On-line calibration method and apparatus for substrate bow height measurements

Abstract

The embodiment of the present specification provides an online calibration method and device for substrate warping height measurement, wherein the method comprises: establishing a linearization calibration model through a polynomial model with a nonlinear transcendental function correction term; synchronously collecting substrate height signals and reference height signals through vertical scanning to obtain substrate height signal vectors and reference height signal vectors; performing zero point correction on the substrate height signal vectors and the reference height signal vectors to keep the zero points of the substrate height signals and the reference height signals consistent; after completing a predetermined number of vertical scans, fusing the obtained data, and adopting a weighted least square fitting method, fitting the parameters of the linearization calibration model through the fused data, and bringing the parameters into the linearization calibration model to obtain corrected substrate linear height. The embodiment of the present specification can perform linearization calibration processing on substrate warping height detection signals.

Description

[0001] Online calibration method and apparatus for measuring substrate warpage height Technical Field

[0002] This document relates to the fields of semiconductor manufacturing and testing technology, and in particular to an online calibration method and apparatus for measuring substrate warpage height. Background Technology

[0003] Substrate warpage is a macroscopic manifestation of interfacial stress and deformation. It not only causes manufacturing difficulties such as incorrect assembly but also leads to 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, solder joints between substrates may crack and detach due to substrate warpage after repeated high and low temperature cycles. Furthermore, substrate warpage often causes substandard assembly of flip chips and ball grid array (BGA) packages, especially preventing correct assembly of large-size substrate BGAs. Therefore, the measurement and control of substrate warpage deformation is crucial.

[0004] Essentially, measuring the warpage of a packaged substrate falls under the category of three-dimensional topography measurement. Currently, the industry commonly uses the shadow moiré method based on grating moiré fringes, which utilizes the interference between a grating and the shadow grating generated by the reflection of the grating onto the sample. The method tests the out-of-plane deformation of the substrate warpage in the package, using a CCD to acquire image signals and algorithms to obtain the amount of topographic deformation. After the substrate warps due to heat, the warpage in the central region is usually less than that in the edge regions; therefore, the surface height detection signal is generally a non-linear signal. To ensure accuracy, linearization correction is performed using the central region, i.e., the area with the least warpage. The measurement accuracy requirements for the central region are higher than those for the edge regions.

[0005] The linearization correction model and method directly determine the measurement accuracy of the substrate surface height. Currently, linearization correction commonly uses polynomial models. The calibration of polynomial coefficients generally employs a polynomial fitting method based on least squares. This method assigns equal weight to the entire measurement range of the substrate height, failing to consider actual measurement conditions and resulting in a lack of calibration method matching. When the calibration accuracy in the edge region meets the requirements, the calibration accuracy in the center region does not; conversely, when the calibration accuracy in the center region meets the requirements, the calibration accuracy in the edge region over-metres. Therefore, the problem of accuracy mismatch caused by the lack of segmented processing in existing substrate warpage height measurement calibration methods urgently needs to be addressed. Summary of the Invention

[0006] The purpose of this invention is to provide an online calibration method and apparatus for measuring substrate warpage height, aiming to solve the above-mentioned problems in the prior art.

[0007] This invention provides an online calibration method for measuring substrate warpage height, comprising:

[0008] A linearized calibration model is established using a polynomial model with a nonlinear transcendental function correction term.

[0009] The substrate height signal and the reference height signal are acquired synchronously by vertical scanning to obtain the substrate height signal vector and the reference height signal vector.

[0010] Zero-point correction is performed on the substrate height signal vector and the reference height signal vector to ensure that the zero points of the substrate height signal and the reference height signal are consistent.

[0011] 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 linearized calibration model. The parameters are then substituted into the linearized calibration model to obtain the corrected linear height of the substrate.

[0012] This invention provides an online calibration device for measuring substrate warpage height, comprising:

[0013] A module is established to build a linearized calibration model from a polynomial model with a nonlinear transcendental function correction term;

[0014] The acquisition module is used to simultaneously acquire the substrate height signal and the reference height signal through vertical scanning, and obtain the substrate height signal vector and the reference height signal vector.

