Wafer profile spectral confocal measurement method based on self-weight distortion model

Abstract

The application discloses a wafer profile spectrum confocal measurement method based on self-weight distortion model, which comprises the following steps: setting a standard reference block and multiple constraint conditions, performing optical axis dynamic registration to obtain a corrected surface height field, determining a coupling registration target function and solving registration parameters, dividing the wafer into three annular zones along the radial direction, applying rigid transformation to the lower surface height field in each annular zone to obtain a registration surface height field, reconstructing a wafer distortion theoretical model caused by three-point support and solving a parameter vector of the wafer distortion theoretical model, calculating a wafer middle surface according to the registration surface height field, quantifying the distortion at each coordinate through the wafer distortion theoretical model and calculating a wafer intrinsic middle surface, and calculating standard geometric parameters according to the wafer intrinsic middle surface. The method can greatly reduce the calculation deviation of wafer standard geometric parameters, provides sub-micron level geometric profile measurement capability for large-diameter thin wafers, and can effectively support process yield control and equipment window optimization in advanced packaging and deep sub-micron processes.

Description

Technical Field

[0001] This invention relates to the field of semiconductor metrology technology, and in particular to a method for wafer profile spectral confocal measurement based on a self-weight distortion model. Background Technology

[0002] In advanced packaging and deep submicron processes, minute deviations in the total thickness variation (TTV), mid-face bending (Bow), and maximum warp of 12-inch large-diameter thin wafers can easily cause systematic shifts in subsequent process windows. Existing dual-spectral confocal metrology systems, when measuring 12-inch wafers (on the 500 μm scale), exhibit three-point support distortion amplitudes caused by their own weight reaching hundreds of micrometers, far exceeding typical process flatness tolerances. Furthermore, during long-term scanning, the upper and lower opposed spectral confocal sensors experience multi-degree-of-freedom optical axis misalignments, including lateral shifts, axial spacing drifts, and relative tilts, resulting in sub-pixel-level rigid misalignments in the height field of the upper and lower surfaces. These error sources are coupled and superimposed, causing the measurement data to be simultaneously mixed with non-intrinsic gravitational deformation, sensor spatial misalignment, and platform motion artifacts, severely interfering with the accurate determination of the wafer's intrinsic morphology.

[0003] In existing technologies, the spatial correspondence problem of dual probes is still addressed by mechanical pre-alignment at the factory or three-spot tilt correction based on diffraction elements. These technologies cannot capture time-varying drift during the scanning process and do not cover the combined effects of optical axis misalignment and platform nonlinearity errors. Furthermore, while existing self-weight distortion compensation models can peel off gravitational deformation based on thin-plate theory, their accuracy is highly dependent on the spatial consistency of measurement data on the upper and lower surfaces. Once there is a registration deviation in the original height field, distortion model identification will introduce spurious topography components, leading to residual systematic errors in standard geometric parameters. This invention proposes a wafer profile spectral confocal measurement method based on a self-weight distortion model. Through dynamic optical axis registration, sub-pixel registration of the height field, and self-weight distortion model identification with hard constraints at support points, a complete error compensation chain is constructed from original data acquisition to intrinsic topography reconstruction, improving the measurement accuracy of wafer profiles and providing a reference for subsequent flatness evaluation and process optimization. Summary of the Invention

[0004] The purpose of this invention is to provide a method for wafer profile spectral confocal measurement based on a self-weight distortion model.

[0005] To achieve the above objectives, the present invention is implemented according to the following technical solution: This invention includes the following steps: The original surface height field and platform scanning coordinates of the wafer were acquired by a dual-spectral confocal sensor. A standard reference block and multiple constraints were set, and the optical axis was dynamically registered to obtain the corrected surface height field. The coupling registration objective function is determined and the registration parameters are solved. The wafer is divided into three annular zones along the radial direction. A rigid transformation is applied to the lower surface height field in each annular zone to obtain the registration surface height field. Construct axisymmetric and triple symmetric basis functions respectively, calculate wafer attitude tilt, reconstruct the theoretical model of wafer distortion caused by three-point support, and solve the parameter vector of the theoretical model of wafer distortion based on the constraint conditions at the support points; The wafer mid-plane is calculated based on the registration surface height field. The distortion at each coordinate is quantified and the intrinsic mid-plane of the wafer is calculated using the wafer distortion theory model. The standard geometric parameters are then calculated based on the intrinsic mid-plane of the wafer. The surface height field includes an upper surface height field and a lower surface height field; The constraint condition at the support point is that the theoretical distortion and the measured value at the support point are strictly consistent. The standard geometric parameters include TTV, Bow, and Warp.

