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

Abstract

The invention provides a temperature drift correction method and device for substrate warping measurement, equipment and a medium, and the method comprises the steps: determining a plurality of to-be-calibrated coefficients according to a calibration coefficient model for substrate height measurement; based on the set temperature calibration points and the calibration times under each temperature calibration point, a plurality of calibration coefficients are obtained based on the result of calibration operation of the corresponding calibration times under each temperature calibration point on the substrate by the substrate warping measurement system, and an average value is solved to obtain a calibration coefficient correction table; on the basis of the calibration coefficient correction table, each corrected calibration coefficient at the to-be-detected temperature is determined through a polynomial difference method or a machine learning method, and the corrected substrate height is determined according to the calibration coefficient model, so that temperature drift correction of the substrate height at the detected temperature is realized. According to the invention, the calibration coefficient of the substrate warpage measurement system is corrected online, and the error caused by the temperature change of the calibration coefficient is compensated, so that the measurement precision of the substrate warpage measurement system is improved.

Description

Technical Field

[0001] The present invention relates to the field of semiconductor detection technology, and in particular to a temperature drift correction method, device, equipment and medium for substrate warpage measurement. Background Art

[0002] 3D packaging with multiple layers of chips and substrates stacked on top of each other is the current packaging development trend. Each functional layer in the 3D package is composed of different materials, such as silicon, FR-4, copper, aluminum, ceramics, polymers and various solders. In the packaging process, these materials will be subjected to the combined effects of multiple loads such as moisture, heat and force. Due to the mismatch of thermal expansion coefficients, each material exhibits different thermomechanical properties under different loads. After the stress and deformation of the multi-layer material accumulate, a large warping will occur, leading to device failure. Therefore, the measurement and control of the warping deformation of each layer in the 3D package is crucial.

[0003] In essence, the warpage measurement of the package substrate belongs to the three-dimensional morphology measurement. At present, the shadow moire method based on grating moiré fringes is commonly used in the industry. The substrate is heated, and the grating and the shadow grating generated by the grating projection to the sample reflection are used to interfere with each other to test the off-plane deformation of the substrate warpage in the package. After the CCD (Charge Coupled Device) camera is used to obtain the image signal, the algorithm processes the moiré fringes to form the height value of each point and obtain the deformation of the morphology. During the measurement process, the substrate is first heated by temperature control, the temperature conditions change, the optical characteristics of the measurement system and a series of temperatures lead to system errors. If the measurement is made directly, there will be a certain deviation between the measured height and the actual height. Therefore, it is necessary to obtain the corresponding correction parameters through calibration to ensure the measurement accuracy.

[0004] In the prior art, commonly used calibration methods include polynomial fitting, linear interpolation and other methods, 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 cannot provide a quantifiable functional relationship between the calibration coefficient and temperature, and cannot accurately characterize the system error caused by temperature changes. As the requirements for substrate warpage measurement accuracy continue to increase, the existing correction parameter methods are no longer applicable to the existing measurement accuracy requirements. Summary of the invention

[0005] In order to overcome the problems existing in the related art, the present disclosure provides a temperature drift correction method, device, equipment and medium for substrate warpage measurement to solve the technical problems in the related art.

[0006] One or more embodiments of the present specification provide a method for correcting temperature drift of substrate warpage measurement, comprising the following steps:

[0007] Determining a plurality of coefficients to be calibrated according to a calibration coefficient model for substrate height measurement;

[0008] Based on the set temperature calibration points and the number of calibrations at each temperature calibration point, and based on the result of the calibration operation performed by the substrate warpage measurement system on the substrate for the corresponding number of calibrations at each temperature calibration point, a plurality of calibration coefficients are obtained, and an average value is calculated for a plurality of values ​​of each calibration coefficient, thereby obtaining a sequence of calibration coefficients for the temperature calibration points as a calibration coefficient correction table; and

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

[0010] One or more embodiments of the present specification provide a temperature drift correction device for substrate warpage measurement, comprising:

[0011] A module for determining coefficients to be calibrated, used for determining a plurality of coefficients to be calibrated according to a calibration coefficient model for substrate height measurement;

[0012] A correction table determination module is used to obtain the result of the calibration operation of the substrate warpage measurement system on the substrate at each temperature calibration point for the corresponding number of calibrations based on the set temperature calibration points and the number of calibrations at each temperature calibration point, obtain multiple calibration coefficients, and average multiple values ​​of each calibration coefficient, so as to obtain a sequence of calibration coefficients for the temperature calibration points as a calibration coefficient correction table; and

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

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

[0015] One or more embodiments of the present specification provide a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the temperature drift correction method for substrate warpage measurement as described above is implemented.

[0016] The present disclosure provides a method, device, equipment and medium for correcting temperature drift of substrate warpage measurement. The advantage is that it is used to solve the problem that the calibration coefficient of substrate warpage measurement cannot correct the system error caused by temperature change. First, in order to determine the relationship between the calibration coefficient related to the measured height and the temperature, the calibration coefficient is determined by pre-calibrating the temperature multiple times, and then the average value is used as the correction calibration coefficient of the corresponding temperature point. In this way, the calibration coefficient corresponding to each temperature is determined to form a calibration coefficient correction table. During online correction (i.e., during the measurement of substrate warpage), the temperature value of the test environment is collected in real time according to the temperature sensor. Based on the calibration coefficient correction table, the polynomial difference method or machine learning method is used to determine the corrected calibration coefficients under the corresponding temperature value. According to the corrected calibration coefficients, the corrected substrate height can be obtained. The method performs online correction on the calibration coefficient of the substrate warpage measurement system, compensates for the error caused by the calibration coefficient changing with temperature, thereby improving the measurement accuracy of the substrate warpage measurement system. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate one or more embodiments of this specification or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0018] Figure 1 A flow chart of a method for correcting temperature drift of substrate warpage measurement provided by one or more embodiments of this specification;

[0019] Figure 2 A flow chart of calibration of parameters of a substrate height measurement model provided for one or more embodiments of this specification;

[0020] Figure 3 A schematic diagram showing how the gain coefficient varies with temperature provided in an embodiment;

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

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

[0023] Figure 6 A schematic diagram of a calibration result using a regression tree provided in an embodiment;

[0024] Figure 7 A schematic diagram of a regression forest calibration result provided by an embodiment;

[0025] Figure 8A schematic diagram of the original value of substrate height provided by an embodiment;

[0026] Fig. 9 A schematic diagram of a linear value of substrate height provided by an embodiment;

[0027] Fig.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] Fig.11 A schematic diagram of the structure of a computer device provided for one or more embodiments of this specification. DETAILED DESCRIPTION

[0029] In order 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 in conjunction with the drawings in one or more embodiments of this specification. Obviously, the described embodiments are only part of the embodiments of this specification, not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0030] The present invention is described in detail below in conjunction with specific implementation methods and the accompanying drawings.

[0031] Method Embodiment

[0032] According to an embodiment of the present invention, a temperature drift correction method for substrate warpage measurement is provided. Figure 1 FIG. 1 is a flow chart of a method for correcting a temperature drift of substrate warpage measurement provided in this embodiment. The method for correcting a temperature drift of substrate warpage measurement according to an embodiment of the present invention comprises the following steps:

[0033] Step S1, determining a plurality of coefficients to be calibrated according to a 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 results of the calibration operation of the substrate warpage measurement system on the substrate for 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, so as to obtain a sequence of calibration coefficients for the temperature calibration point as a calibration coefficient correction table.

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

[0036] In this embodiment, the polynomial interpolation method may be an interpolation method such as linear interpolation and cubic spline interpolation, and the machine learning method may use a regression tree, regression forest, and other methods.

