Temperature drift correction method, device, equipment and medium for substrate warpage measurement

Abstract

This application provides a method, apparatus, device, and medium for correcting temperature drift in substrate warpage measurement. The method includes determining multiple calibration coefficients based on a calibration coefficient model for substrate height measurement; obtaining multiple calibration coefficients based on set temperature calibration points and the number of calibrations at each temperature calibration point, and calculating their average value to obtain a calibration coefficient correction table; determining the corrected calibration coefficients at the detection temperature using a polynomial difference method or machine learning method based on the calibration coefficient correction table, and determining the corrected substrate height according to the calibration coefficient model, thereby achieving temperature drift correction of the substrate height at the detection temperature. This application performs online correction of the calibration coefficients of the substrate warpage measurement system, compensating for errors caused by temperature variations in the calibration coefficients, thereby improving the measurement accuracy of the substrate warpage measurement system.

Description

Technical Field

[0001] This invention relates to the field of semiconductor testing technology, and in particular to a method, apparatus, equipment and medium for correcting temperature drift in substrate warpage measurement. Background Technology

[0002] 3D packaging, which involves stacking multiple layers of chips and substrates, is the current trend in packaging development. In 3D packaging, each functional layer is composed of different materials, such as silicon, FR-4, copper, aluminum, ceramics, polymers, and various solders. During the packaging process, these materials are subjected to various loads such as moisture, heat, and force. Due to the mismatch in thermal expansion coefficients, each material exhibits different thermomechanical properties under different loads. The stress and deformation of the multilayer materials accumulate, resulting in significant warpage that can lead to device failure. Therefore, the measurement and control of the warpage deformation of each layer in 3D packaging is crucial.

[0003] Essentially, measuring the warpage of a packaged substrate falls under the category of three-dimensional topography measurement. Currently, the industry commonly uses the shadow moiré method based on grating moiré fringes. This method involves heating the substrate and interfering with the shadow grating generated by the reflection of the grating onto the sample. The warpage deformation of the substrate within the package is measured. After acquiring the image signal using a CCD (Charge Coupled Device) camera, an algorithm processes the moiré fringes to generate the height value at each point, thus obtaining the amount of topographic deformation. During the measurement process, the substrate is first heated under temperature control. Changes in temperature conditions, the optical characteristics of the measurement system, and a series of temperature-related factors introduce system errors. Direct measurement would result in a deviation between the measured height and the actual height. Therefore, calibration is necessary to obtain appropriate correction parameters to ensure measurement accuracy.

[0004] In existing technologies, commonly used calibration methods include polynomial fitting and linear interpolation, which can correct the gain deviation and nonlinear characteristics of the measurement system to a certain extent. These calibration methods meet the measurement accuracy requirements of the past, but they cannot provide a quantifiable functional relationship between the calibration coefficients and temperature, and cannot accurately characterize the system error caused by temperature changes. As the measurement accuracy requirements for substrate warpage continue to increase, existing correction parameter methods are no longer suitable for current measurement accuracy requirements. Summary of the Invention

[0005] To overcome the problems existing in the related technologies, this disclosure provides a method, apparatus, device and medium for correcting temperature drift in substrate warpage measurement, so as to solve the technical problems in the related technologies.

[0006] This specification provides one or more embodiments of a method for correcting temperature drift in substrate warpage measurements, including the following steps:

[0007] Based on the calibration coefficient model for substrate height measurement, several coefficients to be calibrated are determined;

[0008] Based on the set temperature calibration points and the number of calibrations at each temperature calibration point, and based on the calibration results of the substrate warpage measurement system performing the corresponding number of calibrations at each temperature calibration point, multiple calibration coefficients are obtained. The average of multiple values ​​for each calibration coefficient is then calculated to obtain a sequence of calibration coefficients for each temperature calibration point, which serves as a calibration coefficient correction table.

[0009] Based on the calibration coefficient correction table, the calibration coefficients to be corrected at the test temperature are determined by the polynomial difference method or machine learning method, and the corrected substrate height is determined according to the calibration coefficient model, thereby realizing the temperature drift correction of the substrate height at the test temperature.

[0010] This specification provides one or more embodiments of a temperature drift correction device for substrate warpage measurement, comprising:

[0011] The calibration coefficient determination module is used to determine multiple calibration coefficients based on the calibration coefficient model of substrate height measurement.

[0012] The correction table determination module is used to obtain the calibration results of the substrate warpage measurement system performing corresponding calibration operations on the substrate at each temperature calibration point based on the set temperature calibration points and the number of calibrations at each temperature calibration point. It obtains multiple calibration coefficients and calculates the average of multiple values ​​for each calibration coefficient to obtain a sequence of calibration coefficients for each temperature calibration point, which serves as the calibration coefficient correction table.