[0006] Furthermore, the method for performing dynamic optical axis registration includes: Standard reference blocks are embedded at the start, intermediate checkpoints, and end points of the scanning path. The original surface height field and platform scanning coordinates of the wafer are acquired by a dual-spectrum confocal sensor. The surface height field includes an upper surface height field and a lower surface height field. The measurement coordinate systems of the upper surface height field and the lower surface height field are not consistent. Multiple constraints are determined and a multi-constraint weighted least squares objective function is constructed. The partial derivatives of the multi-constraint weighted least squares objective function with respect to each optical axis offset parameter are obtained, and the multi-constraint weighted least squares objective function is set to zero to obtain a normal equation system. Solving the normal equation system yields the optical axis offset parameters at the corresponding time. The multiple constraints include thickness consistency constraints, surface gradient consistency constraints, and edge contour constraints. The optical axis offset parameters at the start, middle, and end times are calculated, and time-varying compensation is performed on the optical axis offset parameters during the scanning process using linear interpolation to obtain the temporal optical axis offset parameters. Based on the temporal optical axis offset parameters, the coordinate system of the lower spectral sensor probe is transformed to the coordinate system of the upper spectral sensor probe. The lower spectral sensor probe and the upper spectral sensor probe are registered to the same optical axis, and the lower surface height field is adjusted according to the registration result to form a corrected surface height field.

[0007] Furthermore, the method for obtaining the registration surface height field includes: Treat the height field as a two-dimensional grayscale image and calculate the normalized cross-correlation coefficient; Calculate the intrinsic morphology of the upper and lower surfaces, and calculate the difference in bending energy of the thin plate; Extract the wafer edge contour point set and Notch notch feature point set, and calculate the edge alignment error; A coupled registration objective function is constructed based on the normalized cross-correlation coefficient, the difference in bending energy of thin plates, and the edge alignment error. The registration parameters are solved by the Gauss-Newton iterative method. The wafer is divided into three annular zones along the radial direction. Within each annular zone, a rigid transformation is applied to the lower surface height field according to the registration parameters to obtain the registration surface height field.

[0008] Furthermore, the method for reconstructing the theoretical model of wafer distortion caused by three-point support includes: Calculate the deflection at various points on the wafer, and construct axisymmetric basis functions based on the zero distortion condition at the support points. The expression is as follows: ; ; in radius The axisymmetric basis function values ​​at that point. For uniformly distributed loads, The radius of the wafer. The radius of the support point, Let be the bending stiffness of the circular plate. The elastic modulus of the material. Poisson's ratio; The non-axisymmetric distortion components are calculated based on the triple symmetric distribution characteristics of the deflection field, and the triple symmetric basis functions are constructed, with the following expression: ; in The third-order cosine component of the triple symmetric radial basis function. Divide the angle into three equal parts. For the third-order sinusoidal component of the triple symmetric radial basis function, For the third and seventh order cosine components of the triple symmetric radial basis functions. For the third and seventh order sinusoidal components of the triple symmetric radial basis functions; The wafer attitude tilt is calculated based on the rigid body term and the first tilt term, and the expression is: ; in The wafer is tilted. , The coefficients of the first-order sloping term. This is the translation term for a rigid body; Based on the theoretical model of wafer distortion caused by axisymmetric basis functions, triple symmetric basis functions, and wafer attitude tilt reconstruction three-point support, the expression is: ; in for Wafer distortion at the location, This is the axisymmetric response correction factor. , , , The coefficients are triple symmetric basis functions; Extracting the coefficients of each term from the wafer distortion theoretical model as a parameter vector .

[0009] Furthermore, the method for solving the parameter vector of the wafer distortion theoretical model includes: The theoretical distortion at the support point is solved based on the wafer distortion theory model, and the height of the intermediate plane at the support point is calculated from the height field of the registered surface; the height of the intermediate plane at the support point is taken as the average of the height of the upper surface and the height of the lower surface at the support point. Based on the constraints at the support points, the constraint equations are established, and their expressions are as follows: ; ; ; in For the constraint matrix, Represents the constraint matrix of the first row element, For parameter vectors, Let the height vector be the mid-plane at the support point. For the support radius Wafer distortion at the location, , As a support point The coordinates of the location , , , For the support radius and equally divided angles Support point The non-axisymmetric distortion component , , These are the heights of the mid-plane at the three support points; The wafer region is discretized into effective grid points. The distortion of all grid points is summarized using the wafer distortion theory model. The height field of the intermediate plane is calculated by registering the surface height field. A distortion optimization objective function is constructed, with the following expression: ; in To optimize the objective function for distortion, The constraint matrix consists of the remaining valid grid points. The first constraint matrix consisting of valid grid points row element, For valid grid point indexes, radius Wafer distortion at the location, , for The location of the grid points , , , radius Location and steering angle Place Non-axisymmetric distortion components of grid points This represents the height vector of the intermediate plane corresponding to the remaining valid grid points. These are Lagrange multiplier vectors; Using the constraint equation as the constraint condition, the least squares identification method with linear constraints is used to solve the optimal distortion optimization objective function and output the optimal parameter vector of the wafer distortion theoretical model, thus obtaining the optimal wafer distortion theoretical model under the three-point support constraint.