[0037] The temperature drift correction method for substrate warpage measurement provided in this embodiment is used to solve the problem that the calibration coefficient of substrate warpage measurement cannot correct the system error caused by temperature change. First, in order to determine the relationship between the calibration coefficient related to the measured height and the temperature, the calibration coefficient of multiple calibration temperatures is determined in advance, and then the average value is used as the correction calibration coefficient of the corresponding temperature point. In this way, the calibration coefficient corresponding to each temperature is determined to form a calibration coefficient correction table. During online correction (i.e., during the measurement of substrate warpage), the temperature value of the test environment is collected in real time according to the temperature sensor. Based on the calibration coefficient correction table, the polynomial difference method or machine learning method is used to determine the corrected calibration coefficients at the corresponding temperature value. The corrected substrate height can be obtained according to the corrected calibration coefficients. This method performs online correction on the calibration coefficient of the substrate warpage measurement system, compensates for the error caused by the change of the calibration coefficient with temperature, and thus improves the measurement accuracy of the substrate warpage measurement system.

[0038] In this embodiment, step S1 determines a plurality of coefficients to be calibrated according to a calibration coefficient model for substrate height measurement as follows.

[0039] The substrate warpage measurement process is a topography formed by the measurement results of the height of each point on the substrate surface at a certain temperature, and the linear calibration model of the height measurement value adopts a polynomial model. The linear calibration model of the height measurement value is specifically as follows:

[0040]

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

[0042] In formula (1), F(·) is a transcendental function correction term. F(·) is generally described in the form of sine and cosine functions, which can be a linear combination of sine and cosine expressions of different multiples, 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] Among them, a, b and c are the parameters to be calibrated.

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

[0046]

[0047] Among them, p0 is the height bias, p1 is the gain coefficient, and p k is the nonlinear correction coefficient, k=2,…,K, K is the order of the polynomial. F(·) is the transcendental function correction term.

[0048] It can be seen that the height bias, gain coefficient, nonlinear correction coefficient and transcendental function will change with the change of temperature conditions. Therefore, 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 measurement accuracy of the substrate height, and the change in nonlinear coefficient and transcendental function will have a greater impact on the accuracy near the edge of the measurement range.

[0049] In this embodiment, reference Figure 2 As shown, it is a flow chart of the base plate height measurement model parameter calibration process and correction table acquisition process provided in this embodiment. Through step S2, each calibration coefficient correction table can be obtained. The specific implementation process is as follows:

[0050] Step S21, according to the temperature setting range of the substrate warpage measurement system, preset the test temperature range and the temperature selection interval, so as to determine each temperature calibration point, and set the calibration times of the substrate calibration operation at each temperature calibration point; in this embodiment, the calibration times is set to M, where M is a natural number greater than 1.

[0051] In a specific embodiment, the operating temperature range of the substrate height measurement system is [T0, T f ], where T0 and T f The lowest and highest temperatures of the working range are respectively, and the working range is divided into N+1 temperature calibration points {T0, T1, …, T i ,…,T N}∈[T0,T f ] For example, if the operating temperature range is [0,100] and [0,100] is divided into five equally spaced regions, six temperature calibration points {0,20,40,60,80,100} can be obtained.

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

[0053] In this embodiment, during the process of the substrate warpage measurement system measuring the height of the substrate, the height bias, gain coefficient, nonlinear correction coefficient and transcendental function coefficient are obtained by fitting the substrate warpage measurement system using the least square method. The specific process is that the height signal of the substrate is simultaneously collected by the substrate warpage measurement system and the height measurement device integrated in the substrate warpage measurement system through a vertical scanning method, wherein the height of the substrate collected by the height measurement device is used as a reference height, and then the height signal and the reference height signal are fitted by the substrate warpage measurement system using the least square method, and the values ​​of the height bias, gain coefficient, nonlinear correction coefficient and transcendental function coefficient can be obtained. 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 through the prior art, and no further elaboration is given here.

[0054] Step S23, averaging the obtained calibration coefficient values ​​respectively, so as to obtain the calibration coefficient values ​​corresponding to the temperature calibration points;

[0055] Step S24, traverse the temperature calibration points until the calibration coefficient values ​​corresponding to the temperature calibration points are obtained through steps S22-S23, thereby obtaining the calibration coefficient sequences about the temperature calibration points as the calibration coefficient correction table.

