On-line calibration method and device for substrate warping height measurement

Abstract

The embodiment of the invention provides an online calibration method and device for substrate warping height measurement, and the method comprises the steps: building a linearization calibration model through a polynomial model with a nonlinear transcendental function correction term; synchronously acquiring the substrate height signal and the reference height signal through vertical scanning to obtain a substrate height signal vector and a reference height signal vector; zero point correction is carried out on the substrate height signal vector and the reference height signal vector, so that the zero points of the substrate height signal and the reference height signal are kept consistent; and after the vertical scanning of a preset number of times is completed, fusing the obtained data, fitting through the fused data by adopting a weighted least square fitting method to obtain parameters of the linearization calibration model, and substituting the parameters into the linearization calibration model to obtain the corrected linear height of the substrate. According to the embodiment of the invention, linearization calibration processing can be carried out on the substrate warping height detection signal.

Description

Technical Field

[0001] This document relates to the field of semiconductor manufacturing and detection technology, and in particular to an online calibration method and device for measuring the warpage height of a substrate. Background Art

[0002] Substrate warpage is a macroscopic manifestation of interface stress and deformation, which not only causes manufacturing difficulties such as incorrect assembly, but also causes cracks and delamination between the solder layer and the substrate, resulting in component breakage, affecting electrical connection performance and product reliability, and even causing device failure. During chip-level packaging, the solder joints between substrates undergo multiple high and low temperature cycle loadings, resulting in cracks and desoldering due to substrate warpage. At the same time, substrate warpage often causes flip chip and ball grid array (BGA) assembly failures, especially when large-size substrate BGAs are installed and cannot be assembled correctly. Therefore, measurement and control of substrate warpage deformation 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 the grating moiré fringes is commonly used in the industry, which uses the interference between the grating and the shadow grating generated by the reflection of the grating projected onto the sample. The off-plane deformation of the substrate warpage in the test package is used to obtain the image signal using the CCD, and the deformation of the morphology is obtained through the algorithm. After the substrate is heated and warped, the warpage in the center area is usually smaller than that in the edge area. Therefore, the detection signal of the surface height is generally a nonlinear signal. In order to calculate accurately, the center area, that is, the area with small warpage, will be used for linear correction. The measurement accuracy requirement of the center area is higher than that of the edge area.

[0004] The model and method of linear correction directly determine the measurement accuracy of the substrate surface height. At present, the polynomial model is commonly used for linear correction. The calibration of the polynomial coefficients generally adopts a polynomial fitting method based on the least squares method. This method assigns equal weights to the entire measurement range of the substrate height, and is not linked to the actual measurement conditions. There is a problem of lack of matching of the calibration method. When the calibration accuracy of the edge area meets the requirements, the calibration accuracy of the central area does not meet the requirements. When the calibration accuracy of the central area meets the requirements, the calibration accuracy of the edge area exceeds the requirements. Therefore, the problem of mismatched accuracy caused by the lack of segmented processing in the substrate warpage height measurement calibration method in the prior art needs to be solved urgently. Summary of the invention

[0005] The object of the present invention is to provide an online calibration method and device for measuring the warpage height of a substrate, aiming to solve the above-mentioned problems in the prior art.

[0006] The present invention provides an online calibration method for measuring the warpage height of a substrate, comprising:

[0007] A linearized calibration model is established through a polynomial model with a nonlinear transcendental function correction term;

[0008] The substrate height signal and the reference height signal are synchronously collected by vertical scanning to obtain a substrate height signal vector and a reference height signal vector;

[0009] Performing zero point correction on the substrate height signal vector and the reference height signal vector so that the zero points of the substrate height signal and the reference height signal remain consistent;

[0010] After completing a predetermined number of vertical scans, the obtained data are fused, and a weighted least squares fitting method is used to fit the fused data to obtain the parameters of the linear calibration model, and the parameters are introduced into the linear calibration model to obtain the corrected linear height of the substrate.