[0010] Furthermore, the method for calculating the intrinsic mid-plane of a wafer includes: The height field of the intermediate plane is calculated by registering the surface height field. The distortion at each coordinate is quantified by the optimal wafer distortion theory model. Linear superposition is then performed to obtain the intrinsic intermediate plane of the wafer in the free state. The expression is: ; ; in On the intrinsic intermediate surface The height of the location for wafer radius at that location, The height of the intermediate plane is calculated to register the surface height field. The quantification value for the distortion caused by self-weight and three-point support. for wafer distortion; Standard geometric parameters are calculated based on the intrinsic midplane of the wafer; the standard geometric parameters include TTV, Bow, and Warp.

[0011] The beneficial effects of this invention are: This invention is a wafer profile spectral confocal measurement method based on a self-weight distortion model. Compared with existing technologies, this invention has the following technical advantages: This invention establishes a multi-constraint least squares objective function that integrates hard constraints on thickness consistency, soft constraints on surface gradient consistency, and geometric constraints on edge contours by embedding a standard reference block in the scanning path. This enables dynamic identification and real-time compensation of six-degree-of-freedom optical axis offset of dual probes, overcoming the limitations of static mechanical alignment. This invention constructs a coupled registration objective function that integrates normalized cross-correlation similarity, thin plate bending energy constraint, and edge Notch feature alignment. It uses a radial segmented registration strategy to perform independent optimized registration, achieving sub-pixel-level rigid registration and nonlinear distortion compensation of the height field of the upper and lower surfaces. This invention constructs axisymmetric and triple symmetric basis functions with translational correction based on thin plate bending theory, and introduces rigid body tilt terms to establish a complete three-point support self-weight distortion theoretical model. This avoids compensation residues caused by boundary condition mismatch and ensures that the intrinsic intermediate surface after self-weight distortion is determined only by geometric errors and process residual stress. Attached Figure Description

[0012] Figure 1 This is a flowchart of the steps of the wafer profile spectral confocal measurement method based on the self-weight distortion model of the present invention; Figure 2 This is a schematic diagram of a dual-spectral confocal wafer geometry contour measurement system based on a self-weight distortion model in an embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the decomposition and reconstruction of the wafer's intermediate plane in an embodiment of the present invention; Figure 4 This is a graph showing the changes in wafer bow and warp before and after compensation in an embodiment of the present invention. Detailed Implementation

[0013] The present invention will be further described below through specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0014] The wafer profile spectral confocal measurement method based on the self-weight distortion model of this invention includes the following steps: like Figure 1 As shown, this embodiment includes the following steps: The original surface height field and platform scanning coordinates of the wafer were acquired by a dual-spectral confocal sensor. A standard reference block and multiple constraints were set, and the optical axis was dynamically registered to obtain the corrected surface height field. The coupling registration objective function is determined and the registration parameters are solved. The wafer is divided into three annular zones along the radial direction. A rigid transformation is applied to the lower surface height field in each annular zone to obtain the registration surface height field. Construct axisymmetric and triple symmetric basis functions respectively, calculate wafer attitude tilt, reconstruct the theoretical model of wafer distortion caused by three-point support, and solve the parameter vector of the theoretical model of wafer distortion based on the constraint conditions at the support points; The wafer mid-plane is calculated based on the registration surface height field. The distortion at each coordinate is quantified and the intrinsic mid-plane of the wafer is calculated using the wafer distortion theory model. The standard geometric parameters are then calculated based on the intrinsic mid-plane of the wafer. The surface height field includes an upper surface height field and a lower surface height field; The constraint condition at the support point is that the theoretical distortion and the measured value at the support point are strictly consistent. The standard geometric parameters include TTV, Bow, and Warp; In practical evaluation, to achieve high-precision measurement of the geometric profile of large-diameter wafers, a dual-spectral confocal wafer geometric profile measurement system was proposed, such as... Figure 2 As shown, it mainly consists of upper and lower opposing spectral confocal sensors, a 2-degree-of-freedom displacement platform, a three-point support mechanism, and a host computer data acquisition and processing module; The system employs two opposing spectral confocal sensors arranged along the same optical axis, enabling the system to simultaneously acquire height information from both the upper and lower surfaces of the wafer at any scanning position. This avoids the clamping and posture repetition errors introduced by traditional flipping measurements and significantly improves the accuracy and consistency of thickness field and mid-surface reconstruction. The wafer is supported by a three-point support mechanism, and the two-dimensional air-bearing platform completes contour scanning according to a preset trajectory under the closed-loop control of a grating ruler. The platform's high positioning accuracy and motion stability ensure the global consistency of the measurement coordinate system, allowing height data from the dual probes to accurately correspond to the same spatial position. The spectral confocal sensors illuminate the wafer surface with a broadband white light source, and the reflected light enters the spectrometer after optical fiber coupling, forming a spectral signal with axial dispersion coding characteristics. The host computer synchronously acquires and decodes the dual spectral signals to reconstruct the height distribution of the upper and lower surfaces of the wafer.