[0013] The online correction module is used to determine the correction of each calibration coefficient at the temperature to be detected by means of polynomial difference method or machine learning method based on the calibration coefficient correction table, and to determine the corrected substrate height according to the calibration coefficient model, thereby realizing the temperature drift correction of the substrate height at the detection temperature.

[0014] This specification provides one or more embodiments of a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the temperature drift correction method for substrate warpage measurement as described above.

[0015] This specification provides one or more embodiments of a computer-readable storage medium storing a computer program that, when executed by a processor, implements the temperature drift correction method for substrate warpage measurement as described above.

[0016] This disclosure provides a method, apparatus, device, and medium for correcting temperature drift in substrate warpage measurement. Its advantage lies in addressing the problem that calibration coefficients in substrate warpage measurement cannot correct for systematic errors caused by temperature changes. First, to determine the relationship between the measured height and temperature-related calibration coefficients, calibration coefficients are determined through multiple pre-calibrated temperature measurements. The average value of these coefficients is then used as the correction calibration coefficient for the corresponding temperature point. This process establishes a calibration coefficient correction table for each temperature. During online correction (i.e., during substrate warpage measurement), the temperature of the test environment is collected in real-time by a temperature sensor. Based on the calibration coefficient correction table, the corrected calibration coefficients for each corresponding temperature value are determined using a polynomial difference method or machine learning method. The corrected substrate height can then be obtained from these corrected calibration coefficients. This method performs online correction of the calibration coefficients in the substrate warpage measurement system, compensating for errors caused by temperature variations in the calibration coefficients, thereby improving the measurement accuracy of the substrate warpage measurement system. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A flowchart illustrating a method for correcting temperature drift in substrate warpage measurement, provided for one or more embodiments of this specification;

[0019] Figure 2 A flowchart for calibrating the parameters of the substrate height measurement model provided in one or more embodiments of this specification;

[0020] Figure 3 A schematic diagram illustrating the gain coefficient as a function of temperature for one embodiment;

[0021] Figure 4 A schematic diagram of a linear interpolation calibration method provided in one embodiment;

[0022] Figure 5 A schematic diagram of a spline interpolation calibration method provided in one embodiment;

[0023] Figure 6 A schematic diagram of regression tree calibration results provided for one embodiment;

[0024] Figure 7 A schematic diagram of the calibration results using regression forest provided in one embodiment;

[0025] Figure 8A schematic diagram of the original values ​​of the substrate height provided for one embodiment;

[0026] Figure 9 A schematic diagram of linear values ​​for substrate height provided in one embodiment;

[0027] Figure 10 A block diagram of a temperature drift correction device for substrate warpage measurement provided for one or more embodiments of this specification; and

[0028] Figure 11 This is a schematic diagram of the structure of a computer device provided for one or more embodiments of this specification. Detailed Implementation

[0029] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this invention.

[0030] The present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

[0031] Method Implementation Examples

[0032] According to embodiments of the present invention, a method for correcting temperature drift in substrate warpage measurement is provided, such as... Figure 1 The diagram shown is a flowchart of the temperature drift correction method for substrate warpage measurement provided in this embodiment. The temperature drift correction method for substrate warpage measurement according to this embodiment includes the following steps:

[0033] Step S1: Determine multiple coefficients to be calibrated based on the calibration coefficient model for substrate height measurement.

[0034] Step S2: Based on the set temperature calibration points and the number of calibrations at each temperature calibration point, and based on the calibration results of the substrate warping measurement system performing the corresponding number of calibrations at each temperature calibration point, multiple calibration coefficients are obtained, and the average value of multiple values ​​of each calibration coefficient is calculated to obtain a sequence of calibration coefficients for each temperature calibration point, which serves as a calibration coefficient correction table.

[0035] Step S3: Based on the calibration coefficient correction table, determine each calibration coefficient to be corrected at the temperature to be detected by polynomial difference method or machine learning method, and determine the corrected substrate height according to the calibration coefficient model, thereby realizing the temperature drift correction of the substrate height at the detection temperature.

[0036] In this embodiment, the polynomial interpolation method can be linear interpolation, cubic spline interpolation, or other interpolation methods, and the machine learning method can be regression tree, regression forest, or other methods.

