Semiconductor Wafer Production Quality Assessment System
By developing the quality assessment system of semiconductor wafer production, using image data and electrical performance parameters for comprehensive assessment, solving the problem of slow, damage and difficulty reflecting the three -dimensional structure of existing detection methods, and achieve high -efficiency and non -destructive quality assessment.
Patent Information
- Application Number
- CN202411496281.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-25
- Publication Date
- 2025-01-28
- Estimated Expiration
- 2044-10-25
AI Technical Summary
The existing semiconductor wafer production quality detection methods have problems such as slow detection speed, damage to the wafer, and difficulty in fully reflecting the three-dimensional structure and internal defects of the wafer.
A semiconductor wafer production quality assessment system has been developed, including data collection modules, sensor modules, data processing and analysis modules and evaluation modules. The system generates comprehensive evaluation coefficients by obtaining wafer surface image data, electrical performance parameters and production data to perform image cutting, feature extraction and comprehensive evaluation.
The high -efficiency, non -destructive semiconductor wafer quality assessment can be achieved, which can fully reflect the wafer's three -dimensional structure and internal defects, improve the detection speed and accuracy, and reduce cost loss.
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Figure CN119006478B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of semiconductor wafer production, and in particular to a semiconductor wafer production quality assessment system. Background Art
[0002] Semiconductor wafers are silicon chips used to manufacture silicon semiconductor integrated circuits. They are round in shape and are made from high-purity polycrystalline silicon that is dissolved, doped with silicon crystal seeds, and then slowly pulled out to form single crystal silicon, which is then made into silicon wafers through steps such as grinding, polishing, and slicing. The main reason is that various circuit component structures are processed on silicon wafers to become IC products with specific electrical functions. It is the basic material of semiconductor chips and is crucial to the entire semiconductor industry. With the continuous advancement of semiconductor technology, the size of wafers is gradually increasing, from the initial 1 inch to the current 300mm or even larger. At the same time, the application of semiconductor materials such as silicon carbide (SiC) is also gradually increasing, bringing new development opportunities to the wafer industry.
[0003] With the continuous advancement of semiconductor technology, the quality requirements for wafers are becoming increasingly stringent. Although traditional detection methods can detect wafer defects to a certain extent, they often have problems such as slow detection speed and damage to the wafer. In addition, these methods can usually only provide two-dimensional information on the wafer surface, and it is difficult to fully reflect the three-dimensional structure and internal defects of the wafer. Therefore, the development of an efficient, comprehensive, and non-destructive semiconductor wafer quality assessment system has become an urgent need in the industry. Summary of the invention
[0004] In view of the deficiencies in the prior art, the present invention provides a semiconductor wafer production quality assessment system, which solves some of the existing problems of slow wafer production quality inspection speed, damage to wafers, and incomplete defect detection.
[0005] To achieve the above objectives, the present invention is implemented through the following technical solutions: a semiconductor wafer production quality assessment system, comprising:
[0006] Data acquisition module: used to obtain wafer surface image data, historical wafer qualified production image data and corresponding production data; mark wafer surface image data as group A image data; mark historical wafer qualified production image data as group B image data; generate image data sets by analyzing, classifying and image cutting the two types of image data, and transmit the image data sets and corresponding wafer production data to the data processing and analysis module;
[0007] Sensor module: used to obtain the electrical performance parameters of the semiconductor wafer, including resistivity, carrier concentration, carrier lifetime and surface recombination lifetime, as well as rated electrical performance parameters, generate a static data set, and transmit it to the evaluation module;
[0008] Data processing and analysis module: receives the image data set and the corresponding production data from the image acquisition module; analyzes the specifications of the wafer based on the image data set to generate a specification data set; and dynamically analyzes the production process;
[0009] Evaluation module: used to receive specification data set, dynamic data set and static data set, analyze the relationship between the three data sets and generate a comprehensive evaluation coefficient;
[0010] As a further solution of the present invention, it also includes:
[0011] User Interface Module: Provides an intuitive interface to , carrier concentration coefficient n, carrier lifetime coefficient , surface composite life coefficient T, temperature coefficient wd, air pressure coefficient qd, flow rate coefficient ld, size coefficient b2, nano process coefficient c2, thickness coefficient d2, flatness coefficient e2, dynamic evaluation coefficient S, static evaluation coefficient H, specification evaluation coefficient G, and comprehensive evaluation coefficient Z are displayed.
[0012] As a further solution of the present invention, analyzing the group A image data and the group B image data to generate an image data set includes the following steps:
[0013] Performing image segmentation on the wafer image information in the group A image data and the group B image data respectively, dividing the complete image information of a single wafer image into three groups of large-area image information;
[0014] The large-area image information includes front image information, back image information and edge image information; the front image information in Group A image data and Group B image data is loaded into a first-class folder, the back image information in Group A image data and Group B image data is loaded into a second-class folder, and the side image information in Group A image data and Group B image data is loaded into a third-class folder; an image data set is generated.
[0015] As a further solution of the present invention, analyzing the electrical performance parameters and calculating the corresponding coefficients of the electrical performance parameters include the following steps:
[0016] Resistivity coefficient :
[0017] ;
[0018] Where R is the resistance value, A is the cross-sectional area of the material, and L is the length of the current flowing through the material;
[0019] Example: When measuring at room temperature 23°C, the applied current is 1mA and the measured voltage is 9.5mV. Substituting the known values, we can calculate: ;
[0020] Carrier concentration coefficient n:
[0021] ;
[0022] Where ND is the donor impurity concentration, NA is the acceptor impurity concentration, g is the ionization factor, EF is the Fermi level, ED is the donor energy level, k is the Boltzmann constant, and T is the absolute temperature;
[0023] Example: Assume there is an n-type silicon wafer with a donor impurity concentration ND of , the acceptor impurity concentration NA is , the Fermi level EF is 0.1 eV below the conduction band bottom Ec, the donor level ED is 0.05 eV below the conduction band bottom Ec, and the temperature T is 300K; Substituting the known values, we can get ;
[0024] Carrier lifetime coefficient :
[0025] ;
[0026] Where γ is the recombination coefficient, Δp is the non-equilibrium hole concentration, and Δn is the non-equilibrium electron concentration;
[0027] Example: Assume that in a silicon wafer, the non-equilibrium electron concentration Δn is , the non-equilibrium hole concentration Δp is also , the composite coefficient γ is cm³ / s; Substituting the known values into the calculation, we get ;
[0028] Surface composite life factor T:
[0029] ;
[0030] Where, d is the sample thickness, S is the surface recombination velocity;
[0031] Example: Assuming the thickness d of the silicon wafer is 200 μm and the surface recombination velocity S is 100 cm / s, substituting the known values into the calculation, we can get T=1× s.