[0015] In this embodiment, the method for dynamic optical axis registration includes: Standard reference blocks are embedded at the start, intermediate checkpoints, and end points of the scanning path. The original surface height field and platform scanning coordinates of the wafer are acquired by a dual-spectrum confocal sensor. The surface height field includes an upper surface height field and a lower surface height field. The measurement coordinate systems of the upper surface height field and the lower surface height field are not consistent. Multiple constraints are determined and a multi-constraint weighted least squares objective function is constructed. The partial derivatives of the multi-constraint weighted least squares objective function with respect to each optical axis offset parameter are obtained, and the multi-constraint weighted least squares objective function is set to zero to obtain a normal equation system. Solving the normal equation system yields the optical axis offset parameters at the corresponding time. The multiple constraints include thickness consistency constraints, surface gradient consistency constraints, and edge contour constraints. The optical axis offset parameters at the start, middle, and end times are calculated, and time-varying compensation is performed on the optical axis offset parameters during the scanning process using linear interpolation to obtain the temporal optical axis offset parameters. Based on the temporal optical axis offset parameters, the coordinate system of the lower spectral sensor probe is transformed to the coordinate system of the upper spectral sensor probe, and the lower and upper spectral sensor probes are registered to the same optical axis. Based on the registration results, the lower surface height field is adjusted to form a corrected surface height field. In actual evaluation, standard reference blocks (using Zerodur low-expansion ceramic blocks, with optically polished upper and lower surfaces, surface accuracy << 0.1 μm, and thermal expansion coefficient << 0.1 × 10⁻⁶) are embedded at the start, intermediate, and end points of the scanning path. -6 / K), the original surface height field and platform scan coordinates of the wafer are acquired by a dual-spectral confocal sensor; the surface height field includes an upper surface height field and a lower surface height field; the measurement coordinate systems of the upper surface height field and the lower surface height field are not consistent; Determine multiple constraints and construct a multi-constraint weighted least squares objective function. Take the partial derivatives of the multi-constraint weighted least squares objective function with respect to each optical axis offset parameter, and set the multi-constraint weighted least squares objective function to zero to obtain a system of normal equations. Solve the system of normal equations to obtain the optical axis offset parameters at the corresponding time points, expressed as: ; ; ; ; in For the multi-constraint weighted least squares objective function, This is the optical axis offset parameter vector. , For horizontal offset, For axial spacing drift, , These represent the tilt angles of the lower spectral sensor probe's optical axis relative to the upper spectral sensor probe's optical axis around the X and Y axes, respectively. Let be the rotation angle about the Z-axis. for Thickness The residual, For thickness matching point pairs, For thickness weighting coefficient, for Gradient residual, Calculate the neighborhood set for the gradient. These are the gradient weight coefficients. for Edge alignment residual after edge point transformation For the edge point set, These are the edge weight coefficients. For the upper probe at the grid point The height value measured at that location, For the lower probe at the grid point The height value measured at that location, For recommended thickness, For the gradient field of the upper surface, For the gradient field of the lower surface, For rotation matrix sub-block, , These are the coordinates of the edge points; The optical axis offset parameters at the start, middle, and end times are calculated, and time-varying compensation is performed on the optical axis offset parameters during the scanning process using linear interpolation to obtain the temporal optical axis offset parameters, expressed as: ; in for The optical axis offset parameter vector at time t, , The optical axis offset parameters are obtained from two consecutive registrations. , For the corresponding registration time; Based on the time-series optical axis offset parameters, the coordinate system of the lower spectral sensor probe is transformed to the coordinate system of the upper spectral sensor probe. The lower and upper spectral sensor probes are registered to the same optical axis. The lower surface height field is adjusted according to the registration results to form a corrected surface height field. The method for transforming the coordinate system of the lower spectral sensor probe to the coordinate system of the upper spectral sensor probe is as follows: ; ; in( , , ) represents the coordinates of the upper spectral sensor probe. , , ( ) represents the coordinates of the lower spectral sensor probe. It is a rotation matrix.