[0011] The present invention provides an online calibration device for measuring the warpage height of a substrate, comprising:

[0012] A building module for building a linearized calibration model through a polynomial model with a nonlinear transcendental function correction term;

[0013] An acquisition module is used to synchronously acquire the substrate height signal and the reference height signal through vertical scanning to obtain a substrate height signal vector and a reference height signal vector;

[0014] A correction module, used for performing zero point correction on the substrate height signal vector and the reference height signal vector, so that the zero points of the substrate height signal and the reference height signal remain consistent;

[0015] The processing module is used to fuse the obtained data after completing a predetermined number of vertical scans, and adopt a weighted least squares fitting method to fit the fused data to obtain the parameters of the linear calibration model, and bring the parameters into the linear calibration model to obtain the corrected linear height of the substrate.

[0016] An embodiment of the present invention also provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is executed by the processor, the steps of the online calibration method for measuring the warping height of the substrate are implemented.

[0017] An embodiment of the present invention further provides a computer-readable storage medium, on which a program for implementing information transmission is stored. When the program is executed by a processor, the steps of the online calibration method for measuring the warpage height of the substrate are implemented.

[0018] According to the embodiment of the present invention, the support vector regression method is used to calibrate the nonlinear characteristics of the original height of the substrate. The support vector regression machine uses a nonlinear mapping method to map the sample space to a high-dimensional nonlinear inner product space through a kernel function. Since the support vector acts on the support vector regression machine, the requirement for the number of samples is reduced. At the same time, in practical applications, good calibration effects can be obtained by selecting different kernel functions, adjusting penalty coefficients, and other methods. The substrate warpage height detection signal can be linearized and calibrated. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] 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 labor.

[0020] Figure 1 is a flow chart of an online calibration method for measuring substrate warpage height according to an embodiment of the present invention;

[0021] Figure 2 is a schematic diagram of a substrate height signal according to an embodiment of the present invention;

[0022] Figure 3 is a schematic diagram of an uncalibrated substrate height during multiple scans according to an embodiment of the present invention;

[0023] Figure 4 is a partial enlarged schematic diagram of multiple scans without calibrating the height of a substrate according to an embodiment of the present invention;

[0024] Figure 5 is a schematic diagram of substrate height after multiple scanning calibration according to an embodiment of the present invention;

[0025] Figure 6 is a partially enlarged schematic diagram of the height of the substrate after multiple scanning calibration according to an embodiment of the present invention;

[0026] Figure 7 is a schematic diagram comparing substrate height signals before and after calibration according to an embodiment of the present invention;

[0027] Figure 8 is a schematic diagram of linearity after calibration in the linear region of an embodiment of the present invention;

[0028] Fig. 9 3 is a schematic diagram comparing substrate height signals before and after calibration according to the support vector regression method of an embodiment of the present invention;

[0029] Fig.10is a schematic diagram of the linearity after calibration of the support vector regression machine method in the linear region of an embodiment of the present invention;

[0030] Fig.11 is a schematic diagram of an online calibration device for measuring substrate warpage height according to an embodiment of the present invention;

[0031] Fig.12 is a schematic diagram of an electronic device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0032] 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 them. 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 this document.

[0033] Method Embodiment

[0034] According to an embodiment of the present invention, an online calibration method for measuring the warpage height of a substrate is provided. Figure 1 is a flow chart of an online calibration method for measuring substrate warpage height according to an embodiment of the present invention. Figure 1 As shown, the online calibration method for measuring the warpage height of a substrate according to an embodiment of the present invention specifically includes:

[0035] Step S101, establishing a linearized calibration model through a polynomial model with a nonlinear transcendental function correction term; specifically comprising:

[0036] The linearized calibration model is established according to Formula 1 and Formula 2:

[0037]

[0038] F(h raw )=a×sin(b×h raw +c) Formula 2;

[0039] Among them, h lin is the linear height after calibration, h raw Uncalibrated height signal, p j are the polynomial coefficients to be estimated, j = 0, 1, ..., O, O is the order of the polynomial. F(·) is the transcendental function correction term, where F(·) is described in the form of sine and cosine functions, a, b and c are the parameters to be estimated and are obtained by online calibration.