[0032] As a further solution of the present invention, generating a static data set according to the corresponding coefficients of the electrical performance parameters includes the following steps:
[0033] Setting a preset coefficient group, including a preset resistivity coefficient, a preset carrier concentration coefficient, a preset carrier lifetime coefficient, and a preset surface recombination lifetime coefficient;
[0034] When one or more of the electrical performance parameters are less than the preset coefficient, the semiconductor wafer is confirmed to be unqualified and the relevant data is discarded;
[0035] Generate static data sets including resistivity coefficients , carrier concentration coefficient n, carrier lifetime coefficient and surface composite life factor T.
[0036] As a further solution of the present invention, the specifications of the wafer are analyzed based on the image data set to generate a correlation coefficient, including the following steps:
[0037] A defect detection model based on a deep learning algorithm is established, a defect training set is input, a convolutional neural network algorithm is executed, features of the wafer are extracted, including size, nanometer manufacturing, thickness, and flatness, and correlation coefficients are generated.
[0038] As a further embodiment of the present invention, generating a correlation coefficient and a specification data set comprises the following steps:
[0039] A1: For the first and third type folders, count the actual radius b0 of the wafer in the group A images, calculate the ratio of the actual radius b0 to the standard radius b1, record it as the size coefficient, and if the size coefficient b2 is greater than or equal to the size critical value b, mark the wafer as unqualified, exclude the wafers marked as unqualified, count the size coefficient s_b2 of the qualified wafers, and calculate the mean value b3;
[0040] Among them, the size critical value b is the mean value of the wafer radius in group B images;
[0041] A2: For the first and third types of folders, analyze the front and back images of the wafer, identify the transistor structure on the wafer through the edge detection algorithm, and calculate its size and spacing, and then obtain the actual nano-process c0 of the wafer, calculate the ratio of the actual nano-process c0 to the standard nano-process c1, and record it as the nano-process coefficient c2, and if the nano-process coefficient c2 is greater than or equal to the nano-process critical value c, mark the wafer as unqualified, exclude the unqualified wafers, count the nano-process coefficients s_c2 of qualified wafers, and calculate the average c3;
[0042] Among them, the nanometer process critical value c is the average value of the wafer nanometer process in group B images;
[0043] A3: For the second type of folders, count the actual thickness d0 of the wafer in the group A images, calculate the ratio of the actual thickness d0 to the standard thickness d1, record it as the thickness coefficient, and if the thickness coefficient d2 is greater than or equal to the thickness threshold d, mark the wafer as unqualified, exclude the wafers marked as unqualified, count the thickness coefficient s_d2 of the qualified wafers, and calculate the average d3;
[0044] Among them, the thickness critical value d is the average value of the wafer thickness in group B images;
[0045] A4: For the first, second and third category folders, the 3D reconstruction technology is used to generate the 3D structure data of the wafer in the group A images, and the 3D morphology data of the wafer is obtained, which is stored in the form of high-resolution point cloud. Each point represents the height information of a specific position on the wafer surface. Based on the principle of least squares, the wafer surface is fitted to an optimal plane, and then the distance from each measurement point to this plane is calculated. The maximum value of all distances is the flatness e0 of the wafer.
[0046] Count the actual flatness e0 of the wafer, calculate the ratio of the actual flatness e0 to the standard flatness e1, record it as the flatness coefficient, and if the flatness coefficient e2 is greater than or equal to the flatness critical value e, mark the wafer as unqualified, exclude the wafer marked as unqualified, count the flatness coefficient s_e2 of the qualified wafers, and calculate the average value e3;
[0047] Among them, the flatness critical value e is the average value of wafer flatness in group B images;
[0048] A5: Generate a specification data set, including size coefficient b2, nano process coefficient c2, thickness coefficient d2, and flatness coefficient e2.
[0049] As a further solution of the present invention, dynamic analysis is performed based on production data corresponding to the image data set to generate a dynamic data set, including the following steps:
[0050] B1: Clean the data related to unqualified wafers in the first, second and third folders, and analyze the actual production data corresponding to the three folders, where the actual production data includes temperature, air pressure, flow rate and time. The analysis process includes the following steps:
[0051] According to the size data, the wafers are divided into several categories. For any category of wafers, a production temperature curve, a production pressure curve and a production flow rate curve are established respectively, and it is stipulated that the three curves all use the same time axis;
[0052] B2: For the production temperature curve, the production process is divided into several stages according to the temperature change. The steps of stage division are: calculate the absolute value of the temperature change acceleration in the curve, mark the time less than t1, and the absolute value of the temperature change acceleration is greater than or equal to a1, mark the stage as the transition stage, and sort all the transition stages from front to back according to the time axis;
[0053] At the same time, all the divided areas except the transition area are recorded as production areas and sorted from front to back according to the time axis;
[0054] B201: For the production interval, the production temperature curve corresponding to the group B image sets a time node every 0.5 seconds, defines half of the difference between the maximum and minimum values of the production temperature curve at the same time node, recorded as the fluctuation value j0, performs the mean operation on all the points passed by the production temperature curve at the time node, and defines it as the median j1; determines the fluctuation range, and the determination rule is: the upper limit of the fluctuation at each time node is the sum of the median j1 of the node and the fluctuation value j0, and the lower limit of the fluctuation is the difference between the median j1 of the node and the fluctuation value j0;
[0055] B202: For the production interval, the production temperature curve value corresponding to the group A image, at each time node, if there is a production temperature curve that exceeds the fluctuation range at the time node, and the wafer corresponding to the production temperature curve is unqualified, the unqualified wafer data is eliminated; for the production temperature curve of the qualified wafer, the difference between the curve value at the time node and the median j1 and the inverse ratio of the fluctuation value j0 are calculated, recorded as the temperature coefficient wd;