[0016] In this embodiment, the method for obtaining the registration surface height field includes: Treat the height field as a two-dimensional grayscale image and calculate the normalized cross-correlation coefficient; Calculate the intrinsic morphology of the upper and lower surfaces, and calculate the difference in bending energy of the thin plate; Extract the wafer edge contour point set and Notch notch feature point set, and calculate the edge alignment error; A coupled registration objective function is constructed based on the normalized cross-correlation coefficient, the difference in bending energy of thin plates, and the edge alignment error. The registration parameters are solved by the Gauss-Newton iterative method. The wafer is divided into three annular zones along the radial direction. A rigid transformation is applied to the lower surface height field in each annular zone according to the registration parameters to obtain the registration surface height field. In practical evaluation, the height field is treated as a two-dimensional grayscale image, and the normalized cross-correlation coefficient is calculated as follows: ; in To normalize the cross-correlation coefficient, For the effective overlapping area, for The height of the upper surface field at that location, The average height of the upper surface field. For the lower surface field height field From registration parameters The height field after rigid transformation; The difference in bending energy of the thin plate is calculated by separately calculating the Gaussian curvature field and the mean curvature field of the upper and lower surfaces. The expression is as follows: ; in Due to differences in the bending energy of thin plates, Let Gaussian curvature field be the upper surface. For the Gaussian curvature field of the lower surface From registration parameters Gaussian curvature field after rigid transformation , For the translation amount to be registered, The rotation angle to be registered. As curvature weight, The average curvature of the upper surface. The average curvature of the lower surface field Registration parameters The average curvature of the lower surface after rigid transformation; Take the wafer edge contour point set and the Notch notch feature point set, calculate the edge alignment error, and the expression is: ; in This is for edge alignment error. For the upper surface An edge point, For the lower surface, the first A set of edge points It is a planar rotation matrix. These are the Notch strong constraint weighting coefficients. , , The coordinates of the Notch feature center; The coupling registration objective function is constructed using the normalized cross-correlation coefficient, the difference in bending energy of the thin plates, and the edge alignment error. The registration parameters are solved using the Gauss-Newton iteration method, and the expression is: ; ; in For the coupling registration objective function, , For balance coefficient, For the registration parameter vector The The result of the second iteration For the registration parameters The residual vector of the iteration results for right The Jacobian matrix; Iterate to Converge, output registration parameters; The wafer is divided into three annular zones along the radial direction, and the registration parameters are calculated independently for each annular zone. A full-field registration field is constructed through radial weighted interpolation. Within each annular zone, a rigid transformation is applied to the lower surface height field according to the registration parameters to obtain the registered surface height field, expressed as: ; ; in radius Registration parameters of the annular zone in which it is located. It is a circular band index. With center radius Let be the cubic spline basis functions of the nodes. for Registration parameters on the annular strip.

[0017] In this embodiment, the method for reconstructing the theoretical model of wafer distortion caused by three-point support includes: Calculate the deflection at various points on the wafer, and construct axisymmetric basis functions based on the zero distortion condition at the support points. The expression is as follows: ; ; in radius The axisymmetric basis function values ​​at that point. For uniformly distributed loads, The radius of the wafer. The radius of the support point, Let be the bending stiffness of the circular plate. The elastic modulus of the material. Poisson's ratio; The non-axisymmetric distortion components are calculated based on the triple symmetric distribution characteristics of the deflection field, and the triple symmetric basis functions are constructed, with the following expression: ; in The third-order cosine component of the triple symmetric radial basis function. Divide the angle into three equal parts. For the third-order sinusoidal component of the triple symmetric radial basis function, For the third and seventh order cosine components of the triple symmetric radial basis functions. For the third and seventh order sinusoidal components of the triple symmetric radial basis functions; The wafer attitude tilt is calculated based on the rigid body term and the first tilt term, and the expression is: ; in The wafer is tilted. , The coefficients of the first-order sloping term. This is the translation term for a rigid body; Based on the theoretical model of wafer distortion caused by axisymmetric basis functions, triple symmetric basis functions, and wafer attitude tilt reconstruction three-point support, the expression is: ; in for Wafer distortion at the location, This is the axisymmetric response correction factor. , , , The coefficients are triple symmetric basis functions; Extracting the coefficients of each term from the wafer distortion theoretical model as a parameter vector .