[0040] Step S102, synchronously collecting the substrate height signal and the reference height signal by vertical scanning to obtain a substrate height signal vector and a reference height signal vector; specifically includes:

[0041] The substrate is mounted on a translation stage with a vertical motion function through a suction cup, and a large-scale vertical scanning motion is performed through the translation stage. The zero point of the substrate height measurement system is determined by finding the position where the substrate height signal is closest to zero; based on a preset number of scans, a vertical scanning motion relative to the zero point of the substrate height measurement system is performed through the translation stage, and during the vertical scanning process, the substrate height signal and the reference height signal are synchronously acquired through a high-speed acquisition module, wherein the reference height signal is provided by the vertical position feedback of the translation stage or other additional vertical height measurement signals;

[0042] Assume that the measurement range of the substrate height measurement system is L0 and the vertical scanning margin is L re , each scan time is T0, the synchronous sampling frequency is F s , then the substrate height signal vector obtained by each scan is and the reference height signal vector As shown in Formula 3 and Formula 4:

[0043]

[0044] Where k represents the number of scans, N = T0 × F s .

[0045] Step S103, performing zero point correction on the substrate height signal vector and the reference height signal vector to make the zero points of the substrate height signal and the reference height signal consistent; specifically comprising:

[0046] because is obtained by vertical scanning motion through its zero point, traversing Find a value close to zero Where m represents the index of the value. Find the corresponding index Will Subtract all elements of Perform zero point correction, then the corrected Every element of satisfies Formula 5:

[0047]

[0048] Among them, i=1,2,…,N.

[0049] Step S104, after completing a predetermined number of vertical scans, the obtained data is fused, and a weighted least squares fitting method is used to fit the fused data to obtain the parameters of the linear calibration model, and the parameters are introduced into the linear calibration model to obtain the corrected linear height of the substrate. Specifically including:

[0050] After completing all the set K vertical scanning movements, the obtained data are fused according to Formula 6 and Formula 7:

[0051]

[0052]

[0053] According to H RRF Calculate the weight vector W, as shown in Formula 8 and Formula 9:

[0054]

[0055]

[0056] Calculate each element of the weight vector W based on formula 10:

[0057]

[0058] Where, 0≤λ≤1, h0 is the boundary value of the linear range, h1 is the boundary value of the correction range, K represents the number of scans, i=1,2,…,N;

[0059] The weighted least squares fitting method is used, using H RAW , H REF The parameters of the above formula are fitted by W, and the objective function of the fitting is to minimize formula 11:

[0060]

[0061] The fitted parameters are brought into the linear calibration model, and the corrected linear height of the substrate is obtained through the linear calibration model.

[0062] Preferably, in the implementation of the present invention, a support vector regression method can also be used to correct nonlinear errors and select different kernel functions κ(·,·). The different kernel functions κ(·,·) specifically include: linear kernel κ(h raw,i ,h raw,j ), polynomial kernel κ(h raw,i ,h raw,j ) and radial basis kernel κ(h raw,i ,h raw,j ), the expressions are shown in formulas 12, 13, and 14:

[0063] κ(h raw,i ,h raw,j )=h raw,i T h raw,j Formula 12;

[0064] κ(h raw,i ,h raw,j )=(γh raw,i T h raw,j +r) d Formula 13;

[0065] κ(h raw,i ,h raw,j )=exp(-γ||h raw,i -h raw,j || 2 ) Formula 14;

[0066] Among them, γ, r and d are adjustable parameters, h raw,i and h raw,j is the substrate height signal feature vector;

[0067] By introducing the penalty coefficient C and the ε-insensitive loss function, the solution of the support vector regression machine is transformed into the solution of Formula 15 and Formula 16:

[0068]

[0069]

[0070] Among them, C is the penalty coefficient, ε>0 means h lin and h ref,train An insensitive parameter to the degree of deviation allowed between

[0071] The solution of the support vector regression machine is obtained by using the Lagrange multiplier method and the SMO algorithm, as shown in Formula 17 and Formula 18:

[0072]

[0073]

[0074] in, is the Lagrange multiplier, C is the penalty coefficient, κ(·,·) is the kernel function, and ε>0 indicates h lin and h ref The insensitive parameters of the allowed deviation, α and At most one of them is non-zero, here we choose α∈(0,C), h raw,i and h raw,j is the feature vector of the silicon wafer height signal training set, hraw is the characteristic vector of the silicon wafer height signal of the test set or the linear height to be calculated. The insensitive parameter ε is determined by the calibration accuracy. A fixed positive constant is used during the training process. The penalty coefficient is selected through multiple tests to compromise between training error and generalization ability.

[0075] The parameters obtained above are brought into the linear calibration model to obtain the corrected linear height of the substrate.

[0076] Finally, the accuracy of the linear calibration is evaluated by fitting residuals and a general method of linearity.

[0077] The above technical solution of the embodiment of the present invention is described in detail below in conjunction with the accompanying drawings.

[0078] The embodiment of the present invention provides an online calibration method for substrate height measurement, which can perform linear calibration processing on the substrate warpage height detection signal. In order to achieve the above purpose, the implementation steps adopted by the present invention are:

[0079] The original height signal obtained by the substrate height measurement device based on the shadow moiré method usually presents a sinusoidal change pattern as the actual height changes, such as Figure 2 shown.

[0080] Select the middle period with the strongest height signal and intercept a monotonically changing interval near the zero point as the measurement range of the substrate height measurement system, such as Figure 2 The uncalibrated height signal in this interval has certain nonlinear characteristics and needs to be calibrated linearly to obtain the actual linear height signal of the substrate.

[0081] The linearized calibration model uses a polynomial model with a nonlinear transcendental function correction term. The general expression of the model is:

[0082]

[0083] Among them, h lin is the linear height after calibration, h raw Uncalibrated height signal. p j are the polynomial coefficients to be estimated, j = 0, 1, ..., O, O is the order of the polynomial. F(·) is the transcendental function correction term.

[0084] Combined with the characteristics of substrate height measurement, F(·) is generally described in the form of sine and cosine functions, which can be composed of linear combinations of sine and cosine expressions of different multiples, or different orders. Without loss of generality, the most basic expression of F(·) is:

[0085] F(h raw )=a×sin(b×h raw+c)

[0086] Among them, a, b and c are the parameters to be estimated.

[0087] Each parameter to be estimated in the above correction model is obtained through an online calibration method.

[0088] The implementation method of online calibration is to mount the substrate on a translation stage with vertical movement function through a suction cup. The translation stage performs a large-scale vertical scanning movement, and determines the zero point of the substrate height measurement system by finding the position where the substrate height signal is closest to zero.

[0089] The translation stage performs vertical scanning motion relative to the zero point of the substrate height measurement system. The scanning range is determined by the measurement range of the substrate height measurement system, while adding a certain margin. The scanning speed is determined by the scanning time. In order to reduce drift caused by temperature changes, the scanning time of each scan should be as short as possible.

[0090] During the vertical scanning process, the substrate height signal and the reference height signal are synchronously acquired by the high-speed acquisition module. The reference height signal can be provided by the vertical position feedback of the translation stage, or other additional vertical height measurement signals.

[0091] The number of vertical scans can be set in advance. Generally, as the number of scans increases, the numerical fitting accuracy will increase accordingly. When the fitting accuracy meets the preset threshold, the number of vertical scans can be determined.