[0056] B3: For the production air pressure curve, the production process is divided into several stages according to the change of air pressure. The steps of stage division are: calculate the absolute value of the acceleration of the change of air pressure in the curve, mark the time less than t2, and the absolute value of the acceleration of the change of air pressure is greater than or equal to a2, mark the stage as the transition stage, and sort all the transition stages from front to back according to the time axis;
[0057] At the same time, all the divided areas except the transition area are recorded as production areas and sorted from front to back according to the time axis;
[0058] B301: For the production interval, the production pressure curve corresponding to the group B image sets a time node every 2.5 seconds, defines half of the difference between the maximum and minimum values of the production pressure curve at the same time node, recorded as the fluctuation value j2, performs the mean operation on all the points passed by the production pressure curve at the time node, and defines it as the median j3; determines the fluctuation range, and the determination rule is: the upper limit of the fluctuation at each time node is the sum of the median j3 of the node and the fluctuation value j2, and the lower limit of the fluctuation is the difference between the median j3 of the node and the fluctuation value j2;
[0059] B302: For the production interval, the production pressure curve value corresponding to the group A image, at each time node, if there is a production pressure curve that exceeds the fluctuation range at the time node, and the wafer corresponding to the production pressure curve is unqualified, the unqualified wafer data is eliminated; for the production pressure curve of the qualified wafer, the difference between the curve value at the time node and the median j3 and the inverse ratio of the fluctuation value j2 are calculated, and recorded as the pressure coefficient qd;
[0060] B4: For the production flow rate curve, the production process is divided into several stages according to the change of flow rate, wherein the steps of stage division are: calculate the absolute value of the flow rate change acceleration in the curve, mark the time less than t3, and the absolute value of the flow rate change acceleration is greater than or equal to a3, mark the stage as the transition stage, and sort all the transition stages from front to back according to the time axis;
[0061] At the same time, all the divided areas except the transition area are recorded as production areas and sorted from front to back according to the time axis;
[0062] B401: For the production interval, the production flow rate curve corresponding to the group B image sets a time node every 4.5 seconds, defines half of the difference between the maximum and minimum values of the production flow rate curve at the same time node, recorded as the fluctuation value j4, performs the mean operation on all the points passed by the production flow rate curve at the time node, and defines it as the median j5; determines the fluctuation range, and the determination rule is: the upper limit of the fluctuation at each time node is the sum of the median j5 of the node and the fluctuation value j4, and the lower limit of the fluctuation is the difference between the median j5 of the node and the fluctuation value j4;
[0063] B402: For the production interval, the production flow rate curve value corresponding to the group A image, at each time node, if there is a production flow rate curve that exceeds the fluctuation range at the time node, and the wafer corresponding to the production flow rate curve is unqualified, the unqualified wafer data is eliminated; for the production flow rate curve of the qualified wafer, the difference between the curve value at the time node and the median j5 and the inverse ratio of the fluctuation value j4 are calculated, and recorded as the flow rate coefficient ld;
[0064] B5: Generate a dynamic data set, including temperature coefficient wd, air pressure coefficient qd and flow rate coefficient ld.
[0065] As a further solution of the present invention, receiving a specification data set, a dynamic data set, and a static data set, analyzing the three data sets, and generating corresponding evaluation coefficients includes the following steps:
[0066] The static evaluation coefficient H is calculated as follows:
[0067] ;
[0068] Where w1 is the weight value corresponding to resistivity, w2 is the weight value corresponding to carrier concentration, w3 is the weight value corresponding to carrier lifetime, and w4 is the weight value corresponding to surface recombination lifetime;
[0069] After a large amount of data analysis, in the production process of semiconductor wafers, among the four factors of resistivity, carrier concentration, carrier lifetime and surface recombination lifetime, the relationship between the number of times any factor deviates from the specified interval and the corresponding wafer failure rate is used to obtain the weights: w1 is 0.24, w2 is 0.13, w3 is 0.21, and w4 is 0.42;
[0070] The calculation method of the dynamic evaluation coefficient S is:
[0071] ;
[0072] Among them, m1 is the weight ratio of the temperature coefficient, m2 is the weight ratio of the air pressure coefficient, and m3 is the weight ratio of the flow rate coefficient. After sufficient data analysis, in the production process of semiconductor wafers, the relationship between the degree of deviation of any factor of temperature, air pressure and flow rate from the specified value range and the corresponding wafer failure rate is obtained, and the weight ratios are: m1 is 0.54, m2 is 0.15, and m3 is 0.31.
[0073] The specification evaluation factor is calculated as:
[0074] ;
[0075] Among them, p1 is the weight value of the size coefficient b2, p2 is the weight value of the nano-process coefficient c2, p3 is the weight value of the thickness coefficient d2, and p4 is the weight value of the flatness coefficient e2;
[0076] After a large amount of data analysis, in the production process of semiconductor wafers, among the four factors of size, nano-process, thickness and flatness, the correlation between the factor and the wafer qualification rate is defined according to the number of times any factor deviates from the specified interval, and the corresponding weight values are obtained: p1 takes the value of 0.46, p2 takes the value of 0.23, p3 takes the value of 0.16, and p4 takes the value of 0.15.
[0077] As a further solution of the present invention, a static evaluation coefficient H, a dynamic evaluation coefficient S and a specification evaluation coefficient G are comprehensively analyzed to generate a comprehensive evaluation coefficient, which includes the following steps:
[0078] Define the comprehensive evaluation coefficient Z and analyze the following formula:
[0079] ;
[0080] in, is the weight of the dynamic evaluation coefficient S, is the weight of the static evaluation coefficient H, is the weight of the specification evaluation coefficient G;
[0081] , and The determination method is as follows: analyze a large amount of data, study the relationship between the dynamic evaluation coefficient S, static evaluation coefficient H and specification evaluation coefficient G and the corresponding evaluation wafer qualification rate, calculate the evaluation coefficient interval corresponding to the wafer production qualification rate of 100%, and obtain by analyzing the proportional relationship between the lengths of such intervals. , and The proportional relationship between them is set to 1, and the specific values are calculated respectively; among them, is 0.42, is 0.31, is 0.27.