[0037] The temperature drift correction method for substrate warpage measurement provided in this embodiment addresses the problem that the calibration coefficients in substrate warpage measurement cannot correct for systematic errors caused by temperature changes. First, to determine the relationship between the measured height and the temperature-related calibration coefficients, calibration coefficients are determined through multiple pre-calibrated temperature measurements. The average value of these coefficients is then used as the correction calibration coefficient for the corresponding temperature point. This process establishes a calibration coefficient correction table for each temperature. During online correction (i.e., during the substrate warpage measurement process), the temperature of the test environment is collected in real-time by a temperature sensor. Based on the calibration coefficient correction table, a polynomial difference method or machine learning method is used to determine the corrected calibration coefficients for each corresponding temperature value. The corrected substrate height can then be obtained from these corrected calibration coefficients. This method performs online correction of the calibration coefficients of the substrate warpage measurement system, compensating for errors caused by temperature variations in the calibration coefficients, thereby improving the measurement accuracy of the substrate warpage measurement system.

[0038] In this embodiment, step S1 determines several coefficients to be calibrated based on the calibration coefficient model for substrate height measurement, as follows.

[0039] The substrate warpage measurement process involves measuring the height of each point on the substrate surface at a certain temperature, resulting in a topographic image. The linearization calibration model for the height measurements uses a polynomial model, as detailed below:

[0040]

[0041] Among them, h lin h is the linear height of the calibrated substrate. raw Uncalibrated original height of the substrate. k The coefficients of the polynomial to be calibrated are k = 0, 1, ..., K, where K is the order of the polynomial.

[0042] In equation (1), F(·) is the transcendental function correction term. F(·) is generally described in the form of sine and cosine functions. It can be a linear combination of sine and cosine expressions of different harmonic frequencies, or composed of different orders. Without loss of generality, the most basic expression of F(·) is as follows:

[0043] F(h raw )=a×sin(b×h raw +c) (2);

[0044] Where a, b, and c are the parameters to be calibrated.

[0045] Separating equation (1) and representing the height bias (zero-order term), gain coefficient (first-order term), and nonlinear correction coefficient (second-order and higher-order coefficients) separately, the specific model is as follows:

[0046]

[0047] Where p0 is the height offset, p1 is the gain coefficient, and p k are nonlinear correction coefficients, k = 2, ..., K, where K is the order of the polynomial. F(·) is the transcendental function correction term.

[0048] Therefore, it can be seen that the height bias, gain coefficient, nonlinear correction coefficient, and transcendental function will all change with temperature conditions. Thus, the height bias, gain coefficient, nonlinear correction coefficient, and transcendental function are used as calibration coefficients to be calibrated in this embodiment. The change in height bias is equivalent to the drift of the zero point of the height measurement system. The change in gain coefficient will have a direct impact on the accuracy of substrate height measurement. The changes in nonlinear coefficient and transcendental function will have a significant impact on the accuracy near the edge of the measurement range.

[0049] In this embodiment, reference Figure 2 The diagram shows the calibration process and correction table acquisition flowchart for the substrate height measurement model provided in this embodiment. The correction table for each calibration coefficient can be obtained through step S2. The specific implementation process is as follows:

[0050] Step S21: Based on the temperature setting range of the substrate warp measurement system, preset the test temperature range and temperature selection interval to determine each temperature calibration point, and set the number of calibration operations for the substrate calibration operation at each temperature calibration point; in this embodiment, the number of calibrations is set to M, where M is a natural number greater than 1.

[0051] In one specific embodiment, the operating temperature range of the substrate height measurement system is set to [T0, T...]. f ], where T0 and T f These are the minimum and maximum temperatures within the operating range, respectively. The operating range is then divided into N+1 temperature calibration points {T0, T1, ..., T...} at equal intervals. i ,…,T N}∈[T0,T f For example, if the operating temperature range is [0, 100], and [0, 100] is to be divided into 5 equally spaced regions, then 6 temperature calibration points {0, 20, 40, 60, 80, 100} can be obtained.

[0052] Step S22: Based on the preset temperature point, use the substrate warpage measurement system to perform a corresponding number of calibration operations on the substrate to obtain the corresponding number of calibration coefficients w. cThe values ​​of c, where c = 1, 2, 3, 4, and w1, w2, w3, w4 correspond to the height bias p0, gain coefficient p1, and nonlinear correction coefficient p, respectively. k And transcendental functions F(·).

[0053] In this embodiment, during the height measurement of the substrate by the substrate warpage measurement system, the height bias, gain coefficient, nonlinear correction coefficient, and transcendental function coefficient are obtained by least-squares fitting using the substrate warpage measurement system. Specifically, the substrate warpage measurement system and a height measuring device integrated within it simultaneously acquire the substrate height signal via vertical scanning. The substrate height acquired by the height measuring device is used as a reference height. The substrate warpage measurement system then performs least-squares fitting on the height signal and the reference height signal to obtain the values ​​of the height bias, gain coefficient, nonlinear correction coefficient, and transcendental function coefficient. It should be noted that the acquisition of the height bias, gain coefficient, nonlinear correction coefficient, and transcendental function coefficient during the measurement process can be obtained by those skilled in the art using existing technologies, and will not be elaborated upon here.