[0015] The correction module is used to perform zero-point correction on the substrate height signal vector and the reference height signal vector to keep the zero points of the substrate height signal and the reference height signal consistent.

[0016] The processing module is used to fuse the obtained data after completing a predetermined number of vertical scans, and use a weighted least squares fitting method to fit the fused data to obtain the parameters of the linearized calibration model. The parameters are then substituted into the linearized calibration model to obtain the corrected linear height of the substrate.

[0017] This invention also provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the above-described online calibration method for measuring substrate warp height.

[0018] This invention also provides a computer-readable storage medium storing an information transmission implementation program, which, when executed by a processor, implements the steps of the above-described online calibration method for measuring substrate warp height.

[0019] In this embodiment of the invention, a Support Vector Regression (SVR) method is used for calibration to address the nonlinear characteristics of the original height of the substrate. The SVR employs a nonlinear mapping method, mapping the sample space to a high-dimensional nonlinear inner product space through a kernel function. Since the SVR operates on support vectors, the required number of samples is reduced. Furthermore, in practical applications, good calibration results can be obtained by selecting different kernel functions and adjusting penalty coefficients. This allows for linearization calibration of the substrate warpage height detection signal. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart of an online calibration method for measuring substrate warpage height according to an embodiment of the present invention;

[0022] Figure 2 This is a schematic diagram of the substrate height signal according to an embodiment of the present invention;

[0023] Figure 3 This is a schematic diagram of the height of the uncalibrated substrate after multiple scans according to an embodiment of the present invention;

[0024] Figure 4 This is a partially enlarged schematic diagram of the height of the uncalibrated substrate during multiple scans, according to an embodiment of the present invention.

[0025] Figure 5 This is a schematic diagram of the substrate height after multiple scans and calibrations according to an embodiment of the present invention;

[0026] Figure 6 This is a partially enlarged schematic diagram of the substrate height after multiple scans and calibrations according to an embodiment of the present invention;

[0027] Figure 7 This is a schematic diagram comparing the substrate height signal before and after calibration according to an embodiment of the present invention;

[0028] Figure 8 This is a schematic diagram of the linearity after calibration within the linear region according to an embodiment of the present invention;

[0029] Figure 9 This is a schematic diagram comparing the substrate height signal before and after calibration in the support vector regression machine method of this invention.

[0030] Figure 10This is a schematic diagram of the calibrated linearity of the support vector regression machine method within the linear region according to an embodiment of the present invention;

[0031] Figure 11 This is a schematic diagram of an online calibration device for measuring substrate warpage height according to an embodiment of the present invention;

[0032] Figure 12 This is a schematic diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0033] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.

[0034] Method Implementation Examples

[0035] According to embodiments of the present invention, an online calibration method for measuring substrate warpage height is provided. Figure 1 This is a flowchart of an online calibration method for measuring substrate warpage height according to an embodiment of the present invention, as shown below. Figure 1 As shown, the online calibration method for measuring substrate warpage height according to an embodiment of the present invention specifically includes:

[0036] Step S101 involves establishing a linearized calibration model using a polynomial model with a nonlinear transcendental function correction term; specifically, this includes:

[0037] A linearized calibration model is established based on Equations 1 and 2:

[0038] Formula 1;

[0039] Formula 2;

[0040] in, For the calibrated linear height, Uncalibrated altitude signal The coefficients of the polynomial to be estimated are: , Let be the order of the polynomial. For the transcendental function correction term, F(∙) is described in the form of sine and cosine functions, and a, b, and c are parameters to be estimated and obtained through online calibration.