[0082] Beneficial Effects
[0083] The present invention provides a semiconductor wafer production quality assessment system. Compared with the prior art, it has the following beneficial effects:
[0084] The present invention obtains wafer surface image data, historical wafer qualified production image data and corresponding production data through a data acquisition module, and divides a piece of wafer production image data into a front image, a back image and a side image through image data cutting, which facilitates multi-angle defect detection of the wafer, and analyzes specific problems. At the same time, it has a certain ability to restore the three-dimensional structural information of the wafer; through a sensor module, the electrical performance parameters of the semiconductor wafer, including resistivity, carrier concentration, carrier lifetime and surface recombination lifetime, and rated electrical performance parameters are obtained, a static data set is generated, and the electrical performance parameters of the wafer are analyzed. Through the parameter values, the internal defects of the wafer production are intuitively reflected, which is more conducive to the investigation of unqualified products, and in the production process, through the adjustment of parameters, the wafer qualification rate is controlled, the cost loss is reduced, and the benefit is maximized.
[0085] The present invention receives specification data sets, dynamic data sets, and static data sets through an evaluation module, analyzes the relationship between the three data sets, and generates a comprehensive evaluation coefficient; through weighted operations, the comprehensive evaluation coefficient is calculated, and the information of multiple data sets can be integrated, and the problem background can be understood more comprehensively, so as to make more accurate decisions. This method can capture the complex relationships and interactions between different data sources, provide deeper insights, and is an evaluation system that maintains effectiveness in the face of complex and changing application scenarios and needs in a constantly changing environment.
[0086] The present invention explains which are the dominant factors and which are the secondary factors in the wafer production process through the analysis of a large amount of data, and avoids the gap between workers' experience and actual production based on the weight allocation of data. It is also helpful to determine priorities and formulate relevant more effective plans. BRIEF DESCRIPTION OF THE DRAWINGS
[0087] Figure 1 It is a schematic diagram of the principle framework of the present invention. DETAILED DESCRIPTION
[0088] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0089] Embodiment 1
[0090] See also Figure 1 , the present application provides a semiconductor wafer production quality assessment system, including a data acquisition module, a sensor module, a data processing and analysis module, an assessment module and a user interface module;
[0091] Data acquisition module: used to obtain wafer surface image data, historical wafer qualified production image data and corresponding production data; mark wafer surface image data as group A image data; mark historical wafer qualified production image data as group B image data; generate image data sets by analyzing, classifying and image cutting the two types of image data, and transmit the image data sets and corresponding wafer production data to the data processing and analysis module;
[0092] Performing image segmentation on the wafer image information in the group A image data and the group B image data respectively, dividing the complete image information of a single wafer image into three groups of large-area image information;
[0093] Through image data cutting, a wafer production image data is divided into front image, back image and side image, which facilitates multi-angle defect detection of wafers and targeted analysis of specific problems. At the same time, it has a certain ability to restore the three-dimensional structure information of the wafer.
[0094] The large-area image information includes front image information, back image information and edge image information; the front image information in Group A image data and Group B image data is loaded into a first-class folder, the back image information in Group A image data and Group B image data is loaded into a second-class folder, and the side image information in Group A image data and Group B image data is loaded into a third-class folder; an image data set is generated.
[0095] Embodiment 2
[0096] Sensor module: used to obtain the electrical performance parameters of the semiconductor wafer, including resistivity, carrier concentration, carrier lifetime and surface recombination lifetime, as well as rated electrical performance parameters, generate a static data set, and transmit it to the evaluation module;
[0097] In one embodiment of the present invention, analyzing the electrical performance parameters and calculating the corresponding coefficients of the electrical performance parameters include the following steps:
[0098] Resistivity coefficient :
[0099] ;
[0100] Where R is the resistance value, A is the cross-sectional area of the material, and L is the length of the current flowing through the material;
[0101] Example: When measuring at room temperature 23°C, the applied current is 1mA and the measured voltage is 9.5mV. Substituting the known values, we can calculate: ;
[0102] Carrier concentration coefficient n:
[0103] ;
[0104] in, is the donor impurity concentration, is the acceptor impurity concentration, g is the ionization factor, is the Fermi level, is the donor energy level, k is the Boltzmann constant, and T is the absolute temperature;
[0105] Example: Assume there is an n-type silicon wafer with a donor impurity concentration of for , acceptor impurity concentration for , Fermi level Located 0.1eV below the conduction band bottom Ec, the donor level It is 0.05 eV below the bottom of the conduction band Ec, and the temperature T is 300K; Substituting the known values, we get ;
[0106] Carrier lifetime coefficient :
[0107] ;
[0108] Where γ is the recombination coefficient, Δp is the non-equilibrium hole concentration, and Δn is the non-equilibrium electron concentration;
[0109] Example: Assume that in a silicon wafer, the non-equilibrium electron concentration Δn is , the non-equilibrium hole concentration Δp is also , the composite coefficient γ is cm³ / s; Substituting the known values into the calculation, we get ;
[0110] Surface composite life factor T:
[0111] ;
[0112] Where, d is the sample thickness, S is the surface recombination velocity;
[0113] Example: Assuming the thickness d of the silicon wafer is 200 μm and the surface recombination velocity S is 100 cm / s, substituting the known values into the calculation, we can get T=1× s;
[0114] In one embodiment of the present invention, generating a static data set according to corresponding coefficients of electrical performance parameters includes the following steps:
[0115] Setting a preset coefficient group, including a preset resistivity coefficient, a preset carrier concentration coefficient, a preset carrier lifetime coefficient, and a preset surface recombination lifetime coefficient;
[0116] When one or more of the electrical performance parameters are less than the preset coefficient, the semiconductor wafer is confirmed to be unqualified and the relevant data is discarded;
[0117] Generate static data sets including resistivity coefficients , carrier concentration coefficient n, carrier lifetime coefficient and surface composite life factor T;
[0118] Analyzing the electrical performance parameters of the wafer can intuitively reflect the internal defects of wafer production through the parameter values, which is more conducive to the investigation of unqualified products. As well as the control of wafer qualification rate through parameter adjustment during the production process, cost loss can be reduced and benefits can be maximized.