[0092] like Figure 3 and Figure 4 As shown in FIG. 1 , the substrate height signal obtained by vertical scanning presents a sawtooth shape, and the height signal of each independent scan presents certain nonlinear characteristics.

[0093] Assume that the measurement range of the substrate height measurement system is L0 and the vertical scanning margin is L re , each scan time is T0, the synchronous sampling frequency is F s , then the substrate height signal vector and reference height signal vector obtained in each scan are:

[0094]

[0095] Where k represents the number of scans, N = T0 × F s .

[0096] pass right Zero point correction is performed so that the zero points of the substrate height signal and the reference height signal can be kept consistent. In this way, when performing vertical scanning, the measurement range of the substrate height measurement system can always be measured.

[0097] because is obtained by vertical scanning motion through its zero point, traversing You can always find a value close to zero. Where m represents the index of the value. Find the corresponding index Will Subtract all elements of Perform zero point correction, then the corrected Every element of

[0098]

[0099] Where i=1,2,…,N.

[0100] After completing all the set K vertical scanning movements, the obtained data are fused.

[0101]

[0102] The original height and reference height signals after data fusion have the same data length and both contain data samples from all vertical scans.

[0103] According to H REF Calculate the weight vector W, the expression is:

[0104]

[0105] The calculation method of each element of the weight vector W is as follows:

[0106]

[0107] Where, 0≤λ,≤1, h0 is the boundary value of the linear range, h1 is the boundary value of the correction range, k represents the number of scans, and i=1,2,…,N.

[0108] λ is an adjustable parameter and can be adjusted according to actual conditions. The adjustment principle is to make λ as small as possible while ensuring that the substrate height signal in the correction range meets the functional requirements, so as to improve the calibration accuracy of the linear range.

[0109] Without loss of generality, the following modified model is adopted, which adds a sine transcendental function on the basis of the polynomial function.

[0110]

[0111] Among them, h lin is the corrected linear height, h raw Height signal before calibration. jare the coefficients of the polynomial to be estimated, j = 0, 1, ..., O, O is the order of the polynomial. a, b and c are the parameters to be estimated of the correction term of the transcendental function.

[0112] The weighted least squares fitting method is used, using H RAW , H REF And W fit the parameters of the above formula

[0113] The objective function of the fitting is to minimize the following equation.

[0114]

[0115] Substituting the fitted parameters into the above correction model, the corrected linear height of the substrate can be obtained, such as Figure 5 and Figure 6 shown.

[0116] Figure 7 The figure is a schematic diagram of the substrate height comparison before and after linear calibration. It can be clearly seen that the substrate height signal after calibration has a height dimension and shows a linear relationship within the measurement range. The linearity relationship after calibration is as follows: Figure 8 shown.

[0117] The original height and reference height of the substrate obtained above are used to construct a training data set, and the parameters to be estimated of the calibration model are determined using a support vector regression machine method.

[0118] Different kernel functions κ(·,·) can be selected, such as linear kernel, polynomial kernel and radial basis kernel, and the expression is as follows:

[0119] κ(h raw,i ,h raw,j )=h raw,i T h raw,j

[0120] κ(h raw,i ,h raw,j )=(γh raw,i T h raw,j +r) d

[0121] κ(h raw,i ,h raw,j )=exp(-γ‖h raw,i -h raw,j ‖ 2 )

[0122] Among them, γ, r and d are adjustable parameters, h raw,i and h raw,j is the characteristic vector of silicon wafer height signal.

[0123] The choice of kernel function determines the mapping relationship of the silicon wafer height signal to the high-dimensional space. Combined with the relative relationship between the uncalibrated silicon wafer height signal and the reference height signal, a linear kernel or a radial basis kernel can be typically selected.

[0124] Solving the parameters to be estimated of the calibration model is a process of solving a convex quadratic programming problem, and currently mature optimization methods such as the Lagrange multiplier method and the sequential minimum optimization algorithm (SMO algorithm) can be used.