[0054] Step S23: Calculate the average value of each obtained calibration coefficient value to obtain the calibration coefficient value of each corresponding temperature calibration point;

[0055] Step S24: Traverse the temperature calibration points until the calibration coefficient values ​​corresponding to each temperature calibration point are obtained through steps S22-S23, thereby obtaining the calibration coefficient sequence for each temperature calibration point, which serves as the calibration coefficient correction table.

[0056] In one specific embodiment, the process of obtaining the correction table is as follows.

[0057] Set the ambient temperature of the substrate height measurement system to the temperature calibration point T. i Afterwards, the substrate height measurement system will undergo M calibration procedures to obtain M p values. 0,i p 1,i p k,i , F(·) i The average value of the obtained calibration coefficients is used to obtain the calibration coefficient for the corresponding temperature calibration point, as shown in the following formula:

[0058]

[0059]

[0060] Where, p 0,i For the corresponding temperature calibration point T i Height offset, p 1,i For the corresponding temperature calibration point T i The gain coefficient, pk,i For the corresponding temperature calibration point T i The nonlinear correction coefficient, F(·) i For the corresponding temperature calibration point T i The transcendental function, where 0≤i≤N-1 is the index of the temperature calibration point, and 1≤m≤M is the number of calibrations. The height offset is obtained from the m-th calibration. Let be the gain coefficient obtained during the m-th calibration. The nonlinear correction coefficients are obtained from the m-th calibration. Let be the transcendental function obtained from the m-th calibration.

[0061] After measuring the calibration coefficients for all temperature calibration points in step S24, the calibration coefficient sequence for each temperature calibration point is obtained:

[0062] {p 0,0 ,p 0,1 ,…,p 0,i …,p 0,N}

[0063] {p 1,0 ,p 1,1 ,…,p 1,i …,p 1,N}

[0064] {p k,0 ,p k,1 ,…,p k,i …,p k,N}

[0065] {F(·)0,F(·)1,…,F(·) i …,F(·) N};

[0066] Finally, the obtained calibration coefficient sequences and corresponding temperature calibration points are used to form a calibration coefficient correction table according to the corresponding relationship:

[0067] {(T0,p 0,0 ),(T1,p 0,1 ),…,(T i ,p 0,i ),…,(T N ,p 0,N )}

[0068] {(T0,p 1,0 ),(T1,p 1,1 ),…,(T i ,p 1,i ),…,(T N ,p 1,N )}

[0069] {(T0,p k,0 ),(T1,p k,1 ),…,(T i ,p k,i ),…,(T N ,p k,N )}

[0070] {(T0,F(·)0),(T1,F(·)1),…,(T i ,F(·) i ),…,(T N ,F(·) N )}.

[0071] This embodiment uses equally spaced temperatures and multiple calibration operations to obtain the correction calibration coefficients for each corresponding temperature point. The multiple calibration operation process ensures that the obtained calibration coefficients for each temperature point are more accurate, preventing the impact on the measurement accuracy of the substrate warpage measurement system caused by potentially inaccurate calibration coefficients obtained from a single calibration operation. (Reference) Figure 3 The figure shown is a schematic diagram of the gain coefficient obtained through steps S21-S24 as a function of temperature in this embodiment.

[0072] In this embodiment, step S3 determines the corrected calibration coefficients at the temperature to be detected based on the calibration coefficient correction table using the polynomial interpolation method or machine learning method, thereby realizing the temperature drift correction of substrate warpage measurement. The polynomial interpolation method can be linear interpolation, cubic spline interpolation, or other interpolation methods. The following describes in detail the correction process of each calibration coefficient during the online measurement of the substrate warpage measurement system using each method.

[0073] In one embodiment, during the online measurement process, the ambient temperature value is collected in real time by the substrate warpage measurement system. The temperature range of the ambient temperature value is determined according to the correction table, and the calibration coefficients are corrected online using a linear interpolation method, specifically through the following formula:

[0074]

[0075] Among them, w c c = 1, 2, 3, 4 are calibration coefficients, where w1, w2, w3, w4 correspond to the height bias p0, gain coefficient p1, and nonlinearity correction coefficient p1, respectively. k And transcendental function F(·), according to T∈[T i ,T i+1 [i] represents the ambient temperature value during testing, 0 ≤ i ≤ N-1.