[0056] In a specific embodiment, the specific implementation 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 After that, the substrate height measurement system will perform M times of substrate height measurement system calibration process to obtain M p 0,i , p 1,i , p k,i ,F(·) i , calculate the average value of the obtained calibration coefficients, and obtain the calibration coefficient of the corresponding temperature calibration point, which is calculated as follows:

[0058]

[0059]

[0060] Among them, p 0,i Corresponding temperature calibration point T i The height bias, p 1,i Corresponding temperature calibration point T i The gain factor, pk,i Corresponding temperature calibration point T i The nonlinear correction coefficient, F(·) i Corresponding temperature calibration point T i The transcendental function, 0≤i≤N-1 is the serial number of the temperature calibration point, 1≤m≤M is the number of calibrations, is the height bias obtained from the mth calibration, is the gain coefficient obtained from the mth calibration, is the nonlinear correction coefficient obtained from the mth calibration, is the transcendental function obtained from the mth calibration.

[0061] After completing the measurement of the calibration coefficients of all temperature calibration points in step S24, the calibration coefficient sequences corresponding to all temperature calibration points are 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 calibration coefficient sequences and corresponding temperature calibration points are obtained 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 evenly spaced temperatures and multiple calibration operations to obtain the correction calibration coefficients for each corresponding temperature point. The setting of multiple calibration operation processes 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 inaccurate calibration coefficients obtained by a single calibration operation. Figure 3 As shown, it is a schematic diagram of the gain coefficient obtained through steps S21-S24 according to this embodiment changing with temperature;

[0072] In this embodiment, step S3 is based on the calibration coefficient correction table, and the corrected calibration coefficients at the temperature to be detected are determined by a polynomial difference method or a machine learning method, so as to realize the temperature drift correction of the substrate warpage measurement. Among them, the polynomial difference method can be an interpolation method such as linear interpolation and cubic spline interpolation. The following specifically describes 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 test environment temperature value is collected in real time by the substrate warpage measurement system, the temperature range of the test environment temperature value is determined according to the correction table, and the online correction of each calibration coefficient is realized by the linear interpolation method, which is specifically realized by 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 nonlinear correction coefficient p respectively. k and the transcendental function F(·), according to T∈[T i ,T i+1 ] is the test environment temperature value, 0≤i≤N-1.

[0076] In another embodiment, during the online measurement process, the test environment temperature value is collected in real time by the substrate warpage measurement system, the temperature range of the test environment temperature value is determined according to the correction table, and the correction of each calibration coefficient is realized by the cubic spline interpolation method, which is specifically realized by 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] Among them, T∈[T i ,T i+1 ] is the test environment temperature value obtained by collection, 0≤i≤N-1, A i,0 , A i,1 , A i,2 , A i,3 is the interpolation coefficient 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

[0082]

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

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

[0085]

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

[0087] In this embodiment, the correction process of each calibration coefficient during the online measurement process of the substrate warpage measurement system can also be implemented by machine learning methods such as regression tree and regression forest tree. The specific steps are as follows:

[0088] Step S31, inputting 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 a convergence condition;

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

[0090] This embodiment adopts a machine learning method, and performs a linear fitting process of each calibration coefficient and temperature through a calibration coefficient correction table, and determines each calibration coefficient according to the measurement temperature during the measurement process of the substrate warpage measurement system. In this way, the calibration coefficient in the measurement process is determined more objectively and accurately, and the gain deviation, nonlinear characteristics and other coefficients between the original height and the actual height of the substrate are corrected to compensate for the error caused by the change of the calibration coefficient with temperature, thereby improving the measurement accuracy of the substrate warpage measurement system.

[0091] In this embodiment, if the calibration coefficients of each correction in the online measurement process of the substrate warpage measurement system are realized by the regression tree method, first, the main parameters of the regression tree are set, including the maximum depth and the segmentation quality function. The parameters of the regression tree or regression forest need to be trained and evaluated through data and adjusted repeatedly until the prediction result reaches the convergence threshold, wherein the training data may include a training set and a test set, which are composed of correction table data, and the test set data is used to predict and evaluate the prediction results, such as: prediction score, etc.