[0125] In order to improve the generalization ability, the penalty coefficient C and ε-insensitive loss function are introduced. At this time, the solution of the support vector regression machine is transformed into the solution of the following formula

[0126]

[0127] Among them, C>0 is the penalty coefficient, ε>0 means h lin and h ref An insensitive parameter to the degree of allowed deviation.

[0128] Through the Lagrange multiplier method and SMO algorithm, the solution of the support vector regression machine can be obtained, as shown in the following formula

[0129]

[0130] in, is the Lagrange multiplier, C is the penalty coefficient, κ(·,·) is the kernel function, and ε>0 indicates h lin and h ref An insensitive parameter to the allowed deviation. α and At most one of them is non-zero, here we choose α∈(0,C). raw,i and h raw,j is the feature vector of the silicon wafer height signal training set, h raw It is the feature vector of the test set or the silicon wafer height signal whose linear height is to be calculated.

[0131] The insensitive parameter ε is determined by the calibration accuracy. For the silicon wafer height measurement device, the accuracy index is generally used as an input parameter condition of the calibration method. A fixed positive constant is used for the above solution process.

[0132] The penalty coefficient C needs to be selected through multiple tests to strike a balance between training error and generalization ability. If the value is too large, it can improve the calibration accuracy, but it is easy to cause overfitting and reduce the generalization ability; on the contrary, if the value is too small, it is easy to cause the calibration accuracy to fail to meet the standard.

[0133] The substrate height signals before and after calibration are as follows: Fig. 9It can be clearly seen that the calibration model based on the support vector regression machine not only determines the proportional relationship between the uncalibrated silicon wafer height signal and the actual height, but also corrects the nonlinear characteristics in the uncalibrated signal.

[0134] By using a silicon wafer height detection device and the same vertical scanning method, test set data can be obtained to verify the above calibration model.

[0135] The accuracy of the calibration model can be evaluated by fitting residuals and general linearity methods. Fig.10 As shown, the calibrated silicon wafer height signal has a height dimension and is linearly related to the actual height position.

[0136] The support vector regression machine can obtain better fitting effect and has better correction effect on the nonlinear error of the gain coefficient.

[0137] The data analysis process of the support vector regression machine described above can be performed offline.

[0138] In summary, the technical solution of the embodiment of the present invention first performs segmented processing on the uncorrected height signal, and different weighting coefficients are used in different areas, which fully takes into account the different physical functions of different areas within the measurement signal range. Then, a nonlinear transcendental function correction term is added to the polynomial linearization model to characterize the physical principle characteristics of the uncorrected height signal. Furthermore, the support vector regression method is used for calibration in view of the nonlinear characteristics of the original height of the substrate. The support vector regression machine uses a nonlinear mapping method to map the sample space to a high-dimensional nonlinear inner product space through a kernel function. Since the support vector acts on the support vector regression machine, the requirement for the number of samples is reduced. At the same time, in practical applications, good calibration effects can be obtained by selecting different kernel functions, adjusting penalty coefficients, and other methods.

[0139] Device Example 1

[0140] According to an embodiment of the present invention, an online calibration device for measuring the warpage height of a substrate is provided. Fig.11 Schematic diagram of an online calibration device for measuring substrate warpage height according to an embodiment of the present invention. Fig.11 As shown, the online calibration device for measuring the warpage height of a substrate according to an embodiment of the present invention specifically includes:

[0141] Establishing module 110, for establishing a linearized calibration model through a polynomial model with a nonlinear transcendental function correction term;

[0142] An acquisition module 112 is used to synchronously acquire the substrate height signal and the reference height signal by vertical scanning to obtain a substrate height signal vector and a reference height signal vector;

[0143] A correction module 114 is used to perform zero point correction on the substrate height signal vector and the reference height signal vector so that the zero points of the substrate height signal and the reference height signal are consistent;

[0144] The processing module 116 is used to fuse the obtained data after completing a predetermined number of vertical scans, and adopt a weighted least squares fitting method to fit the fused data to obtain the parameters of the linear calibration model, and then bring the parameters into the linear calibration model to obtain the corrected linear height of the substrate.