[0076] In another embodiment, during the online measurement process, the ambient temperature value is collected in real time by the substrate warpage measurement system. The temperature range of the ambient temperature value is determined according to the correction table, and the correction of each calibration coefficient is achieved by cubic spline interpolation, specifically through the following formula:

[0077] w c =A i,0 +A i,1 (TT i )+A i,2 (TT i ) 2 +A i,3 (TT i ) 3 (6);

[0078] Where, T∈[T i ,T i+1 [The collected data represents the ambient temperature value, 0 ≤ i ≤ N-1, A] i,0 、A i,1 、A i,2 、A i,3 These are the interpolation coefficients corresponding to this temperature range.

[0079] spline interpolation coefficient A i,0 、A i,1 、A i,2 、A i,3 The calculation formula is as follows:

[0080]

[0081] The above formula can be simplified as follows:

[0082]

[0083] Where, ΔT=T i+1 -T i Δw c,i =w c,i+1 -w c,i , 0≤i≤N-1.

[0084] In the above formula (8), S i Determined by the following formula:

[0085]

[0086] In one embodiment, reference Figure 4-5 The figures shown are schematic diagrams of the calibration method using linear interpolation and the calibration method using spline interpolation, respectively, in this embodiment.

[0087] In this embodiment, machine learning methods such as regression trees and regression forest trees can also be used to correct the calibration coefficients during the online measurement of the substrate warpage measurement system. The specific steps are as follows:

[0088] Step S31: Input the calibration coefficient correction table as training data into the machine learning model so that it learns the linear relationship between each calibration coefficient and temperature until the model reaches the convergence condition.

[0089] In step S32, during the online measurement process, the temperature value of the test environment is collected in real time by the substrate warping measurement system and input into the machine learning model trained in step S31 to calculate and determine the calibration coefficients of each correction. Thus, the linear height of the calibrated substrate can be determined by equation (3).

[0090] This embodiment employs a machine learning approach, using a calibration coefficient correction table to perform a linear fitting process between each calibration coefficient and temperature. Furthermore, it determines each calibration coefficient based on the measurement temperature during the substrate warpage measurement process. This method more objectively and accurately determines the calibration coefficients during the measurement process, correcting for gain deviations and nonlinear characteristics between the original height and the actual height of the substrate. This compensates for errors caused by temperature variations in the calibration coefficients, thereby improving the measurement accuracy of the substrate warpage measurement system.

[0091] In this embodiment, when using a regression tree method to implement the calibration coefficients for each correction during the online measurement process of the substrate warpage measurement system, the main parameters of the regression tree are first set, including maximum depth and segmentation quality function. The parameters of the regression tree or regression forest need to be trained, evaluated, and repeatedly adjusted using data until the prediction result reaches the convergence threshold. The training data may include a training set and a test set, which consists of correction table data. The test set data is used to make predictions and evaluate the prediction results, such as prediction scores.

[0092] To improve correction accuracy, the regression tree method can be extended to a regression forest tree to implement the calibration coefficients for each correction during the online measurement process of the substrate warp measurement system. First, the number of regression trees needs to be set, with other parameters similar to those of the regression trees. Then, the correction table data obtained through steps S21-S24 is divided into training and testing sets in a 6:4 or 7:3 ratio to train the regression forest tree until convergence is achieved, thus determining the parameters of the regression forest tree. Finally, the obtained parameters and regression forest tree results are saved. In this way, the regression forest tree learns the linear relationship between temperature and each calibration coefficient. (Refer to...) Figure 6 The figures shown are schematic diagrams illustrating the regression tree calibration results provided in this embodiment.

[0093] During online measurement, the ambient temperature value collected in real time by the substrate warpage measurement system is input into the trained regression tree or regression forest tree to predict the corresponding calibration coefficients. The calibrated linear height of the substrate can then be determined using equation (3). In this embodiment, the regression forest method is more complex than the regression tree method, but it achieves better prediction results and provides better correction for the gain coefficient. Furthermore, the training process for both the regression tree and the regression forest method can be performed offline. (Refer to...) Figure 7 The diagram shown is a schematic representation of the calibration results obtained by using a regression forest in this embodiment.

[0094] This embodiment can be referred to. Figure 8-9 The figures show schematic diagrams of the original substrate height obtained by the substrate warpage measurement system and the linear substrate height after correction according to this embodiment, respectively. The independent variable of the calibration model uses the original height signal, and the linear height obtained after correction corrects for the gain deviation and other coefficients between the original height and the actual substrate height. The linear height and the actual substrate height have a linear relationship, thus calibrating the measurement result deviation caused by temperature drift.