[0092] In order to improve the correction accuracy, the regression tree method can also be expanded to a regression forest tree to realize the calibration coefficients of various corrections during the online measurement process of the substrate warpage measurement system. First, the number of regression trees needs to be set, and other parameters are similar to the regression tree parameters; then the correction table data obtained through steps S21 to S24 is divided into a training set and a test set in a ratio of 6:4 or 7:3 to train the regression forest tree until the convergence condition is reached, thereby determining the parameters of the regression forest tree, and finally saving the obtained parameters and the regression forest tree results. In this way, the regression forest tree learns the linear relationship between temperature and each calibration coefficient, which can be referred to Figure 6 As shown, they are schematic diagrams of the calibration results using the regression tree provided in this embodiment.

[0093] During the online measurement process, the test environment temperature value collected in real time by the substrate warpage measurement system is input into the above-mentioned trained regression tree or regression forest tree to predict the corresponding corrected calibration coefficients, so that the calibrated substrate linear height can be determined by formula (3). In this embodiment, the complexity of the regression forest method is relatively large compared with the regression tree, but it can obtain better prediction effect, and the correction effect of the gain coefficient is better. The training process of the regression tree and regression forest can be performed offline, refer to Figure 7 As shown, it is a schematic diagram of the calibration result by using regression forest provided in this embodiment.

[0094] In this embodiment, reference may be made to Figure 8-9 As shown, they are respectively a schematic diagram of the original value of the substrate height obtained by normal measurement of the substrate warpage measurement system and a schematic diagram of the linear value of the substrate height corrected by this embodiment. The independent variable of the calibration model adopts the original height signal, and the linear height obtained after correction corrects the gain deviation and other coefficients between the original height and the actual height of the substrate. The linear height is linearly related to the actual height of the substrate, and the measurement result deviation caused by temperature drift is calibrated.

[0095] Device Embodiment

[0096] According to an embodiment of the present invention, a temperature drift correction device for substrate warpage measurement is provided. Fig.10 FIG. 1 is a block diagram of a temperature drift correction system for substrate warpage measurement provided in this embodiment. The temperature drift correction device for substrate warpage measurement according to an embodiment of the present invention includes:

[0097] The module 10 for determining coefficients to be calibrated is used to determine a plurality of coefficients to be calibrated according to a calibration coefficient model for substrate height measurement.

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

[0099] The online correction module 30 is used to determine the calibration coefficients corrected at the temperature to be detected by a polynomial difference method or a machine learning method based on the calibration coefficient correction table, 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. The temperature to be detected can be acquired by the substrate warpage measurement system.

[0100] In this embodiment, the polynomial interpolation method may be an interpolation method such as linear interpolation and cubic spline interpolation, and the machine learning method may use a regression tree, regression forest, and 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 coefficient of substrate warpage measurement cannot correct the system error caused by temperature change. First, in order to determine the relationship between the measured height and the calibration coefficient related to temperature, the calibration coefficient of multiple temperatures is pre-calibrated by the correction table determination module 20, and then the average value is used as the correction calibration coefficient of the corresponding temperature point. In this way, the calibration coefficient corresponding to each temperature is determined to form a calibration coefficient correction table. During online correction (i.e., during the measurement of substrate warpage), the online correction module 30 collects the temperature value of the test environment in real time according to the temperature sensor, and based on the calibration coefficient correction table, the polynomial difference method or machine learning method is used to determine the corrected calibration coefficients under the corresponding test environment temperature value. According to the corrected calibration coefficients, the corrected substrate height can be obtained. This method performs online correction on the calibration coefficient of the substrate warpage measurement system, compensates for the error caused by the change of the calibration coefficient with temperature, and thus improves the measurement accuracy of the substrate warpage measurement system.