[0145] The embodiment of the present invention is a device embodiment corresponding to the above method embodiment. The specific operations of each module can be understood by referring to the description of the method embodiment, which will not be repeated here.

[0146] Device Example 2

[0147] An embodiment of the present invention provides an electronic device, such as Fig.12 As shown, it includes: a memory 120, a processor 122, and a computer program stored in the memory 120 and executable on the processor 122, and when the computer program is executed by the processor 122, the steps described in the method embodiment are implemented.

[0148] Device Example 3

[0149] An embodiment of the present invention provides a computer-readable storage medium, on which a program for implementing information transmission is stored. When the program is executed by the processor 122, the steps described in the method embodiment are implemented.

[0150] The computer-readable storage medium in this embodiment includes, but is not limited to, ROM, RAM, magnetic disk or optical disk, etc.

[0151] 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 aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements 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.

Claims

1. An online calibration method for measuring substrate warpage height, characterized in that: include: A linearized calibration model is established through a polynomial model with a nonlinear transcendental function correction term; The substrate height signal and the reference height signal are synchronously collected by vertical scanning to obtain a substrate height signal vector and a reference height signal vector; Performing zero point correction on the substrate height signal vector and the reference height signal vector so that the zero points of the substrate height signal and the reference height signal remain consistent; After completing a predetermined number of vertical scans, the obtained data are fused, and a weighted least squares fitting method is used to fit the fused data to obtain the parameters of the linear calibration model, and the parameters are introduced into the linear calibration model to obtain the corrected linear height of the substrate.

2. The method according to claim 1, characterized in that The linearized calibration model is established through a polynomial model with a nonlinear transcendental function correction term, specifically including: The linearized calibration model is established according to Formula 1 and Formula 2: F(h raw )=a×sin(b×h raw +c) Formula 2; Among them, h lin is the linear height after calibration, h raw Uncalibrated height signal, p j are the polynomial coefficients to be estimated, j = 0, 1, ..., O, O is the order of the polynomial. F(·) is the transcendental function correction term, where F(·) is described in the form of sine and cosine functions, a, b and c are the parameters to be estimated and are obtained by online calibration.

3. The method according to claim 2, characterized in that The substrate height signal and the reference height signal are synchronously collected by vertical scanning to obtain the substrate height signal vector and the reference height signal vector, which specifically include: The substrate is mounted on a translation stage with a vertical motion function through a suction cup, and a large-scale vertical scanning motion is performed through the translation stage. The zero point of the substrate height measurement system is determined by finding the position where the substrate height signal is closest to zero; based on a preset number of scans, a vertical scanning motion relative to the zero point of the substrate height measurement system is performed through the translation stage, and during the vertical scanning process, the substrate height signal and the reference height signal are synchronously acquired through a high-speed acquisition module, wherein the reference height signal is provided by the vertical position feedback of the translation stage or other additional vertical height measurement signals; Assume that the measurement range of the substrate height measurement system is L0 and the vertical scanning margin is L re , each scan time is T0, the synchronous sampling frequency is F s , then the substrate height signal vector obtained by each scan is and the reference height signal vector As shown in Formula 3 and Formula 4: Where k represents the number of scans, N = T0 × F s .

4. The method according to claim 3, characterized in that The zero point correction of the substrate height signal vector and the reference height signal vector is performed to make the zero points of the substrate height signal and the reference height signal consistent, specifically including: because is obtained by vertical scanning motion through its zero point, traversing Find a value close to zero Where m represents the index of the value. Find the corresponding index Will Subtract all elements of Perform zero point correction, then the corrected Every element of satisfies Formula 5: Among them, i=1,2,…,N.