[0119] Data processing and analysis module: receives the image data set and the corresponding production data from the image acquisition module; analyzes the specifications of the wafer based on the image data set to generate a specification data set; and dynamically analyzes the production process;
[0120] In one embodiment of the present invention, the specifications of the wafer are analyzed based on the image data set to generate a correlation coefficient, including the following steps:
[0121] Establish a defect detection model based on deep learning algorithm, input defect training set, execute convolutional neural network algorithm, extract features of wafers, including size, nanometer manufacturing, thickness and flatness, and generate correlation coefficients;
[0122] In one embodiment of the present invention, generating a correlation coefficient and a specification data set comprises the following steps:
[0123] A1: For the first and third type folders, count the actual radius b0 of the wafer in the group A images, calculate the ratio of the actual radius b0 to the standard radius b1, record it as the size coefficient, and if the size coefficient b2 is greater than or equal to the size critical value b, mark the wafer as unqualified, exclude the wafers marked as unqualified, count the size coefficient s_b2 of the qualified wafers, and calculate the mean value b3;
[0124] Among them, the size critical value b is the mean value of the wafer radius in group B images;
[0125] A2: For the first and third types of folders, analyze the front and back images of the wafer, identify the transistor structure on the wafer through the edge detection algorithm, and calculate its size and spacing, and then obtain the actual nano-process c0 of the wafer, calculate the ratio of the actual nano-process c0 to the standard nano-process c1, and record it as the nano-process coefficient c2, and if the nano-process coefficient c2 is greater than or equal to the nano-process critical value c, mark the wafer as unqualified, exclude the unqualified wafers, count the nano-process coefficients s_c2 of qualified wafers, and calculate the average c3;
[0126] Among them, the nanometer process critical value c is the average value of the wafer nanometer process in group B images;
[0127] A3: For the second type of folders, count the actual thickness d0 of the wafer in the group A images, calculate the ratio of the actual thickness d0 to the standard thickness d1, record it as the thickness coefficient, and if the thickness coefficient d2 is greater than or equal to the thickness threshold d, mark the wafer as unqualified, exclude the wafers marked as unqualified, count the thickness coefficient s_d2 of the qualified wafers, and calculate the average d3;
[0128] Among them, the thickness critical value d is the average value of the wafer thickness in group B images;
[0129] A4: For the first, second and third category folders, the 3D reconstruction technology is used to generate the 3D structure data of the wafer in the group A images, and the 3D morphology data of the wafer is obtained, which is stored in the form of high-resolution point cloud. Each point represents the height information of a specific position on the wafer surface. Based on the principle of least squares, the wafer surface is fitted to an optimal plane, and then the distance from each measurement point to this plane is calculated. The maximum value of all distances is the flatness e0 of the wafer.
[0130] Count the actual flatness e0 of the wafer, calculate the ratio of the actual flatness e0 to the standard flatness e1, record it as the flatness coefficient, and if the flatness coefficient e2 is greater than or equal to the flatness critical value e, mark the wafer as unqualified, exclude the wafer marked as unqualified, count the flatness coefficient s_e2 of the qualified wafers, and calculate the average value e3;
[0131] Among them, the flatness critical value e is the average value of wafer flatness in group B images;
[0132] A5: Generate specification data set, including size coefficient b2, nano process coefficient c2, thickness coefficient d2 and flatness coefficient e2;
[0133] In one embodiment of the present invention, dynamic analysis is performed based on production data corresponding to the image data set to generate a dynamic data set, including the following steps:
[0134] B1: Clean the data related to unqualified wafers in the first, second and third folders, and analyze the actual production data corresponding to the three folders, where the actual production data includes temperature, air pressure, flow rate and time. The analysis process includes the following steps:
[0135] According to the size data, the wafers are divided into several categories. For any category of wafers, a production temperature curve, a production pressure curve and a production flow rate curve are established respectively, and it is stipulated that the three curves all use the same time axis;
[0136] B2: For the production temperature curve, the production process is divided into several stages according to the temperature change. The steps of stage division are: calculate the absolute value of the temperature change acceleration in the curve, mark the time less than t1, and the absolute value of the temperature change acceleration is greater than or equal to a1, mark the stage as the transition stage, and sort all the transition stages from front to back according to the time axis;
[0137] At the same time, all the divided areas except the transition area are recorded as production areas and sorted from front to back according to the time axis;
[0138] B201: For the production interval, the production temperature curve corresponding to the group B image sets a time node every 0.5 seconds, defines half of the difference between the maximum and minimum values of the production temperature curve at the same time node, recorded as the fluctuation value j0, performs the mean operation on all the points passed by the production temperature curve at the time node, and defines it as the median j1; determines the fluctuation range, and the determination rule is: the upper limit of the fluctuation at each time node is the sum of the median j1 of the node and the fluctuation value j0, and the lower limit of the fluctuation is the difference between the median j1 of the node and the fluctuation value j0;
[0139] B202: For the production interval, the production temperature curve value corresponding to the group A image, at each time node, if there is a production temperature curve that exceeds the fluctuation range at the time node, and the wafer corresponding to the production temperature curve is unqualified, the unqualified wafer data is eliminated; for the production temperature curve of the qualified wafer, the difference between the curve value at the time node and the median j1 and the inverse ratio of the fluctuation value j0 are calculated, recorded as the temperature coefficient wd;
[0140] B3: For the production air pressure curve, the production process is divided into several stages according to the change of air pressure. The steps of stage division are: calculate the absolute value of the acceleration of the change of air pressure in the curve, mark the time less than t2, and the absolute value of the acceleration of the change of air pressure is greater than or equal to a2, mark the stage as the transition stage, and sort all the transition stages from front to back according to the time axis;
[0141] At the same time, all the divided areas except the transition area are recorded as production areas and sorted from front to back according to the time axis;
[0142] B301: For the production interval, the production pressure curve corresponding to the group B image sets a time node every 2.5 seconds, defines half of the difference between the maximum and minimum values of the production pressure curve at the same time node, recorded as the fluctuation value j2, performs the mean operation on all the points passed by the production pressure curve at the time node, and defines it as the median j3; determines the fluctuation range, and the determination rule is: the upper limit of the fluctuation at each time node is the sum of the median j3 of the node and the fluctuation value j2, and the lower limit of the fluctuation is the difference between the median j3 of the node and the fluctuation value j2;
[0143] B302: For the production interval, the production pressure curve value corresponding to the group A image, at each time node, if there is a production pressure curve that exceeds the fluctuation range at the time node, and the wafer corresponding to the production pressure curve is unqualified, the unqualified wafer data is eliminated; for the production pressure curve of the qualified wafer, the difference between the curve value at the time node and the median j3 and the inverse ratio of the fluctuation value j2 are calculated, and recorded as the pressure coefficient qd;
[0144] B4: For the production flow rate curve, the production process is divided into several stages according to the change of flow rate, wherein the steps of stage division are: calculate the absolute value of the flow rate change acceleration in the curve, mark the time less than t3, and the absolute value of the flow rate change acceleration is greater than or equal to a3, mark the stage as the transition stage, and sort all the transition stages from front to back according to the time axis;
[0145] At the same time, all the divided areas except the transition area are recorded as production areas and sorted from front to back according to the time axis;
[0146] B401: For the production interval, the production flow rate curve corresponding to the group B image sets a time node every 4.5 seconds, defines half of the difference between the maximum and minimum values of the production flow rate curve at the same time node, recorded as the fluctuation value j4, performs the mean operation on all the points passed by the production flow rate curve at the time node, and defines it as the median j5; determines the fluctuation range, and the determination rule is: the upper limit of the fluctuation at each time node is the sum of the median j5 of the node and the fluctuation value j4, and the lower limit of the fluctuation is the difference between the median j5 of the node and the fluctuation value j4;
[0147] B402: For the production interval, the production flow rate curve value corresponding to the group A image, at each time node, if there is a production flow rate curve that exceeds the fluctuation range at the time node, and the wafer corresponding to the production flow rate curve is unqualified, the unqualified wafer data is eliminated; for the production flow rate curve of the qualified wafer, the difference between the curve value at the time node and the median j5 and the inverse ratio of the fluctuation value j4 are calculated, and recorded as the flow rate coefficient ld;
[0148] B5: Generate a dynamic data set, including temperature coefficient wd, air pressure coefficient qd and flow rate coefficient ld.
