dimensional vector, represents the jth parameter value of the i-th data point.

[0059] The current data point As the target data point, calculate the target data point and all other data points in turn (j ≠ i). Select the first K data points with the smallest distance to the target data point and record them as the neighbor set of the target data point. .

[0060] The parameter K is a preset constant that specifies the number of nearest neighbor data points to be selected for each data point. The K value is selected based on experience or data set characteristics. In practical applications, a smaller K value can better reflect the sensitivity of the local structure and is suitable for capturing small abnormal changes; while a larger K value has stronger noise resistance and statistical stability and is suitable for overall trend assessment. In this embodiment, the K value is set to 5, and some data examples of the generated K nearest neighbor index matrix are as follows: Figure 4 shown.

[0061] The relative distance between a target data point and its most similar sample data point in high-dimensional space is calculated to measure the relative distance and distribution characteristics of the data point and surrounding data points in the feature space, and to characterize the local spatial structure of the point. The nearest neighbor set can reflect the probability density of each data point in the local spatial neighborhood. This can capture small disturbances or abnormal changes in the data distribution and improve sensitivity to abnormal machine operation.

[0062] In this embodiment, the distance between data points is calculated using any one of Euclidean distance, Manhattan distance, and Chebyshev distance.

[0063] Euclidean distance is the most commonly used distance metric, which is used to calculate the straight-line distance between two points in high-dimensional space. , its Euclidean distance Defined as:

[0064]

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

[0066] Manhattan distance is used to calculate the total distance between two points along the coordinate axis in the standard coordinate system (the sum of the absolute axis distances). Defined as:

[0067]

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

[0069]

[0070] Step S4: Based on the neighbor sets of all target data points, the information entropy value of the full high-dimensional data set is calculated. The information entropy value is used to evaluate the quantitative index of the wafer processing machine operation stability.

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

[0072] Step S401: sort the neighboring data points in ascending order by distance from the target data point, and take the distance corresponding to the Kth neighboring data point as the neighboring distance.

[0073] Based on the constructed set of nearest neighbors, the distance values ​​are sorted from smallest to largest. The distance corresponding to the Kth nearest neighbor in the sorted result is selected as the nearest 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. This nearest neighbor distance is not only the local boundary of the target data point but also a key variable in the subsequent construction of the high-dimensional hypersphere and density estimation, which directly affects the accuracy and stability of the entropy value.

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

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

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

[0077]

[0078] in, is the volume of a high-dimensional hypersphere with 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 nearest neighbor distance, data space dimension and total number of data samples, an information entropy estimation model is constructed, and the information entropy value reflecting the overall uncertainty of the full high-dimensional data set is calculated.

[0080] Combining the neighbor distances of the target data points obtained in step S401 and step S402 with the volume parameters 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 entire data set is calculated.

[0081] The information entropy estimation model is constructed in the following ways:

[0082] The nearest neighbor distance of each target data point Take the natural logarithm to get the logarithmic distance value , serving as a density estimation indicator for the target data point within its high-dimensional hypersphere. This logarithmic distance value reflects the spatial density of the target point within its local high-dimensional hypersphere neighborhood, indirectly representing the inverse of its local probability density estimate, and can therefore be used as an uncertainty assessment indicator for the point.

[0083] The logarithmic distance values ​​of all N target data points are accumulated and divided by the total number of data samples N to obtain the mean logarithmic neighbor distance . It is used to represent the average local density level of sample data points in the entire data set.

[0084] Multiply the mean of the log-neighbor distance by the dimension of the data space , which is used to quantify local density fluctuations in high-dimensional space. 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 , for bias correction under finite samples, and adjustment terms , for consistency improvement of entropy estimation.

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

[0086]

[0087] in, is the information entropy of the full high-dimensional data set, N is the total number of data samples, D is the data space dimension, is the distance between the i-th data point and the K-th neighboring 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, As a deviation correction term between the number of samples and the number of neighbors, is a constant term used to correct the estimation bias, is the volume of a high-dimensional hypersphere of unit radius.

[0088] The information entropy value is used to measure the overall distribution uncertainty of a 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 operation is.

[0089] This information entropy estimation model, without any distributional assumptions, leverages the spatial neighborhood structure of sample data points to measure the overall uncertainty of high-dimensional datasets. Because it does not rely on annotations or yield labels, it is suitable for in-line tool stability testing. Furthermore, it does not require data to conform to specific distributions, such as Gaussian distributions, making it versatile and applicable to a wide range of wafer processing equipment. This information entropy estimation model can be deployed as an anomaly detection module within existing FDC systems to quantitatively assess tool stability and assist with early warning, root cause analysis, and yield prediction.

[0090] In this embodiment, the information entropy value is correlated with the wafer yield data of the corresponding batch, 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 graphically output and displayed in the FDC system.

[0091] Specifically, the information entropy value is derived from an information entropy estimation model and corresponds to the process parameters collected for that wafer batch. Yield is the actual output statistic for that wafer batch. By combining these two values ​​for correlation analysis, we can reveal the correlation between entropy fluctuations and yield changes. 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 a higher entropy value is associated with a lower yield, this indicates a negative correlation.