[0095] Device Examples

[0096] According to embodiments of the present invention, a temperature drift correction device for substrate warpage measurement is provided, such as... Figure 10 The diagram shown is a block diagram of a temperature drift correction system for substrate warpage measurement provided in this embodiment. According to an embodiment of the present invention, a temperature drift correction device for substrate warpage measurement includes:

[0097] The calibration coefficient determination module 10 is used to determine multiple calibration coefficients based on the calibration coefficient model of substrate height measurement.

[0098] The correction table determination module 20 is used to obtain the calibration results of the substrate warpage measurement system performing corresponding calibration operations on the substrate at each temperature calibration point based on the set temperature calibration point and the number of calibrations at each temperature calibration point, obtain multiple calibration coefficients, and calculate the average of multiple values ​​of each calibration coefficient to obtain a sequence of calibration coefficients for each temperature calibration point, which serves as a calibration coefficient correction table.

[0099] The online correction module 30 is used to determine the correction coefficients at the temperature to be tested based on the calibration coefficient correction table, using a polynomial difference method or machine learning method, and to determine the corrected substrate height according to the calibration coefficient model, thereby realizing the temperature drift correction of the substrate height at the test temperature. The temperature to be tested can be obtained through a substrate warpage measurement system.

[0100] In this embodiment, the polynomial interpolation method can be linear interpolation, cubic spline interpolation, or other interpolation methods, and the machine learning method can be regression tree, regression forest, or other methods.

[0101] The temperature drift correction device for substrate warpage measurement provided in this embodiment is used to solve the problem that the calibration coefficients for substrate warpage measurement cannot correct for systematic errors caused by temperature changes. First, to determine the relationship between the measured height and the temperature-related calibration coefficients, the correction table determination module 20 pre-calibrates the calibration coefficients at multiple temperatures. The average value of these calibration coefficients is then used as the correction calibration coefficient for the corresponding temperature point. This process determines the calibration coefficient for each temperature, forming a calibration coefficient correction table. During online correction (i.e., during the substrate warpage measurement process), the online correction module 30 collects the temperature value of the test environment in real time from the temperature sensor. Based on the calibration coefficient correction table, it uses a polynomial difference method or machine learning method to determine the corrected calibration coefficients for the corresponding test environment temperature value. The corrected substrate height can be obtained based on these corrected calibration coefficients. This method performs online correction of the calibration coefficients of the substrate warpage measurement system, compensating for errors caused by temperature changes in the calibration coefficients, thereby improving the measurement accuracy of the substrate warpage measurement system.

[0102] In this embodiment, the correction table determination module 20 further includes the following modules:

[0103] The parameter setting submodule 201 is used to set the test temperature range and temperature selection interval according to the temperature setting range of the substrate warp measurement system, thereby determining each temperature calibration point, and setting the number of calibration operations for the substrate calibration operation at each temperature calibration point; in this embodiment, the number of calibrations is set to M, where M is a natural number greater than 1.

[0104] In one specific embodiment, the operating temperature range of the substrate height measurement system is set to [T0, T...]. f ], where T0 and T f These are the minimum and maximum temperatures within the operating range, respectively. The operating range is then divided into N+1 temperature calibration points {T0, T1, ..., T...} at equal intervals. i ,…,T M}∈[T0,T f For example, if the operating temperature range is [0, 100], and [0, 100] is to be divided into 5 equally spaced regions, then 6 temperature calibration points {0, 20, 40, 60, 80, 100} can be obtained, and M can be set to 5-10.

[0105] The calibration operation submodule 202 is used to obtain the calibration operation results of the substrate warpage measurement system performing a corresponding number of calibrations on the substrate based on the selected temperature point, thereby obtaining the corresponding number of calibration coefficients w. c Values, where c = 1, 2, 3, 4, w1, w2, w3, w4 correspond to the height bias p0, gain coefficient p1, and nonlinear correction coefficient p, respectively. l And transcendental functions F(·).

[0106] The calculation submodule 203 is used to calculate the average value of each obtained calibration coefficient value, thereby obtaining the calibration coefficient value of each corresponding temperature calibration point;

[0107] The traversal submodule 204 is used to traverse the temperature calibration points according to the preset temperature calibration points until the calibration coefficient values ​​corresponding to each temperature calibration point are obtained, thereby obtaining the calibration coefficient sequence for each temperature calibration point, which serves as the calibration coefficient correction table.