[0149] Evaluation module: used to receive specification data set, dynamic data set and static data set, analyze the relationship between the three data sets and generate a comprehensive evaluation coefficient;
[0150] In one embodiment of the present invention, receiving a specification data set, a dynamic data set, and a static data set, analyzing the three data sets, and generating corresponding evaluation coefficients includes the following steps:
[0151] The static evaluation coefficient H is calculated as follows:
[0152] ;
[0153] Where w1 is the weight value corresponding to resistivity, w2 is the weight value corresponding to carrier concentration, w3 is the weight value corresponding to carrier lifetime, and w4 is the weight value corresponding to surface recombination lifetime;
[0154] After a large amount of data analysis, in the production process of semiconductor wafers, among the four factors of resistivity, carrier concentration, carrier lifetime and surface recombination lifetime, the relationship between the number of times any factor deviates from the specified interval and the corresponding wafer failure rate is used to obtain the weights: w1 is 0.24, w2 is 0.13, w3 is 0.21, and w4 is 0.42;
[0155] The calculation method of the dynamic evaluation coefficient S is:
[0156] ;
[0157] Among them, m1 is the weight ratio of the temperature coefficient, m2 is the weight ratio of the air pressure coefficient, and m3 is the weight ratio of the flow rate coefficient. After sufficient data analysis, in the production process of semiconductor wafers, the relationship between the degree of deviation of any factor of temperature, air pressure and flow rate from the specified value range and the corresponding wafer failure rate is obtained, and the weight ratios are: m1 is 0.54, m2 is 0.15, and m3 is 0.31.
[0158] The specification evaluation factor is calculated as:
[0159] ;
[0160] Among them, p1 is the weight value of the size coefficient b2, p2 is the weight value of the nano-process coefficient c2, p3 is the weight value of the thickness coefficient d2, and p4 is the weight value of the flatness coefficient e2;
[0161] After a large amount of data analysis, in the production process of semiconductor wafers, among the four factors of size, nano-process, thickness and flatness, the correlation between the factor and the wafer qualification rate is defined according to the number of times any factor deviates from the specified interval, and the corresponding weight values are obtained: p1 takes the value of 0.46, p2 takes the value of 0.23, p3 takes the value of 0.16, and p4 takes the value of 0.15;
[0162] In one embodiment of the present invention, a comprehensive analysis of the static evaluation coefficient H, the dynamic evaluation coefficient S and the specification evaluation coefficient G to generate a comprehensive evaluation coefficient includes the following steps:
[0163] Define the comprehensive evaluation coefficient Z and analyze the following formula:
[0164] ;
[0165] in, is the weight of the dynamic evaluation coefficient S, is the weight of the static evaluation coefficient H, is the weight of the specification evaluation coefficient G;
[0166] , and The determination method is as follows: analyze a large amount of data, study the relationship between the dynamic evaluation coefficient S, static evaluation coefficient H and specification evaluation coefficient G and the corresponding evaluation wafer qualification rate, calculate the evaluation coefficient interval corresponding to the wafer production qualification rate of 100%, and obtain by analyzing the proportional relationship between the lengths of such intervals. , and The proportional relationship between them is set to 1, and the specific values are calculated respectively; among them, is 0.42, is 0.31, is 0.27;
[0167] Through the analysis of a large amount of data, it is explained which are the dominant factors and which are the secondary factors in the wafer production process. The weight allocation based on the data avoids the gap between workers' experience and actual production, and is beneficial to determine priorities and formulate relevant more effective plans.
[0168] User Interface Module: Provides an intuitive interface to , carrier concentration coefficient n, carrier lifetime coefficient , surface composite life coefficient T, temperature coefficient wd, air pressure coefficient qd, flow rate coefficient ld, size coefficient b2, nano process coefficient c2, thickness coefficient d2, flatness coefficient e2, dynamic evaluation coefficient S, static evaluation coefficient H, specification evaluation coefficient G, and comprehensive evaluation coefficient Z are displayed.
[0169] Embodiment 3
[0170] The specific implementation process of this embodiment includes the entire implementation process of the above two groups of embodiments.
[0171] Some of the data in the above formulas are dimensionless and numerically calculated. Meanwhile, the contents not described in detail in this specification belong to the prior art known to those skilled in the art.
[0172] The above embodiments are only used to illustrate the technical method of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical method of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical method of the present invention.