[0041] Step S102 involves synchronously acquiring the substrate height signal and the reference height signal through vertical scanning to obtain the substrate height signal vector and the reference height signal vector; specifically including:

[0042] The substrate is mounted on a displacement stage with vertical motion function using a suction cup. The displacement stage performs a large-range vertical scanning motion. By finding the position where the substrate height signal is closest to zero, the zero point of the substrate height measurement system is determined. Based on a preset number of scans, the displacement stage performs a vertical scanning motion relative to the zero point of the substrate height measurement system. During the vertical scanning process, a high-speed acquisition module synchronously acquires the substrate height signal and the reference height signal. The reference height signal is provided by the vertical position feedback of the displacement stage or by other additional vertical height measurement signals.

[0043] Assume the measurement range of the substrate height measurement system is The margin for vertical scanning is The time for each scan is The synchronous sampling frequency is The substrate height signal vector obtained in each scan and reference height signal vector As shown in formulas 3 and 4:

[0044] Formula 3;

[0045] Formula 4;

[0046] in, Indicates the number of scans. .

[0047] Step S103 involves zero-point correction of the substrate height signal vector and the reference height signal vector to ensure that the zero points of the substrate height signal and the reference height signal are consistent; specifically, this includes:

[0048] because It is obtained through a vertical scan motion passing through its zero point, traversing... Find one close to zero ,in This represents the index of the value, in Find the corresponding index ,Will Subtract all elements Perform zero-point correction, then the corrected Each element satisfies Formula 5:

[0049] Formula 5;

[0050] in, .

[0051] Step S104: 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 linearized calibration model. These parameters are then input into the linearized calibration model to obtain the corrected linear height of the substrate. Specifically, this includes:

[0052] Complete all settings After the second vertical scan, the obtained data are fused according to Formulas 6 and 7:

[0053] Formula 6;

[0054] Formula 7;

[0055] according to Calculate the weight vector The expressions are shown in Formulas 8 and 9:

[0056] Formula 8;

[0057] Formula 9;

[0058] Calculate the weight vector based on Formula 10. Each element:

[0059] Formula 10;

[0060] in, , For the boundary values ​​of the linear range, To correct the range boundary values, Indicates the number of scans. ;

[0061] The weighted least squares fitting method is used, utilizing , and The parameters of the above equation are fitted, and the objective function of the fitting is to minimize Equation 11:

[0062] Formula 11;

[0063] The fitted parameters are then input into the linearized calibration model, and the corrected linear height of the substrate is obtained through the linearized calibration model.

[0064] Preferably, in the implementation of this invention, a support vector regression machine method can also be used to correct nonlinear errors by selecting different kernel functions. The different kernel functions Specifically, this includes: linear kernels polynomial kernel and radial base nucleus The expressions are shown in formulas 12, 13, and 14:

[0065] Formula 12;

[0066] Formula 13;

[0067] Formula 14;

[0068] in, , and It is an adjustable parameter. and The substrate height signal feature vector;

[0069] Introducing penalty coefficient C and - The loss function is insensitive, and the solution for the support vector regression machine is transformed into solving Equations 15 and 16:

[0070] Formula 15;

[0071] Formula 16;

[0072] in, The penalty coefficient is... To indicate and An insensitive parameter relating to the degree of deviation that can be allowed between them;

[0073] The solution to the support vector regression machine is obtained by using the Lagrange multiplier method and the SMO algorithm, as shown in Equations 17 and 18:

[0074] Formula 17;

[0075] Formula 18;

[0076] in, For Lagrange multipliers, The penalty coefficient is... For kernel function, To indicate and The insensitive parameter for the degree of allowable deviation. and At most one of them is not zero, so we choose... , and The feature vector of the silicon wafer height signal training set. For the test set or the feature vector of the silicon height signal whose linear height is to be calculated, the insensitive parameter is... To ensure accuracy, a fixed set of positive constants is used during training. The penalty coefficient is selected through multiple tests, striking a balance between training error and generalization ability.

[0077] Substituting the parameters obtained above into the linearization calibration model yields the corrected linear height of the substrate.

[0078] Finally, the accuracy of the linear calibration is evaluated using a general method of fitting residuals and linearity.

