Wafer surface adhesion work statistical distribution characterization method based on force-distance curve

Abstract

This invention relates to a method for characterizing the statistical distribution of adhesion work on wafer surfaces based on force-distance curves. The method includes: acquiring force-distance curve data from multiple measurement points based on the interaction between a functional group-modified probe and the wafer surface; smoothing and differentiating the probe branches, identifying abrupt change points and extracting tail intervals based on quantile thresholds; performing restricted least-squares fitting when the tail interval is stable, taking the intercept as the reference baseline, otherwise taking the force value at the abrupt change point; identifying attraction signal intervals below the baseline, integrating the continuous sub-segment with the maximum attraction depth as the main attraction interval to obtain the adhesion work characterization value; constructing a dataset based on the characterization values ​​from all measurement points, fitting it using a single-peak or multi-peak Gaussian model, and outputting the Gaussian component peak position, peak width, and weight parameters to characterize the statistical distribution characteristics of the adhesion state. Compared with existing technologies, this invention can stably extract local interface attraction information from the force curve, achieving multi-component statistical distribution characterization of the adhesion state on the wafer surface.

Description

Technical Field

[0001] This invention relates to the field of integrated circuit three-dimensional packaging and interface characterization technology, and in particular to a method for characterizing the statistical distribution of adhesion work on wafer surfaces based on force-distance curves. Background Technology

[0002] In hybrid bonding technology, the surface adhesion work of the wafer is one of the key factors affecting bonding quality. The hydrophilicity, chemical composition, and functional group distribution of the wafer surface directly affect the interactions between interfaces, manifested as differences in adhesion work, which in turn determine the contact state and interfacial bonding behavior before bonding. If the interfacial interactions are weak, it can easily lead to poor bonding between copper and dielectric, causing microvoids or interfacial delamination, and reducing device reliability. Therefore, accurately measuring and statistically characterizing the adhesion work of the wafer surface is crucial for pre-assessment of the interfacial state and process optimization before bonding.

[0003] In existing technologies, methods for characterizing wafer interface states mostly focus on macroscopic mechanical properties or indirect parameter analysis. For example, patent document CN119092421A proposes to indirectly calculate bonding strength by applying pressure to generate cracks and measuring the crack size. While this method avoids destructive measurements, it emphasizes bonding strength rather than the direct acquisition of adhesion work or surface energy, and the crack formation and measurement process is easily affected by various factors. Another patent document, CN110349877A, uses particles placed on the wafer surface and the size of the resulting bubbles after bonding to reflect bonding strength. However, its measurement accuracy is easily affected by particle distribution and bubble size stability, limiting its ability to accurately characterize adhesion work.

[0004] While atomic force microscopy (AFM)-based measurement methods can acquire nanoscale force-distance curves and extract adhesion-related parameters, they still have shortcomings in force curve data processing and statistical characterization. Specifically, in determining the reference baseline, existing methods often rely on fixed thresholds or empirical judgments. When thermal drift or noise perturbations exist at the tail of the force curve, the baseline estimation is prone to inaccuracy, affecting the consistency and reliability of the adhesion work calculation results. Regarding the selection of the attraction region, existing methods typically integrate the entire region below the baseline directly, lacking the ability to discriminate and screen multiple consecutive attractor segments, making it difficult to accurately extract the most representative interfacial interaction information. Furthermore, in the statistical analysis of adhesion parameters, existing techniques often use histograms or single-peak Gaussian models for fitting, only obtaining average values ​​or single distribution characteristics. However, for wafer samples with multiple surface chemical states, uneven local processing, or differences in functional group distribution, single average values ​​or single-peak statistics cannot fully characterize the complexity of their adhesion states. For example, patent document CN109633211A only fits the adhesion force data to an approximate unimodal normal distribution, without considering the possible multi-component distribution patterns.

[0005] Therefore, the existing technology has not yet provided a method that can stably extract the interface attraction information in the AFM force curve and further accurately obtain its statistical distribution characteristics through a multi-peak statistical model. Summary of the Invention

[0006] The purpose of this invention is to solve the technical problems of inaccurate baseline determination, unreasonable extraction of attraction intervals, and inability to reveal the distribution characteristics of multi-component adhesion states in the force curve data processing of existing technologies, and to provide a method for characterizing the statistical distribution of adhesion work on wafer surfaces based on force-distance curves.

[0007] The objective of this invention can be achieved through the following technical solutions: This invention provides a method for characterizing the statistical distribution of adhesion work on a wafer surface based on force-distance curves, comprising: Force-distance curve data collected at multiple measurement points are acquired, the force-distance curve data being collected based on the interaction between a functional group-modified atomic force microscope probe and the surface of a wafer sample; The needle insertion branches of each force-distance curve are smoothed and their derivatives are calculated. Abrupt change points are identified based on a preset quantile threshold, and the tail interval after the abrupt change point is extracted. When the tail interval satisfies the stationarity condition, a restricted least squares fit is performed on the tail interval, and the fitting intercept is taken as the reference baseline; otherwise, the force value at the abrupt change point is taken as the reference baseline. Identify the attraction signal interval below the reference baseline in the needle insertion branch, take the continuous sub-segment corresponding to the maximum attraction depth as the main attraction range, and perform numerical integration on the main attraction range to obtain the adhesion work characterization value of each measuring point. The dataset is constructed based on the adhesion work values ​​of all measurement points. A single-peak or multi-peak Gaussian model is used for fitting, and the peak position, peak width and weight parameters of each Gaussian component are output to characterize the statistical distribution characteristics of the adhesion state on the wafer surface.