Claims
1. A semiconductor wafer production quality assessment system, characterized in that: include: Data acquisition module: used to obtain wafer surface image data and historical wafer qualified production image data and corresponding production data; Mark the wafer surface image data as group A image data; mark the historical wafer qualified production image data as group B image data; generate an image data set by analyzing, classifying and image cutting the two types of image data, and transmit the image data set and the corresponding wafer production data to the data processing and analysis module; Sensor module: used to obtain the electrical performance parameters of the semiconductor wafer, including resistivity, carrier concentration, carrier lifetime and surface recombination lifetime, as well as rated electrical performance parameters, generate a static data set, and transmit it to the evaluation module; Data processing and analysis module: receiving the image data set and corresponding production data from the image acquisition module; Based on the image data set, the specifications of the wafer are analyzed to generate a specification data set; And conduct dynamic analysis of the production process; Evaluation module: used to receive specification data set, dynamic data set and static data set, analyze the relationship between the three data sets and generate a comprehensive evaluation coefficient; Based on the image data set, the wafer specifications are analyzed to generate correlation coefficients, including the following steps: Establish a defect detection model based on deep learning algorithm, input defect training set, execute convolutional neural network algorithm, extract features of wafers, including size, nanometer manufacturing, thickness and flatness, and generate correlation coefficients; Analyzing group A image data and group B image data to generate an image data set includes the following steps: Performing image segmentation on the wafer image information in the group A image data and the group B image data respectively, dividing the complete image information of a single wafer image into three groups of large-area image information; The large area image information includes front image information, back image information and edge image information; the front image information in group A image data and group B image data is loaded into a first folder, the back image information in group A image data and group B image data is loaded into a second folder, and the side image information in group A image data and group B image data is loaded into a third folder; an image data set is generated; Generate the correlation coefficient and specification data set, including the following steps: A1: For the first and third type folders, count the actual radius b0 of the wafer in the group A images, calculate the ratio of the actual radius b0 to the standard radius b1, record it as the size coefficient, and if the size coefficient b2 is greater than or equal to the size critical value b, mark the wafer as unqualified, exclude the wafers marked as unqualified, count the size coefficient s_b2 of the qualified wafers, and calculate the mean value b3; Among them, the size critical value b is the mean value of the wafer radius in group B images; A2: For the first and third types of folders, analyze the front and back images of the wafer, identify the transistor structure on the wafer through the edge detection algorithm, and calculate its size and spacing, and then obtain the actual nano-process c0 of the wafer, calculate the ratio of the actual nano-process c0 to the standard nano-process c1, and record it as the nano-process coefficient c2, and if the nano-process coefficient c2 is greater than or equal to the nano-process critical value c, mark the wafer as unqualified, exclude the unqualified wafers, count the nano-process coefficients s_c2 of qualified wafers, and calculate the average c3; Among them, the nanometer process critical value c is the average value of the wafer nanometer process in group B images; A3: For the second type of folders, count the actual thickness d0 of the wafer in the group A images, calculate the ratio of the actual thickness d0 to the standard thickness d1, record it as the thickness coefficient, and if the thickness coefficient d2 is greater than or equal to the thickness threshold d, mark the wafer as unqualified, exclude the wafers marked as unqualified, count the thickness coefficient s_d2 of the qualified wafers, and calculate the average d3; Among them, the thickness critical value d is the average value of the wafer thickness in group B images; A4: For the first, second and third category folders, the 3D reconstruction technology is used to generate the 3D structure data of the wafer in the group A images, and the 3D morphology data of the wafer is obtained, which is stored in the form of high-resolution point cloud. Each point represents the height information of a specific position on the wafer surface. Based on the principle of least squares, the wafer surface is fitted to an optimal plane, and then the distance from each measurement point to this plane is calculated. The maximum value of all distances is the flatness e0 of the wafer. Count the actual flatness e0 of the wafer, calculate the ratio of the actual flatness e0 to the standard flatness e1, record it as the flatness coefficient, and if the flatness coefficient e2 is greater than or equal to the flatness critical value e, mark the wafer as unqualified, exclude the wafer marked as unqualified, count the flatness coefficient s_e2 of the qualified wafers, and calculate the average value e3; Among them, the flatness critical value e is the average value of wafer flatness in group B images; A5: Generate specification data set, including size coefficient b2, nano process coefficient c2, thickness coefficient d2 and flatness coefficient e2; Based on the production data corresponding to the image data set, dynamic analysis is performed to generate a dynamic data set, including the following steps: B1: Clean the data related to unqualified wafers in the first, second and third folders, and analyze the actual production data corresponding to the three folders, where the actual production data includes temperature, air pressure, flow rate and time. The analysis process includes the following steps: According to the size data, the wafers are divided into several categories. For any category of wafers, a production temperature curve, a production pressure curve and a production flow rate curve are established respectively, and it is stipulated that the three curves all use the same time axis; B2: For the production temperature curve, the production process is divided into several stages according to the temperature change. The steps of stage division are: calculate the absolute value of the temperature change acceleration in the curve, mark the time less than t1, and the absolute value of the temperature change acceleration is greater than or equal to a1, mark the stage as the transition stage, and sort all the transition stages from front to back according to the time axis; At the same time, all the divided areas except the transition area are recorded as production areas and sorted from front to back according to the time axis; B201: For the production interval, the production temperature curve corresponding to the group B image sets a time node every 0.5 seconds, defines half of the difference between the maximum and minimum values of the production temperature curve at the same time node, recorded as the fluctuation value j0, performs the mean operation on all the points passed by the production temperature curve at the time node, and defines it as the median j1; determines the fluctuation range, and the determination rule is: the upper limit of the fluctuation at each time node is the sum of the median j1 of the node and the fluctuation value j0, and the lower limit of the fluctuation is the difference between the median j1 of the node and the fluctuation value j0; B202: For the production interval, the production temperature curve value corresponding to the group A image, at each time node, if there is a production temperature curve that exceeds the fluctuation range at the time node, and the wafer corresponding to the production temperature curve is unqualified, the unqualified wafer data is eliminated; for the production temperature curve of the qualified wafer, the difference between the curve value at the time node and the median j1 and the inverse ratio of the fluctuation value j0 are calculated, recorded as the temperature coefficient wd; B3: For the production air pressure curve, the production