[0079] The technical solutions of the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0080] This invention proposes an online calibration method for substrate height measurement, which can perform linearization calibration on the substrate warpage height detection signal. To achieve the above objective, the implementation steps of this invention are as follows:

[0081] The original height signal obtained by the substrate height measurement device based on the shadow moiré method typically exhibits a sinusoidal variation pattern as the actual height changes, such as... Figure 2 As shown.

[0082] The strongest mid-cycle of the height signal is selected, and a monotonically changing interval near the zero point is extracted as the measurement range of the substrate height measurement system, such as... Figure 2 The rectangular region is shown in the image. The uncalibrated height signal in this region exhibits some non-linear characteristics and requires linear calibration to obtain the actual linear height signal of the substrate.

[0083] The linearized calibration model is a polynomial model with a nonlinear transcendental function correction term. The general expression for this model is:

[0084]

[0085] in, For the calibrated linear height, Uncalibrated altitude signal. The coefficients of the polynomial to be estimated are: , Let be the order of the polynomial. This is a correction term for a transcendental function.

[0086] Combining the characteristics of substrate height measurement, It is generally described in the form of sine and cosine functions, which can be linear combinations of sine and cosine expressions of different harmonics, or composed of different orders. Without loss of generality, The most basic form of expression:

[0087]

[0088] in, , c are the parameters to be estimated.

[0089] The parameters to be estimated in the above modified model are obtained through online calibration.

[0090] The online calibration method involves mounting the substrate on a displacement stage with vertical motion function using a suction cup. The displacement stage performs a large-range vertical scanning motion, and the zero point of the substrate height measurement system is determined by finding the position where the substrate height signal is closest to zero.

[0091] The displacement stage performs a 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 also allowing for a certain margin. The scanning speed is determined by the scanning time; to reduce drift caused by temperature changes, the scanning time for each scan should be as short as possible.

[0092] During the vertical scanning process, the substrate height signal and the reference height signal are acquired synchronously through a high-speed acquisition module. The reference height signal can be provided through the vertical position feedback of the displacement stage, or other additional vertical height measurement signals.

[0093] 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.

[0094] like Figure 3 and Figure 4 As shown, the substrate height signal obtained through vertical scanning exhibits a sawtooth shape. The height signal of each independent scan displays certain nonlinear characteristics.

[0095] Assume the measurement range of the substrate height measurement system is The margin for vertical scanning is The time for each scan is The synchronous sampling frequency is Then, the substrate height signal vector and reference height signal vector obtained in each scan are:

[0096]

[0097]

[0098] in, Indicates the number of scans. .

[0099] pass right Zero-point correction is performed to ensure that the zero points of the substrate height signal and the reference height signal are consistent. This guarantees that the entire measurement range of the substrate height measurement system can be measured during vertical scanning.

[0100] because It is obtained through a vertical scan motion passing through its zero point, traversing... You can always find one that is close to zero. in Indicates the index of this value. Find the corresponding index ,Will Subtract all elements Perform zero-point correction, then the corrected Each element satisfies

[0101]

[0102] in, .

[0103] Complete all settings After the vertical scan motion, the acquired data are fused.

[0104]

[0105]

[0106] The raw height and reference height signals after data fusion have the same data length and both contain data samples from all sub-vertical scans.

[0107] according to Calculate the weight vector The expression is:

[0108]

[0109]

[0110] weight vector The calculation method for each element is as follows:

[0111]

[0112] in, , For the boundary values ​​of the linear range, To correct the range boundary values, Indicates the number of scans. .

[0113] As the parameters are adjustable, they can be adjusted according to actual conditions. The adjustment principle is to ensure that the substrate height signal within the correction range meets functional requirements. To improve the calibration accuracy of the linear range, the value should be as small as possible.

[0114] Without loss of generality, the following modified model is adopted, which adds a sinusoidal transcendental function to the polynomial function.