[0018] In this embodiment, the method for solving the parameter vector of the wafer distortion theoretical model includes: The theoretical distortion at the support point is solved based on the wafer distortion theory model, and the height of the intermediate plane at the support point is calculated from the height field of the registered surface; the height of the intermediate plane at the support point is taken as the average of the height of the upper surface and the height of the lower surface at the support point. Based on the constraints at the support points, the constraint equations are established, and their expressions are as follows: ; ; ; in For the constraint matrix, Represents the constraint matrix of the first row element, For parameter vectors, Let the height vector be the mid-plane at the support point. For the support radius Wafer distortion at the location, , As a support point The coordinates of the location , , , For the support radius and equally divided angles Support point The non-axisymmetric distortion component , , These are the heights of the mid-plane at the three support points; The wafer region is discretized into effective grid points. The distortion of all grid points is summarized using the wafer distortion theory model. The height field of the intermediate plane is calculated by registering the surface height field. A distortion optimization objective function is constructed, with the following expression: ; in To optimize the objective function for distortion, The constraint matrix consists of the remaining valid grid points. The first constraint matrix consisting of valid grid points row element, For valid grid point indexes, radius Wafer distortion at the location, , for The location of the grid points , , , radius Location and steering angle Place Non-axisymmetric distortion components of grid points This represents the height vector of the intermediate plane corresponding to the remaining valid grid points. These are Lagrange multiplier vectors; Using the constraint equation as the constraint condition, the least squares identification method with linear constraints is used to solve the optimal distortion optimization objective function and output the optimal parameter vector of the wafer distortion theoretical model, thus obtaining the optimal wafer distortion theoretical model under the three-point support constraint.

[0019] In this embodiment, the method for calculating the intrinsic mid-plane of a wafer includes: The height field of the intermediate plane is calculated by registering the surface height field. The distortion at each coordinate is quantified by the optimal wafer distortion theory model. Linear superposition is then performed to obtain the intrinsic intermediate plane of the wafer in the free state. The expression is: ; ; in On the intrinsic intermediate surface The height of the location for wafer radius at that location, The height of the intermediate plane is calculated to register the surface height field. The quantification value for the distortion caused by self-weight and three-point support. for wafer distortion; Standard geometric parameters are calculated based on the intrinsic mid-plane of the wafer; the standard geometric parameters include TTV, Bow, and Warp. In practical evaluation, to assess the effectiveness of the proposed wafer profile spectral confocal measurement method based on the self-weight distortion model, the aforementioned dual-spectral confocal wafer geometric profile measurement system was used to measure multiple 12-inch wafer test samples. The sample material parameters are as follows: elastic modulus... Poisson's ratio ,density The nominal thicknesses are 500μm, 600μm, and 775μm, respectively. These parameters represent the typical material and thickness ranges in current wafer manufacturing processes, covering the main variation laws of self-weight distortion of mainstream thickness wafers under three-point support conditions. The three-point support mechanism used in the experiment consists of three silicon spheres with a diameter of 2mm. The three silicon spheres are arranged at equal angular intervals of 120° on the support circumference of the wafer. The radius of the support circle is 2mm smaller than the nominal radius of the wafer to avoid the wafer edge notch from interfering with the support stability and geometric profile measurement results. At the same time, it ensures that the support force acts on the internal region of the wafer, reducing the impact of boundary effects on the overall deflection distribution. The support point height is finely set by a fine-tuning leveling mechanism. By adjusting point by point, the three-point support is made to meet the same height condition as much as possible geometrically, minimizing the overall tilt and additional bending caused by the difference in support height. The leveled three-point support can provide highly stable and repeatable boundary conditions for subsequent self-weight distortion measurement and model verification. To verify the effectiveness and stability of the wafer profile spectral confocal measurement method based on the self-weight distortion model proposed in this invention, 10 consecutive repeated scan measurements were performed on the same 12-inch wafer, and the test results are shown in Table 1. Table 1 Measurement results of 12-inch wafer geometry profile In Table 1, regarding the TTV index, regardless of whether it was before or after compensation, the results of the ten measurements remained stable within the range of 9.84 to 10.01 μm. This indicates that the dual-spectral confocal wafer geometric profile measurement method constructed in this invention has high stability and can provide reliable data support for subsequent self-weight distortion modeling and wafer intrinsic geometric parameter measurement. In addition, the self-weight distortion compensation only affects the reconstruction process of the mid-surface deflection field and does not affect the thickness field calculation results. Figure 3 The results of the intermediate plane decomposition are presented, including the measured intermediate plane, the self-weight distortion calculated based on the established model, and the reconstructed intrinsic intermediate plane after removing the distortion. Figure 3 -a represents the measured intermediate plan view. Figure 3 -b represents the self-weight distortion component. Figure 3 -c represents the intrinsic intermediate plane; Subsequently, the TTV, Bow, and Warp indices before and after compensation were calculated, and their trends are shown below. Figure 4 As shown, where Figure 4 -a represents the curve of change before and after Bow compensation. Figure 4 -b represents the change curves before and after Warp compensation; where the standard geometric parameters of the wafer are TTV 9.98μm, Bow 13μm, and Warp 45μm; like Figure 4As shown in -a, the method proposed in this invention demonstrates significant improvement in the Bow index: Before compensation, the Bow is stably distributed within the range of -62.45 to -62.22 μm, with a fluctuation range of less than 0.2 μm, indicating that the central concave distortion caused by the three-point support has extremely high reproducibility; however, before compensation, the Bow differs from the standard value (13 μm) by approximately 75 μm, and this deviation is mainly caused by the distortion caused by gravity and the three-point support conditions; after compensation, the Bow successfully decreases to the range of 12.4 to 14.0 μm, with an average value of approximately 13.1 μm, differing from the standard value of 13 μm by only 0.1 μm; the measurement deviation is significantly reduced from approximately 75 μm before compensation to the range of 0.1 to 1 μm, improving the measurement accuracy by approximately 56%-60%; at the same time, the Bow fluctuation after compensation is only 0.8 μm, demonstrating the high robustness of the compensation algorithm; like Figure 4 As shown in -b, significant improvements were also observed in the Warp index: Before compensation, the Warp was distributed in the range of 147.9 to 148.7 μm, mainly dominated by self-weight distortion caused by three-point support, with little correlation to the wafer's own morphology; after compensation, the Warp steadily decreased to the range of 41.5 to 44.9 μm, with an average of about 43.6 μm, and the deviation from the standard value (45 μm) decreased from about 103 μm before compensation to the range of 1 to 4 μm, improving the measurement accuracy by about 69%-73%; since the gravity distortion was completely removed, the compensated Warp is more sensitive to the wafer's own micro-morphology, and therefore exhibits slightly higher relative fluctuations, but the overall change is still less than 4%, which is within an acceptable range.