[0108] In this embodiment, the correction table determination module 20 uses equally spaced temperatures and multiple calibration operations to obtain the correction calibration coefficients for each corresponding temperature point. The setting of the multiple calibration operation process makes the calibration coefficients of the obtained temperature points more accurate, and will not affect the measurement accuracy of the substrate warpage measurement system due to the possibility that the calibration coefficients obtained by a single calibration operation may be inaccurate.

[0109] In this embodiment, the online correction module 30 determines the correction of each calibration coefficient at the temperature to be detected based on the calibration coefficient correction table, using a polynomial interpolation method or a machine learning method, thereby realizing the temperature drift correction of the substrate warpage measurement. The polynomial interpolation method can be a linear interpolation method, a cubic spline interpolation method, or other interpolation methods. For the specific methods used to implement the correction process of each calibration coefficient in the online measurement process of the substrate warpage measurement system, please refer to the above method embodiments, which will not be repeated here.

[0110] The embodiments of the present invention are device embodiments corresponding to the above method embodiments. The specific operations of each module processing step can be understood with reference to the description of the method embodiments, and will not be repeated here.

[0111] like Figure 11 As shown, the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the temperature drift correction method for substrate warpage measurement in the above embodiments.

[0112] The present invention also provides a computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it implements the temperature drift correction method for substrate warpage measurement in the above embodiments, or when the computer program is executed by a processor, it implements the temperature drift correction method for substrate warpage measurement in the above embodiments. When the computer program is executed by the processor, it implements the following method steps:

[0113] Step S1: Determine multiple coefficients to be calibrated based on the calibration coefficient model for substrate height measurement.

[0114] Step S2: Based on the set temperature calibration points and the number of calibrations at each temperature calibration point, and based on the calibration results of the substrate warping measurement system performing the corresponding number of calibrations at each temperature calibration point, multiple calibration coefficients are obtained, and the average value of multiple values ​​of each calibration coefficient is calculated to obtain a sequence of calibration coefficients for each temperature calibration point, which serves as a calibration coefficient correction table.

[0115] Step S3: Based on the calibration coefficient correction table, determine each calibration coefficient to be corrected at the temperature to be detected by polynomial difference method or machine learning method, and determine the corrected substrate height according to the calibration coefficient model, thereby realizing the temperature drift correction of the substrate height at the detection temperature.

[0116] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Furthermore, any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory.

[0117] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for apparatus or system embodiments, since they are basically similar to method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The apparatus and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. These modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and the contents not described in detail in the specification of the present invention are well known to those skilled in the art.

Claims

1. A method for correcting temperature drift in substrate warpage measurement, characterized in that, Includes the following steps: Based on the calibration coefficient model for substrate height measurement, several coefficients to be calibrated are determined; Based on the set temperature calibration points and the number of calibrations at each temperature calibration point, and based on the calibration results of the substrate warp measurement system performing the corresponding number of calibrations at each temperature calibration point, multiple calibration coefficients are obtained. The average of multiple values ​​for each calibration coefficient is then calculated to obtain a sequence of calibration coefficients for each temperature calibration point, which serves as a calibration coefficient correction table. Specifically, the following steps are included: Based on the temperature setting range of the substrate warp measurement system, the test temperature range and temperature selection interval are preset to determine each temperature calibration point, and the number of calibration operations for the substrate calibration operation at each temperature calibration point is set. Based on the preset temperature point, the substrate is calibrated a corresponding number of times using the substrate warpage measurement system to obtain the values ​​of each calibration coefficient for the corresponding number of times. The average value of each calibration coefficient is calculated to obtain the calibration coefficient value for the corresponding temperature calibration point. The process iterates through the temperature calibration points until the calibration coefficient values ​​corresponding to each temperature calibration point are obtained, thus generating a sequence of calibration coefficients for each temperature calibration point, which serves as a calibration coefficient correction table; and Based on the calibration coefficient correction table, the calibration coefficients to be corrected at the test temperature are determined by the polynomial difference method or machine learning method, and the corrected substrate height is determined according to the calibration coefficient model, thereby realizing the temperature drift correction of the substrate height at the test temperature.

2. The temperature drift correction method for substrate warpage measurement as described in claim 1, characterized in that, The determination of multiple coefficients to be calibrated based on the calibration coefficient model obtained from substrate height measurement includes the following steps: The linearized calibration model based on the height measurement values ​​is as follows: Among them, h lin h is the linear height of the calibrated substrate. raw Uncalibrated original height of the substrate; p k Here are the polynomial coefficients to be calibrated, k = 0, 1, ..., K, where K is the order of the polynomial; F(·) is the transcendental function correction term, expressed as follows: F(h raw )=a×sin(b×h raw +c) (2); Where a, b, and c are the parameters to be calibrated; Separating equation (1) and representing the height bias, gain coefficient, and nonlinear correction coefficient separately, the specific model is as follows: The calibration coefficients to be corrected include the height bias p0, the gain coefficient p1, and the nonlinearity correction coefficient p. k , and the transcendental function F(·).