[0115]

[0116] in, The corrected linear height, The altitude signal before calibration. The polynomial coefficients to be estimated are... , Let be the order of the polynomial. , c and c are the parameters to be estimated for the transcendental function correction term.

[0117] The weighted least squares fitting method is used, utilizing , and Fitting the parameters of the above equation

[0118] The objective function for fitting is to minimize the following expression.

[0119]

[0120] Substituting the fitted parameters into the above correction model yields the corrected linear height of the substrate, such as... Figure 5 and Figure 6 As shown.

[0121] Figure 7 This is a schematic diagram comparing the substrate height before and after linear calibration. It is clear that the calibrated substrate height signal has height dimensions and exhibits a linear relationship within the measurement range. The linearity relationship after calibration is as follows: Figure 8 As shown.

[0122] Using the original height and reference height of the substrate obtained above, a training dataset is constructed, and the parameters to be estimated for the calibration model are determined by using the support vector regression method.

[0123] Different kernel functions can be selected For example, linear kernels, polynomial kernels, and radial basis kernels are expressed as follows:

[0124]

[0125]

[0126]

[0127] in, , and It is an adjustable parameter. and This is the feature vector of the silicon wafer height signal.

[0128] The choice of kernel function determines the mapping relationship between the silicon wafer height signal and the high-dimensional space. Combining the relative relationship between the uncalibrated silicon wafer height signal and the reference height signal, a linear kernel or a radial basis kernel can typically be selected.

[0129] Solving for the parameters to be estimated in the calibration model is a process of solving a convex quadratic programming problem. Mature optimization methods can be used, such as the Lagrange multiplier method and the Sequence Minimum Optimization (SMO) algorithm.

[0130] To improve generalization ability, a penalty coefficient C is introduced. - Insensitive loss function. Solving the support vector regression machine at this point transforms into solving the following equation.

[0131]

[0132]

[0133] in, The penalty coefficient is... To indicate and The insensitive parameter for the degree of deviation that can be allowed.

[0134] The solution to the Support Vector Regression (SVR) problem can be obtained using the Lagrange multiplier method and the SMO algorithm, as shown in the following equation.

[0135]

[0136]

[0137] in, For Lagrange multipliers, The penalty coefficient, For kernel function, To indicate and The insensitive parameter for the degree of deviation that can be allowed. and At most one of them is not zero, so we choose... . and The feature vector of the silicon wafer height signal training set. The feature vector of the silicon height signal for the test set or the linear height to be calculated.

[0138] Insensitive parameters As determined by the calibration accuracy, for silicon wafer height measuring devices, the accuracy index is generally used as the input parameter condition of the calibration method, and fixed positive constants are used for the above solution process.

[0139] Penalty coefficient Multiple tests are needed to find a compromise between training error and generalization ability. If the value is too large, although it can improve calibration accuracy, it can easily lead to overfitting and reduce generalization ability; conversely, if the value is too small, the calibration accuracy may not meet the requirements.

[0140] The substrate height signals before and after calibration are as follows: Figure 9 As shown, it is clear that the calibration model based on support vector regression 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.

[0141] Using a silicon wafer height detection device and the same vertical scanning method, test set data can be obtained to verify the calibration model.

[0142] The accuracy of the calibration model can be evaluated using general methods such as fitting residuals and linearity. For example... Figure 10 As shown, the calibrated silicon wafer height signal has height dimensions and exhibits a linear relationship with the actual height position.

[0143] Support vector regression machines can achieve better fitting results and are more effective at correcting nonlinear errors in the gain coefficient.

[0144] The data analysis process of the support vector regression machine described above can be performed offline.

[0145] In summary, the technical solution of this invention first segments the uncorrected height signal, using different weighting coefficients for different regions to fully consider the different physical functions of different regions within the measurement signal range. Then, a nonlinear transcendental function correction term is added to the polynomial linearization model to characterize the physical properties of the uncorrected height signal. Furthermore, for the nonlinear characteristics of the original substrate height, a support vector regression (SVR) method is used for calibration. SVR employs a nonlinear mapping method, mapping the sample space to a high-dimensional nonlinear inner product space through a kernel function. Since the SVR is powered by support vectors, the requirement for a large number of samples is reduced. Moreover, in practical applications, good calibration results can be obtained by selecting different kernel functions and adjusting penalty coefficients.