[0020] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for wafer profile spectral confocal measurement based on a self-weight distortion model, characterized in that, Includes the following steps: S1. The original surface height field and platform scanning coordinates of the wafer are acquired by a dual-spectral confocal sensor. A standard reference block and multiple constraints are set, and the optical axis is dynamically registered to obtain the corrected surface height field. S2. Determine the coupling registration objective function and solve the registration parameters. Divide the wafer into three annular zones along the radial direction. Apply a rigid transformation to the lower surface height field in each annular zone to obtain the registration surface height field. S3. Construct axisymmetric basis functions and triple symmetric basis functions respectively, calculate wafer attitude tilt, reconstruct the theoretical model of wafer distortion caused by three-point support, and solve the parameter vector of the theoretical model of wafer distortion according to the constraint conditions at the support points. S4. Calculate the wafer mid-plane based on the registration surface height field, quantify the distortion at each coordinate using the wafer distortion theory model and calculate the intrinsic mid-plane of the wafer, and calculate the standard geometric parameters based on the intrinsic mid-plane of the wafer. The surface height field includes an upper surface height field and a lower surface height field; The constraint condition at the support point is that the theoretical distortion and the measured value at the support point are strictly consistent. The standard geometric parameters include TTV, Bow, and Warp.

2. The wafer profile spectral confocal measurement method based on the self-weight distortion model according to claim 1, characterized in that, The method for dynamic optical axis registration includes: Standard reference blocks are embedded at the start, intermediate checkpoints, and end points of the scanning path. The original surface height field and platform scanning coordinates of the wafer are acquired by a dual-spectrum confocal sensor. The surface height field includes an upper surface height field and a lower surface height field. The measurement coordinate systems of the upper surface height field and the lower surface height field are not consistent. Multiple constraints are determined and a multi-constraint weighted least squares objective function is constructed. The partial derivatives of the multi-constraint weighted least squares objective function with respect to each optical axis offset parameter are obtained, and the multi-constraint weighted least squares objective function is set to zero to obtain a normal equation system. Solving the normal equation system yields the optical axis offset parameters at the corresponding time. The multiple constraints include thickness consistency constraints, surface gradient consistency constraints, and edge contour constraints. The optical axis offset parameters at the start, middle, and end times are calculated, and time-varying compensation is performed on the optical axis offset parameters during the scanning process using linear interpolation to obtain the temporal optical axis offset parameters. Based on the temporal optical axis offset parameters, the coordinate system of the lower spectral sensor probe is transformed to the coordinate system of the upper spectral sensor probe. The lower spectral sensor probe and the upper spectral sensor probe are registered to the same optical axis, and the lower surface height field is adjusted according to the registration result to form a corrected surface height field.