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

[0103] The parameter setting submodule 201 is used to set the test temperature range and the temperature selection interval according to the temperature setting range of the substrate warpage measurement system, so as to determine each temperature calibration point, and set the calibration times of the substrate calibration operation at each temperature calibration point; in this embodiment, the calibration times is set to M, where M is a natural number greater than 1.

[0104] In a specific embodiment, the operating temperature range of the substrate height measurement system is [T0, T f ], where T0 and T f The lowest and highest temperatures of the working range are respectively, and the working range is divided into N+1 temperature calibration points {T0, T1, …, T 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, 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 for the corresponding number of calibrations on the substrate according to the selected temperature point, so as to obtain the corresponding number of calibration coefficients w c Value, where c = 1, 2, 3, 4, w1, w2, w3, w4 correspond to the height bias p0, gain coefficient p1, nonlinear correction coefficient p l and the transcendental function F(·).

[0106] The calculation submodule 203 is used to calculate the average value of each calibration coefficient obtained, so as to obtain the calibration coefficient value of the 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 the temperature calibration points are obtained, thereby obtaining the calibration coefficient sequences about the temperature calibration points as the calibration coefficient correction table.

[0108] The correction table determination module 20 of this embodiment adopts equally spaced temperatures and multiple calibration operations to obtain the correction calibration coefficients for each corresponding temperature point. The setting of multiple calibration operation processes 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 possible inaccuracy of the calibration coefficients obtained by a single calibration operation.

[0109] In this embodiment, the online correction module 30 determines the corrected calibration coefficients at the temperature to be detected based on the calibration coefficient correction table through a polynomial difference method or a machine learning method, thereby realizing temperature drift correction of substrate warpage measurement. Among them, the polynomial difference method can be an interpolation method such as linear interpolation and cubic spline interpolation. The specific methods for realizing the correction process of each calibration coefficient during the online measurement of the substrate warpage measurement system can refer to the above method embodiments, which will not be repeated here.

[0110] The embodiment of the present invention is an apparatus embodiment corresponding to the above-mentioned method embodiment. The specific operations of the processing steps of each module can be understood by referring to the description of the method embodiment, which will not be repeated here.

[0111] like Fig.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, the temperature drift correction method for substrate warpage measurement in the above-mentioned embodiment is implemented.

[0112] The present invention also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the temperature drift correction method for substrate warpage measurement in the above embodiment is implemented. Alternatively, when the computer program is executed by a processor, the temperature drift correction method for substrate warpage measurement in the above embodiment is implemented. When the computer program is executed by the processor, the following method steps are implemented:

[0113] Step S1, determining a plurality of coefficients to be calibrated according to a 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 results of the calibration operation of the substrate warpage measurement system on the substrate for 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, so as to obtain a sequence of calibration coefficients for the temperature calibration point as a calibration coefficient correction table.

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

[0116] A person skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory.

[0117] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device or system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. The device and system embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions 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 belong to the common knowledge of those skilled in the art.

Claims

1. A temperature drift correction method for substrate warpage measurement, characterized in that: The following steps are involved: Determining a plurality of coefficients to be calibrated according to a calibration coefficient model for substrate height measurement; Based on the set temperature calibration points and the number of calibrations at each temperature calibration point, and based on the result of the calibration operation performed by the substrate warpage measurement system on the substrate for the corresponding number of calibrations at each temperature calibration point, a plurality of calibration coefficients are obtained, and an average value is calculated for a plurality of values ​​of each calibration coefficient, thereby obtaining a sequence of calibration coefficients for the temperature calibration point as a calibration coefficient correction table; as well as Based on the calibration coefficient correction table, the calibration coefficients to be corrected at the temperature to be detected are determined by a polynomial difference method or a machine learning method, and the corrected substrate height is determined according to the calibration coefficient model, thereby realizing temperature drift correction of the substrate height at the detection temperature.