[0146] Device Example 1

[0147] According to embodiments of the present invention, an online calibration device for measuring substrate warpage height is provided. Figure 11 This is a schematic diagram of an online calibration device for measuring substrate warp height according to an embodiment of the present invention, as shown below. Figure 11 As shown, the online calibration device for measuring substrate warpage height according to an embodiment of the present invention specifically includes:

[0148] Module 110 is established to build a linearized calibration model from a polynomial model with a nonlinear transcendental function correction term.

[0149] The acquisition module 112 is used to synchronously acquire the substrate height signal and the reference height signal through vertical scanning to obtain the substrate height signal vector and the reference height signal vector.

[0150] The correction module 114 is used to perform zero-point correction on the substrate height signal vector and the reference height signal vector to keep the zero points of the substrate height signal and the reference height signal consistent.

[0151] The processing module 116 is used to fuse the obtained data after completing a predetermined number of vertical scans, and use a weighted least squares fitting method to fit the fused data to obtain the parameters of the linearized calibration model, and then input the parameters into the linearized calibration model to obtain the corrected linear height of the substrate.

[0152] The embodiments of the present invention are device embodiments corresponding to the above method embodiments. The specific operation of each module can be understood with reference to the description of the method embodiments, and will not be repeated here.

[0153] Device Example 2

[0154] This invention provides an electronic device, such as... Figure 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, wherein the computer program, when executed by the processor 122, performs the steps as described in the method embodiment.

[0155] Device Example 3

[0156] This invention provides a computer-readable storage medium storing an information transmission implementation program, which, when executed by a processor 122, implements the steps described in the method embodiment.

[0157] The computer-readable storage media described in this embodiment include, but are not limited to, ROM, RAM, disk, or optical disk.

[0158] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An online calibration method for measuring substrate warpage height, characterized in that, include: A linearized calibration model is established using a polynomial model with a nonlinear transcendental function correction term. The substrate height signal and the reference height signal are acquired synchronously by vertical scanning to obtain the substrate height signal vector and the reference height signal vector. Zero-point correction is performed on the substrate height signal vector and the reference height signal vector to ensure that the zero points of the substrate height signal and the reference height signal are 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 linearized calibration model. The parameters are then substituted into the linearized calibration model to obtain the corrected linear height of the substrate.

2. The method according to claim 1, characterized in that, Establishing a linearized calibration model through a polynomial model with a nonlinear transcendental function correction term specifically includes: A linearized calibration model is established based on Equations 1 and 2: Formula 1: Formula 2: in, For the calibrated linear height, This is an uncalibrated altitude signal. The coefficients of the polynomial to be estimated are: , Let the order be the order of the polynomial. For the transcendental function correction term, F(∙) is described in the form of sine and cosine functions, and a, b, and c are parameters to be estimated and obtained through online calibration.

3. The method according to claim 2, characterized in that, The substrate height signal and reference height signal are simultaneously acquired through vertical scanning, resulting in the substrate height signal vector and reference height signal vector, which specifically include: The substrate is mounted on a displacement stage with vertical motion function using a suction cup. The displacement stage performs a large-range vertical scanning motion. By finding the position where the substrate height signal is closest to zero, the zero point of the substrate height measurement system is determined. Based on a preset number of scans, the displacement stage performs a vertical scanning motion relative to the zero point of the substrate height measurement system. During the vertical scanning process, a high-speed acquisition module synchronously acquires the substrate height signal and the reference height signal. The reference height signal is provided by the vertical position feedback of the displacement stage or by other additional vertical height measurement signals. Assume the measurement range of the substrate height measurement system is The margin for vertical scanning is The time for each scan is The synchronous sampling frequency is The substrate height signal vector obtained in each scan and reference height signal vector As shown in formulas 3 and 4: Formula 3: Formula 4: in, Indicates the number of scans. .