[0092] Predictive models based on the correlation between information entropy and yield can be constructed using methods such as regression analysis, machine learning, or time series modeling. This mapping model from entropy to yield is constructed to evaluate entropy's ability to predict yield. Once the model is trained, it can be used to input entropy values ​​for the current or forecast cycle and output yield predictions or trend changes for future batches.

[0093] The prediction results are graphically displayed through the FDC system interface. Engineers can quickly identify potential quality risks based on the diagrams, implement a pre-emptive quality warning mechanism based on stability evaluation, and thus reduce yield losses caused by sudden anomalies.

[0094] In summary, the present application provides a method for calculating information entropy for evaluating the stability of wafer processing machines. The method obtains a full high-dimensional data set collected by the FDC system, wherein each data point in the full high-dimensional data set corresponds to a set of process parameter values ​​and has characteristic information of multiple dimensions; the full high-dimensional data set is normalized and preprocessed to eliminate the dimensional differences between the parameters; the full high-dimensional data set is traversed, each data point is used as a target data point, the distance between the target data point and the remaining data points is calculated, and the K data points closest to the target data point are selected to form a neighbor set of the target data point; based on the 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 to evaluate the quantitative index of the operational stability of the wafer processing machine. The present application utilizes the massive data of the FDC system and adopts information entropy as a measurement indicator to convert the complex high-dimensional parameter operating status into a single comparable value, which can intuitively and quantitatively characterize the operational stability of the wafer processing machine. Compared to existing technologies that rely on physical modeling of each machine or expert-set parameter thresholds, this application is independent of the type of equipment. Even if different machines correspond to different parameter types, as long as a vector can be formed, entropy information can be calculated. It can be applied to any type of wafer processing machine and has strong engineering applicability and promotion value. The algorithm realizes automated stability assessment, replacing the manual parameter-by-parameter judgment method, significantly reducing the manual analysis workload of engineers and improving the response speed and intelligence level of the production line.

[0095] Those skilled in the art will understand that in the above-mentioned method of the specific implementation method, 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 present application further provide an electronic device. The electronic device may be various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, etc. The electronic device may also be various forms of mobile devices, such as personal digital assistants, cellular phones, smartphones, wearable devices, and other similar computing devices.

[0097] The electronic device includes: one or more processors; and a memory storing computer program instructions, and when the computer program instructions are executed, the processor executes the information entropy calculation method for wafer processing tool stability assessment provided by any one or more of the above embodiments. Figure 5 An exemplary structural diagram of the electronic device is disclosed. Figure 5As shown, the electronic device includes: one or more processors 1101, memory 1102, and interfaces for connecting various components, including high-speed and low-speed interfaces. The various components are interconnected using different buses and can be mounted on a common motherboard or in other ways as needed. The processor can process instructions executed within the electronic device, including instructions stored in or on the memory for displaying graphical information of a GUI on an external input / output device (such as a display device coupled to the interface). In some other embodiments, if desired, multiple processors and / or multiple buses can be used with multiple memories and multiple storage devices. Similarly, multiple electronic devices can be connected, with each device providing some of the necessary operations (for example, as a server array, a group of blade servers, or a multi-processor system). 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 application described and / or claimed herein.

[0098] The electronic device may further 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 may be connected via a bus or other means. Figure 5 The bus connection is taken as an example.

[0099] 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. Examples include a touch screen, keypad, mouse, trackpad, touchpad, pointing stick, one or more mouse buttons, trackball, joystick, and other input devices. Output device 1104 may include a display device, auxiliary lighting devices (e.g., LEDs), and tactile feedback devices (e.g., vibration motors). The display device may 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 may be a touch screen.

[0100] To provide user interaction, the electronic device may be a computer. The computer includes a display device (e.g., a cathode ray tube (CRT) or LCD monitor) for displaying information to the user, and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices may also be used to provide user interaction; for example, feedback provided to the user may be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback), and input from the user may be received in any form, including acoustic input, voice input, or tactile input.

[0101] In an embodiment of the present application, a computer program / instruction is stored on a computer-readable medium. When executed by a processor, the computer program / instruction implements the information entropy calculation method for wafer processing tool stability assessment provided by any one or more of the above-mentioned embodiments. The computer-readable medium may be included in the electronic device described in the above-mentioned embodiments; or it may exist independently and not be incorporated into the device. The above-mentioned 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 the non-transitory software programs, instructions, and modules stored in the memory 1102 to execute various functional applications and data processing of the server, thereby implementing the program instructions / modules corresponding to the method provided in any one or more of the above embodiments of the present application.

[0103] The memory 1102 may include a program storage area and a data storage area, wherein the program storage area may store an operating system and applications required for at least one function; the data storage area may store data created based on the use of the electronic device, etc. In addition, the memory 1102 may include a high-speed random access memory, and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory 1102 may optionally include a memory remotely located relative to the processor 1101, and these remote memories may be connected to the electronic device via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0104] It should be noted that more specific examples of computer-readable storage media may include, but are not limited to, an electrical connection having one or more conductors, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disc read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this application, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0105] Computer-readable storage media include permanent and non-permanent, removable and non-removable media, and can be implemented by any method or technology to store information. 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 random-access 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 technologies, compact disc-read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic tape, disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device.