2. The temperature drift correction method for substrate warpage measurement according to claim 1, characterized in that: The method of obtaining a plurality of calibration coefficients based on the set temperature calibration points and the number of calibrations at each temperature calibration point and the result of the calibration operation performed by the substrate warpage measurement system on the substrate at each temperature calibration point for a corresponding number of calibrations is based on the set temperature calibration points and the number of calibrations at each temperature calibration point ... According to the temperature setting range of the substrate warpage measurement system, the test temperature range and the temperature selection interval are preset, so as to determine each temperature calibration point, and set the calibration times of the substrate calibration operation at each temperature calibration point; According to the preset temperature points, the substrate is calibrated a corresponding number of times using the substrate warpage measurement system to obtain values ​​of the corresponding number of calibration coefficients; Calculating the average value of each calibration coefficient obtained, thereby obtaining the calibration coefficient value corresponding to the temperature calibration point; and The temperature calibration points are traversed until the calibration coefficient values ​​corresponding to the temperature calibration points are obtained, thereby obtaining the calibration coefficient sequences about the temperature calibration points as the calibration coefficient correction table.

3. The temperature drift correction method for substrate warpage measurement according to claim 1 or 2, characterized in that: Determining a plurality of coefficients to be calibrated according to the calibration coefficient model of substrate height measurement specifically comprises the following steps: The linear calibration model based on the height measurement is as follows: Among them, h lin is the linear height of the substrate after calibration, h raw Uncalibrated original height of substrate; p k are the polynomial coefficients to be calibrated, k=0,1,…,K, 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); Among them, a, b and c are the parameters to be calibrated; Separate equation (1) and express the height bias, gain coefficient and nonlinear correction coefficient separately. The model is as follows: Then the calibration coefficients to be corrected include height offset p0, gain coefficient p1, nonlinear correction coefficient p k , and the transcendental function F(·).

4. The temperature drift correction method for substrate warpage measurement according to claim 1, characterized in that: The polynomial interpolation method is a linear interpolation method or a cubic spline interpolation method; The machine learning method is either regression tree or regression forest of trees algorithm.

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

6. The temperature drift correction method for substrate warpage measurement according to claim 1, characterized in that: The test environment temperature value collected in real time by the substrate warpage measurement system is used to determine the temperature range of the test environment temperature value according to the correction table, and the online correction of each calibration coefficient is realized by the cubic spline interpolation method, which is specifically realized 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); Among them, T∈[T i ,T i+1 ] is the test environment temperature value, 0≤i≤N-1, N is the number of temperature calibration points, A i,0 , A i,1 , A i,2 , A i,3 is the interpolation coefficient corresponding to the temperature interval; 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 abbreviated as follows: where ΔT = T i+1 - T i , Δw c,i = w c,i+1 - w c,i ; Then S in formula (8) i Determined by the following formula:

7. The temperature drift correction method for substrate warpage measurement according to claim 1, characterized in that: The process of correcting the calibration coefficients during the online measurement of the substrate warpage measurement system by machine learning method includes the following steps: Input the calibration coefficient correction table as training data into the machine learning model to make it 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 test environment 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 of each correction.

8. A temperature drift correction device for substrate warpage measurement, characterized in that: include: A module for determining coefficients to be calibrated, used for determining a plurality of coefficients to be calibrated according to a calibration coefficient model for substrate height measurement; A correction table determination module is used to obtain the result of the calibration operation of the substrate warpage measurement system on the substrate at each temperature calibration point for the corresponding number of calibrations based on the set temperature calibration points and the number of calibrations at each temperature calibration point, obtain multiple calibration coefficients, and average multiple values ​​of each calibration coefficient, so as to obtain a sequence of calibration coefficients about the temperature calibration point as a calibration coefficient correction table; as well as The online correction module is used to determine the calibration coefficients to be corrected at the temperature to be detected based on the calibration coefficient correction table by a polynomial difference method or a machine learning method, and to determine the corrected substrate height according to the calibration coefficient model, thereby realizing temperature drift correction of the substrate height at the detection temperature.

9. 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, the temperature drift correction method for substrate warpage measurement according to any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the temperature drift correction method for substrate warpage measurement according to any one of claims 1 to 4 is implemented.

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