process is divided into several stages according to the change of air pressure. The steps of stage division are: calculate the absolute value of the acceleration of the change of air pressure in the curve, mark the time less than t2, and the absolute value of the acceleration of the change of air pressure is greater than or equal to a2, mark the stage as the transition stage, and sort all the transition stages from front to back according to the time axis; At the same time, all the divided areas except the transition area are recorded as production areas and sorted from front to back according to the time axis; B301: For the production interval, the production pressure curve corresponding to the group B image sets a time node every 2.5 seconds, defines half of the difference between the maximum and minimum values of the production pressure curve at the same time node, recorded as the fluctuation value j2, performs the mean operation on all the points passed by the production pressure curve at the time node, and defines it as the median j3; determines the fluctuation range, and the determination rule is: the upper limit of the fluctuation at each time node is the sum of the median j3 of the node and the fluctuation value j2, and the lower limit of the fluctuation is the difference between the median j3 of the node and the fluctuation value j2; B302: For the production interval, the production pressure curve value corresponding to the group A image, at each time node, if there is a production pressure curve that exceeds the fluctuation range at the time node, and the wafer corresponding to the production pressure curve is unqualified, the unqualified wafer data is eliminated; for the production pressure curve of the qualified wafer, the difference between the curve value at the time node and the median j3 and the inverse ratio of the fluctuation value j2 are calculated, and recorded as the pressure coefficient qd; B4: For the production flow rate curve, the production process is divided into several stages according to the change of flow rate, wherein the steps of stage division are: calculate the absolute value of the flow rate change acceleration in the curve, mark the time less than t3, and the absolute value of the flow rate change acceleration is greater than or equal to a3, mark the stage as the transition stage, and sort all the transition stages from front to back according to the time axis; At the same time, all the divided areas except the transition area are recorded as production areas and sorted from front to back according to the time axis; B401: For the production interval, the production flow rate curve corresponding to the group B image sets a time node every 4.5 seconds, defines half of the difference between the maximum and minimum values of the production flow rate curve at the same time node, recorded as the fluctuation value j4, performs the mean operation on all the points passed by the production flow rate curve at the time node, and defines it as the median j5; determines the fluctuation range, and the determination rule is: the upper limit of the fluctuation at each time node is the sum of the median j5 of the node and the fluctuation value j4, and the lower limit of the fluctuation is the difference between the median j5 of the node and the fluctuation value j4; B402: For the production interval, the production flow rate curve value corresponding to the group A image, at each time node, if there is a production flow rate curve that exceeds the fluctuation range at the time node, and the wafer corresponding to the production flow rate curve is unqualified, the unqualified wafer data is eliminated; for the production flow rate curve of the qualified wafer, the difference between the curve value at the time node and the median j5 and the inverse ratio of the fluctuation value j4 are calculated, and recorded as the flow rate coefficient ld; B5: Generate dynamic data set, including temperature coefficient wd, air pressure coefficient qd and flow rate coefficient ld; Receiving a specification data set, a dynamic data set, and a static data set, analyzing the three data sets, and generating corresponding evaluation coefficients includes the following steps: The static evaluation coefficient H is calculated as follows: ; Where w1 is the weight value corresponding to resistivity, w2 is the weight value corresponding to carrier concentration, w3 is the weight value corresponding to carrier lifetime, and w4 is the weight value corresponding to surface recombination lifetime; The calculation method of the dynamic evaluation coefficient S is: ; Among them, m1 is the weight ratio of the temperature coefficient, m2 is the weight ratio of the air pressure coefficient, and m3 is the weight ratio of the flow rate coefficient; The specification evaluation factor G is calculated as follows: ; Among them, p1 is the weight value of the size coefficient b2, p2 is the weight value of the nano-process coefficient c2, p3 is the weight value of the thickness coefficient d2, and p4 is the weight value of the flatness coefficient e2; Comprehensively analyzing the static evaluation coefficient H, the dynamic evaluation coefficient S and the specification evaluation coefficient G to generate a comprehensive evaluation coefficient includes the following steps: Define the comprehensive evaluation coefficient Z and analyze the following formula: ; in, is the weight of the dynamic evaluation coefficient S, is the weight of the static evaluation coefficient H, is the weight of the specification evaluation coefficient G; , and The determination method is as follows: analyze a large amount of data, study the relationship between the dynamic evaluation coefficient S, static evaluation coefficient H and specification evaluation coefficient G and the corresponding evaluation wafer qualification rate, calculate the evaluation coefficient interval corresponding to the wafer production qualification rate of 100%, and obtain by analyzing the proportional relationship between the lengths of such intervals. , and The proportional relationship between them is set to 1, and the specific values are calculated respectively; among them, is 0.42, is 0.31, is 0.
27.
2. The semiconductor wafer production quality assessment system according to claim 1, characterized in that: Also includes: User Interface Module: Provides an intuitive interface to , carrier concentration coefficient n, carrier lifetime coefficient , surface composite life coefficient T, temperature coefficient wd, air pressure coefficient qd, flow rate coefficient ld, size coefficient b2, nano process coefficient c2, thickness coefficient d2, flatness coefficient e2, dynamic evaluation coefficient S, static evaluation coefficient H, specification evaluation coefficient G, and comprehensive evaluation coefficient Z are displayed.
3. The semiconductor wafer production quality assessment system according to claim 2, characterized in that: Analyzing the electrical performance parameters and calculating the corresponding coefficients of the electrical performance parameters includes the following steps: Resistivity coefficient : ; Where R is the resistance value, A is the cross-sectional area of the material, and L is the length of the current flowing through the material; Carrier concentration coefficient n: ; in, is the donor impurity concentration, is the acceptor impurity concentration, g is the ionization factor, is the Fermi level, is the donor energy level, k is the Boltzmann constant, and T is the absolute temperature; Carrier lifetime coefficient : ; Where γ is the recombination coefficient, Δp is the non-equilibrium hole concentration, and Δn is the non-equilibrium electron concentration; Surface composite life factor T: ; Where d is the sample thickness and S is the surface recombination velocity.
4. The semiconductor wafer production quality assessment system according to claim 3, characterized in that: According to the corresponding coefficients of the electrical performance parameters, a static data set is generated, including the following steps: Setting a preset coefficient group, including a preset resistivity coefficient, a preset carrier concentration coefficient, a preset carrier lifetime coefficient, and a preset surface recombination lifetime coefficient; When one or more of the electrical performance parameters are less than the preset coefficient, the semiconductor wafer is confirmed to be unqualified and the relevant data is discarded; Generate static data sets including resistivity coefficients , carrier concentration coefficient n, carrier lifetime coefficient and surface composite life factor T.
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