3. The temperature drift correction method for substrate warpage measurement as described in claim 1, characterized in that, The polynomial interpolation method is a linear interpolation or cubic spline interpolation method; The machine learning method is the regression tree or regression forest tree algorithm.

4. The temperature drift correction method for substrate warpage measurement as described in claim 1, characterized in that, The specific steps for determining the calibration coefficients corrected at the temperature to be detected using linear interpolation are as follows: The ambient temperature value is collected in real time by the substrate warpage measurement system. The temperature range of the ambient temperature value is determined according to the correction table. The calibration coefficients are corrected online using a linear interpolation method, specifically by the following formula: Among them, w c For calibration coefficients, c = 1, 2, 3, 4, where w1, w2, w3, w4 correspond to the height bias p0, gain coefficient p1, and nonlinearity correction coefficient p, respectively. k And transcendental function F(·), according to T∈[T i ,T i+1 ] represents the ambient temperature value, 0≤i≤N-1, where N is the number of temperature calibration points.

5. The temperature drift correction method for substrate warpage measurement as described in claim 1, characterized in that, The ambient temperature value is collected in real time by the substrate warpage measurement system. The temperature range of the ambient temperature value is determined according to the correction table. The calibration coefficients are corrected online using cubic spline interpolation, specifically by the following formula: w c =A i,0 +A i,1 (T-T i )+A i,2 (T-T i ) 2 +A i,3 (T-T i ) 3 (6); Where, T∈[T i ,T i+1 [i] represents the ambient temperature value, 0 ≤ i ≤ N-1, where N is the number of temperature calibration points, and A i,0 、A i,1 、A i,2 、A i,3 These are the interpolation coefficients corresponding to the temperature range; spline interpolation coefficient A i,0 、A i,1 、A i,2 、A i,3 The calculation formula is as follows: Formula (7) can be simplified as follows: where ΔT = T i+1 - T i , Δw c,i = w c,i+1 - w c,i ; Then S in equation (8) i Determined by the following formula:

6. The temperature drift correction method for substrate warpage measurement as described in claim 1, characterized in that, The process of correcting various calibration coefficients during online measurement in a substrate warpage measurement system using machine learning methods includes the following steps: The calibration coefficient correction table is used as training data and input into the machine learning model to learn the linear relationship between each calibration coefficient and temperature until the model reaches the convergence condition. as well as During the online measurement process, the ambient temperature value is collected in real time by the substrate warpage measurement system and input into the trained machine learning model to calculate and determine the calibration coefficients for each correction.

7. A temperature drift correction device for measuring substrate warpage, characterized in that, include: The calibration coefficient determination module is used to determine multiple calibration coefficients based on the calibration coefficient model of substrate height measurement. The correction table determination module is used to obtain the calibration results of the substrate warpage measurement system performing the corresponding number of calibrations at each temperature calibration point based on the set temperature calibration point and the number of calibrations at each temperature calibration point, obtain multiple calibration coefficients, and calculate the average of multiple values ​​of each calibration coefficient to obtain a sequence of calibration coefficients for each temperature calibration point, which serves as a calibration coefficient correction table. The correction table determines the specific configuration of the module for: determining each temperature calibration point based on the temperature setting range of the substrate warp measurement system, preset the test temperature range and temperature selection interval, and setting the number of calibration operations for the substrate calibration operation at each temperature calibration point; and using the substrate warp measurement system to perform the corresponding number of calibration operations on the substrate according to the preset temperature points, thereby obtaining the values ​​of each calibration coefficient for the corresponding number of calibrations. The average value of each calibration coefficient is calculated to obtain the calibration coefficient value for the corresponding temperature calibration point. Traverse the temperature calibration points until you obtain the calibration coefficient values ​​corresponding to each temperature calibration point, thereby obtaining the calibration coefficient sequence for each temperature calibration point, which serves as the calibration coefficient correction table. as well as The online correction module is used to determine the correction of each calibration coefficient at the temperature to be detected by means of polynomial difference method or machine learning method based on the calibration coefficient correction table, and to determine the corrected substrate height according to the calibration coefficient model, thereby realizing the temperature drift correction of the substrate height at the detection temperature.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the temperature drift correction method for substrate warpage measurement as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the temperature drift correction method for substrate warpage measurement as described in any one of claims 1 to 6.

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