[0106] Computer program code for performing the operations of the present application may be written in one or more programming languages, or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, C++, and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0107] In the above embodiments, all or part of the above embodiments may be implemented using software, hardware, firmware, or any combination thereof. For example, an application-specific integrated circuit (ASIC), a general-purpose computer, or any other similar hardware device may be used for implementation. In some embodiments, the software program of the present application may be executed by a processor to implement the above steps or functions. Similarly, the software program of the present application (including related data structures) may be stored in a computer-readable recording medium, such as a RAM memory, a magnetic or optical drive, a floppy disk, or the like. In addition, some steps or functions of the present application may be implemented using hardware, for example, as a circuit that cooperates with a processor to perform the various steps or functions.

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

[0109] The flowcharts or block diagrams in the accompanying drawings illustrate the possible architectures, functions and operations of the devices, methods and computer program products according to various embodiments of the present application. In this regard, each box in the flowchart or block diagram can represent a module, program segment or part of code, and the module, program segment or part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, as well as the combination of boxes in the block diagram and / or flowchart, can be implemented with a dedicated hardware-specific system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0110] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any person skilled in the art may easily propose variations or substitutions within the technical scope disclosed in the present application, and such variations or substitutions shall be encompassed within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be subject to the scope of protection of the claims, and the above embodiments shall be regarded as exemplary and non-limiting.

Claims

1. A method for calculating information entropy for wafer processing machine stability evaluation, characterized in that: include: Obtaining a full high-dimensional data set collected by the FDC system, where each data point in the full high-dimensional data set corresponds to a set of process parameter values ​​and has feature information in multiple dimensions; Performing normalization preprocessing on the full high-dimensional data set to eliminate dimensional differences between parameters; Traverse the entire high-dimensional dataset, take each data point as the target data point, calculate the distance between the target data point and the remaining data points, and select the K data points with the closest distance to form the neighbor set of the target data point; Based on the neighbor sets of all the target data points, the information entropy value of the full high-dimensional data set is calculated, and the information entropy value is used to evaluate the quantitative index of the operating stability of the wafer processing machine.

2. The information entropy calculation method for wafer processing machine stability evaluation according to claim 1, characterized in that: The step of calculating the information entropy value of the full high-dimensional data set based on the neighbor sets of all the target data points includes: In the neighbor set, sort in ascending order by the distance to the target data point, and take the distance corresponding to the Kth neighbor data point as the neighbor distance; constructing a high-dimensional hypersphere with the target data point as the center and the nearest neighbor distance as the radius, and calculating the volume of the high-dimensional hypersphere; Based on the volume of the high-dimensional hypersphere, combined with the neighbor distance, data space dimension and total number of data samples, an information entropy estimation model is constructed, and an information entropy value reflecting the overall uncertainty of the full high-dimensional data set is calculated.

3. The information entropy calculation method for wafer processing machine stability evaluation according to claim 2, characterized in that: The information entropy estimation model is constructed by the following steps: Taking the natural logarithm of the nearest neighbor distance of each target data point to obtain a logarithmic distance value as a density estimation indicator of the target data point within its high-dimensional hypersphere; The logarithmic distance values ​​of all the target data points are accumulated and divided by the total number of data samples to obtain the mean logarithmic nearest neighbor distance; The mean of the logarithmic nearest neighbor distance is multiplied by the dimension of the data space, and together with the volume of the high-dimensional hypersphere and the statistical correction term, constitutes the variable term of the information entropy estimation model.

4. The information entropy calculation method for wafer processing machine stability evaluation according to claim 3, characterized in that: The calculation formula of the information entropy estimation model is: in, is the information entropy of the full high-dimensional data set, N is the total number of data samples, D is the data space dimension, is the distance between the i-th data point and the K-th neighboring 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, As a deviation correction term between the number of samples and the number of neighbors, is a constant term used to correct the estimation bias, is the volume of a high-dimensional hypersphere with unit radius, , is the gamma function.

5. The information entropy calculation method for wafer processing machine stability evaluation according to claim 1, characterized in that: The full high-dimensional data set is processed using a minimum-maximum normalization method to scale the values ​​of each process parameter to a predetermined range.

6. The information entropy calculation method for wafer processing machine stability evaluation according to claim 1, characterized in that: The distance between data points can be calculated using Euclidean distance, Manhattan distance, or Chebyshev distance.

7. The information entropy calculation method for wafer processing machine stability evaluation according to claim 1, characterized in that: The information entropy value is correlated with the wafer yield data of the corresponding batch, 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 graphically output and displayed in the FDC system.

8. An electronic device, characterized in that: The electronic device comprises: One or more processors; and a memory storing computer program instructions, wherein when the computer program instructions are executed, the processor executes the information entropy calculation method for wafer processing tool stability evaluation according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the information entropy calculation method for wafer processing tool stability evaluation according to any one of claims 1 to 7 is implemented.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the information entropy calculation method for wafer processing tool stability evaluation according to any one of claims 1 to 7 is implemented.

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