5. The method according to claim 4, characterized in that After completing the predetermined number of vertical scans, the obtained data are fused, and the weighted least squares fitting method is used to fit the fused data to obtain the parameters of the linear calibration model, and the parameters are brought into the linear calibration model to obtain the corrected linear height of the substrate, which specifically includes: After completing all the set K vertical scanning movements, the obtained data are fused according to Formula 6 and Formula 7: According to H REF Calculate the weight vector W, as shown in Formula 8 and Formula 9: Calculate each element of the weight vector W based on formula 10: Where, 0≤λ≤1, h0 is the boundary value of the linear range, h1 is the boundary value of the correction range, K represents the number of scans, i=1,2,…,N; The weighted least squares fitting method is used, using H RAW , H REF The parameters of the above formula are fitted by W, and the objective function of the fitting is to minimize formula 11: The fitted parameters are brought into the linear calibration model, and the corrected linear height of the substrate is obtained through the linear calibration model.

6. The method according to claim 5, characterized in that The method further comprises: The support vector regression method is used to correct the nonlinear error and select different kernel functions κ(·,·). The different kernel functions κ(·,·) specifically include: linear kernel κ(h raw,i ,h raw,j ), polynomial kernel κ(h raw,i ,h raw,j ) and radial basis kernel κ(h raw,i ,h raw,j ), the expressions are shown in formulas 12, 13, and 14: κ(h raw,i ,h raw,j ) = h raw,i T h raw,j Formula 12; κ(h raw,i ,h raw,j ) = (γh raw,i T h raw,j + r) d Formula 13; κ(h raw,i ,h raw,j )=exp(-γ||h raw,i -h raw,j || 2 ) Formula 14; Among them, γ, r and d are adjustable parameters, h raW,i and h raw,j is the substrate height signal feature vector; By introducing the penalty coefficient C and the ε-insensitive loss function, the solution of the support vector regression machine is transformed into the solution of Formula 15 and Formula 16: Among them, C is the penalty coefficient, ε>0 means h lin and h ref,train An insensitive parameter to the degree of deviation allowed between The solution of the support vector regression machine is obtained by using the Lagrange multiplier method and the SMO algorithm, as shown in Formula 17 and Formula 18: in, is the Lagrange multiplier, C is the penalty coefficient, κ(·,·) is the kernel function, and ε>0 indicates h lin and h ref The insensitive parameters of the allowed deviation, α and At most one of them is non-zero, here we choose α∈(0,C), h raw,i and h raw,j is the feature vector of the silicon wafer height signal training set, h raw is the characteristic vector of the silicon wafer height signal of the test set or the linear height to be calculated. The insensitive parameter ε is determined by the calibration accuracy. A fixed positive constant is used during the training process. The penalty coefficient is selected through multiple tests to compromise between training error and generalization ability. The parameters obtained above are brought into the linear calibration model to obtain the corrected linear height of the substrate.

7. The method according to claim 6 or 5, characterized in that: The method further comprises: The accuracy of the linear calibration was assessed by fitting residuals, using the general method of linearity.

8. An online calibration device for measuring substrate warpage height, characterized in that: include: A building module for building a linearized calibration model through a polynomial model with a nonlinear transcendental function correction term; An acquisition module is used to synchronously acquire the substrate height signal and the reference height signal through vertical scanning to obtain a substrate height signal vector and a reference height signal vector; A correction module, used for performing zero point correction on the substrate height signal vector and the reference height signal vector, so that the zero points of the substrate height signal and the reference height signal remain consistent; The processing module is used to fuse the obtained data after completing a predetermined number of vertical scans, and adopt a weighted least squares fitting method to fit the fused data to obtain the parameters of the linear calibration model, and bring the parameters into the linear calibration model to obtain the corrected linear height of the substrate.

9. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is executed by the processor, the steps of the on-line calibration method for measuring the warpage height of a substrate according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores an implementation program for information transmission, and when the program is executed by a processor, the steps of the online calibration method for measuring the warpage height of a substrate according to any one of claims 1 to 7 are implemented.

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