4. The method according to claim 3, characterized in that, Zero-point correction is performed on the substrate height signal vector and the reference height signal vector to ensure that the zero points of the substrate height signal and the reference height signal are consistent. This specifically includes: because It is obtained through a vertical scan motion passing through its zero point, traversing... Find one close to zero ,in This represents the index of the value, in Find the corresponding index ,Will Subtract all elements Perform zero-point correction, then the corrected Each element satisfies Formula 5: Formula 5: in, .

5. The method according to claim 4, characterized in that, 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 linearized calibration model. These parameters are then input into the linearized calibration model to obtain the corrected linear height of the substrate. Specifically, this includes: Complete all settings After the second vertical scan, the obtained data are fused according to Formulas 6 and 7: Formula 6: Formula 7: according to Calculate the weight vector The expressions are shown in Formulas 8 and 9: Formula 8: Formula 9; Calculate the weight vector based on Formula 10. Each element: Formula 10; in, , For the boundary values ​​of the linear range, To correct the range boundary values, Indicates the number of scans. ; The weighted least squares fitting method is used, utilizing , and The parameters of the above equation are fitted, and the objective function of the fitting is to minimize Equation 11: Formula 11; The fitted parameters are then input into the linearized calibration model, and the corrected linear height of the substrate is obtained through the linearized calibration model.

6. The method according to claim 5, characterized in that, The method further includes: The support vector regression method is used to correct nonlinear errors by selecting different kernel functions. The different kernel functions Specifically, this includes: linear kernels polynomial kernel and radial base nucleus The expressions are shown in formulas 12, 13, and 14: Formula 12; Formula 13; Formula 14; in, , and It is an adjustable parameter. and The substrate height signal feature vector; Introducing penalty coefficient C and - The loss function is insensitive, and the solution for the support vector regression machine is transformed into solving Equations 15 and 16: Formula 15; Formula 16; in, The penalty coefficient is... To indicate and An insensitive parameter relating to the degree of deviation that can be allowed between them; The solution to the support vector regression machine is obtained by using the Lagrange multiplier method and the SMO algorithm, as shown in Equations 17 and 18: Formula 17; Formula 18; in, For Lagrange multipliers, The penalty coefficient is... For kernel function, To indicate and The insensitive parameter for the degree of allowable deviation. and At most one of them is not zero, so we choose... , and The feature vector of the silicon wafer height signal training set. For the test set or the feature vector of the silicon height signal whose linear height is to be calculated, the insensitive parameter is... To ensure accuracy, a fixed set of positive constants is used during training; the penalty coefficient is selected through multiple tests, striking a balance between training error and generalization ability. Substituting the parameters obtained above into the linearization calibration model yields the corrected linear height of the substrate.

7. The method according to claim 6 or 5, characterized in that, The method further includes: The accuracy of linear calibration is evaluated using a general method based on fitting residuals and linearity.

8. An online calibration device for measuring substrate warpage height, characterized in that, include: A module is established to build a linearized calibration model from a polynomial model with a nonlinear transcendental function correction term; The acquisition module is used to simultaneously acquire the substrate height signal and the reference height signal through vertical scanning, and obtain the substrate height signal vector and the reference height signal vector. The correction module is used to perform zero-point correction on the substrate height signal vector and the reference height signal vector to keep the zero points of the substrate height signal and the reference height signal consistent. The processing module is used to fuse the obtained data after completing a predetermined number of vertical scans, and use a weighted least squares fitting method to fit the fused data to obtain the parameters of the linearized calibration model. The parameters are then substituted into the linearized 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 the computer program, when executed by the processor, implements the steps of the online calibration method for measuring substrate warp height as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores an information transmission implementation program, which, when executed by a processor, implements the steps of the online calibration method for measuring substrate warp height as described in any one of claims 1 to 7.

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