3. The wafer profile spectral confocal measurement method based on the self-weight distortion model according to claim 1, characterized in that, The method for obtaining the registration surface height field includes: Treat the height field as a two-dimensional grayscale image and calculate the normalized cross-correlation coefficient; Calculate the intrinsic morphology of the upper and lower surfaces, and calculate the difference in bending energy of the thin plate; Extract the wafer edge contour point set and Notch notch feature point set, and calculate the edge alignment error; A coupled registration objective function is constructed based on the normalized cross-correlation coefficient, the difference in bending energy of thin plates, and the edge alignment error. The registration parameters are solved by the Gauss-Newton iterative method. The wafer is divided into three annular zones along the radial direction. Within each annular zone, a rigid transformation is applied to the lower surface height field according to the registration parameters to obtain the registration surface height field.

4. The wafer profile spectral confocal measurement method based on the self-weight distortion model according to claim 1, characterized in that, The method for reconstructing the theoretical model of wafer distortion caused by three-point support includes: Calculate the deflection at various points on the wafer, and construct axisymmetric basis functions based on the zero distortion condition at the support points. The expression is as follows: ； ； in radius The axisymmetric basis function values ​​at that point. For uniformly distributed loads, The radius of the wafer. The radius of the support point, Let be the bending stiffness of the circular plate. The elastic modulus of the material. Poisson's ratio; The non-axisymmetric distortion components are calculated based on the triple symmetric distribution characteristics of the deflection field, and the triple symmetric basis functions are constructed, with the following expression: ； in The third-order cosine component of the triple symmetric radial basis function. Divide the angle into three equal parts. For the third-order sinusoidal component of the triple symmetric radial basis function, For the third and seventh order cosine components of the triple symmetric radial basis functions. For the third and seventh order sinusoidal components of the triple symmetric radial basis functions; The wafer attitude tilt is calculated based on the rigid body term and the first tilt term, and the expression is: ； in The wafer is tilted. , The coefficients of the first-order sloping term. This is the translation term for a rigid body; Based on the theoretical model of wafer distortion caused by axisymmetric basis functions, triple symmetric basis functions, and wafer attitude tilt reconstruction three-point support, the expression is: ； in for Wafer distortion at the location, This is the axisymmetric response correction factor. , , , The coefficients are triple symmetric basis functions; Extracting the coefficients of each term from the wafer distortion theoretical model as a parameter vector .

5. The wafer profile spectral confocal measurement method based on the self-weight distortion model according to claim 1, characterized in that, The method for solving the parameter vector of the wafer distortion theoretical model includes: The theoretical distortion at the support point is solved based on the wafer distortion theory model, and the height of the intermediate plane at the support point is calculated from the height field of the registered surface; the height of the intermediate plane at the support point is taken as the average of the height of the upper surface and the height of the lower surface at the support point. Based on the constraints at the support points, the constraint equations are established, and their expressions are as follows: ； ； ； in For the constraint matrix, Represents the constraint matrix of the first row element, For parameter vectors, Let the height vector be the mid-plane at the support point. For the support radius Wafer distortion at the location, , As a support point The coordinates of the location , , , For the support radius and equally divided angles Support point The non-axisymmetric distortion component , , These are the heights of the mid-plane at the three support points; The wafer region is discretized into effective grid points. The distortion of all grid points is summarized using the wafer distortion theory model. The height field of the intermediate plane is calculated by registering the surface height field. A distortion optimization objective function is constructed, with the following expression: ； in To optimize the objective function for distortion, The constraint matrix consists of the remaining valid grid points. The first constraint matrix consisting of valid grid points row element, For valid grid point indexes, radius Wafer distortion at the location, , for The location of the grid points , , , radius Location and steering angle Place Non-axisymmetric distortion components of grid points This represents the height vector of the intermediate plane corresponding to the remaining valid grid points. These are Lagrange multiplier vectors; Using the constraint equation as the constraint condition, the least squares identification method with linear constraints is used to solve the optimal distortion optimization objective function and output the optimal parameter vector of the wafer distortion theoretical model, thus obtaining the optimal wafer distortion theoretical model under the three-point support constraint.

6. The wafer profile spectral confocal measurement method based on the self-weight distortion model according to claim 1, characterized in that, The method for calculating the intrinsic mid-plane of a wafer includes: The height field of the intermediate plane is calculated by registering the surface height field. The distortion at each coordinate is quantified by the optimal wafer distortion theory model. Linear superposition is then performed to obtain the intrinsic intermediate plane of the wafer in the free state. The expression is: ； ； in On the intrinsic intermediate surface The height of the location for wafer radius at that location, The height of the intermediate plane is calculated to register the surface height field. The quantification value for the distortion caused by self-weight and three-point support. for wafer distortion; Standard geometric parameters are calculated based on the intrinsic midplane of the wafer; the standard geometric parameters include TTV, Bow, and Warp.

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