[0008] Furthermore, the tail interval satisfies the stationarity condition, specifically by calculating the statistical parameters and fluctuation amplitude of the tail interval. When both the statistical parameters and fluctuation amplitude fall within a preset threshold range, the tail interval is determined to be a stationary interval.

[0009] Furthermore, the continuous sub-segment corresponding to the maximum attraction depth is defined as the main attraction zone, including: The signal interval in the needle insertion branch that is below the reference baseline is divided into multiple continuous sub-segments; Calculate the maximum attraction depth of each continuous sub-segment relative to the reference baseline; The continuous sub-segment with the largest maximum attraction depth is defined as the main attraction zone.

[0010] Furthermore, a dataset is constructed based on the adhesion work characterization values ​​of all measurement points, and a unimodal or multimodal Gaussian model is used for fitting, including: Outlier removal is performed on the adhesion work characterization dataset, and statistical histograms and density distribution curves are generated. Candidate peak positions are identified based on the local maxima of the density distribution curve, and these candidate peak positions are used as the initial mean parameters for fitting the Gaussian model. The dataset was fitted using both unimodal and multimodal Gaussian candidate models, and the optimal model was selected as the fitted model based on the goodness-of-fit index.

[0011] Furthermore, after fitting the dataset using unimodal and multimodal Gaussian candidate models respectively, the process further includes: Based on the peak spacing, peak width and weight ratio of each Gaussian component obtained by fitting, similar peaks are merged and spurious peaks caused by noise are removed. The weights of the filtered Gaussian components are normalized, and the final peak position, peak width, and weight parameters are output.

[0012] Furthermore, after outputting the peak position, peak width, and weight parameters of each Gaussian component, the following is also included: By associating the adhesion work characterization value of each measuring point with its spatial location coordinates, a two-dimensional spatial distribution map of the adhesion work characterization value is generated. Based on the categories of each Gaussian component obtained by fitting the Gaussian model, each measurement point is classified to generate a peak category spatial distribution map, which is used to evaluate the spatial uniformity of the adhesion state on the wafer surface.

[0013] Furthermore, before acquiring force-distance curve data collected from multiple measuring points, the following steps are also included: Surface cleaning pretreatment was performed on the atomic force microscope probe and the wafer sample; The pretreated probe and wafer sample were placed in a plasma cleaner and a reaction gas was introduced for simultaneous plasma activation treatment to build the same functional group modification layer on the surface of the probe and wafer sample. The activated probe is then calibrated for bending sensitivity, elastic coefficient, and equivalent radius of curvature.

[0014] Further, the equivalent radius of curvature calibration includes: Scan the morphology of standard samples and extract morphology data of multiple feature tips; The topographic data is processed using a three-dimensional convolution inversion algorithm, and the equivalent radius of curvature of the probe is calibrated by combining the indentation depth data in the force curve.

[0015] Furthermore, before smoothing the needle insertion branches of each force-distance curve and calculating the derivative, the following steps are also included: Baseline drift correction and noise suppression were performed on the acquired force-distance curves.

[0016] Furthermore, the restricted least squares fitting is: during the fitting process, a least squares fitting is performed by imposing a range restriction on the fitting parameters based on the physical constraints of the tail interval in the non-interacting region.

[0017] Compared with the prior art, the present invention has the following beneficial effects: The statistical characterization method for wafer surface adhesion work provided by this invention overcomes the shortcomings of traditional fixed threshold methods, which suffer from inaccurate estimation under baseline drift and noise disturbances, by adaptively determining the reference baseline of the force-distance curve and identifying the main attraction range based on physical constraints. This ensures the stable extraction of local interface attraction information. Furthermore, the adhesion work characterization values ​​at all measurement points are fitted using a single-peak or multi-peak Gaussian model, which can accurately identify and distinguish various adhesion states on the wafer surface, outputting the peak position, peak width, and weight parameters of each Gaussian component. Compared to existing methods that only output average values ​​or single-peak distributions, this significantly improves the accuracy and precision of the statistical distribution characteristic characterization, providing a reliable basis for evaluating the uniformity and consistency of surface treatment in bonding processes.

[0018] Compared with existing technologies, this method can provide a quantitative description of the distribution of multiple components, such as distinguishing regions on the wafer surface with different levels of hydrophilicity and their proportions. This method can be directly applied to the optimization of hybrid bonding processes. By comparing the changes in Gaussian components under different process parameters, it can more accurately screen activation schemes that can achieve specific adhesion states and high uniformity, avoiding bonding defects caused by surface chemical inhomogeneity, and fundamentally improving the efficiency and scientific nature of interface state assessment. Attached Figure Description

[0019] Figure 1 This is a flowchart of the measurement method in the application example; Figure 2 This is a calibration diagram of the equivalent radius of curvature of the probe in the application example; Figure 3 This is a graph showing the force curve measurement of the sample in an application example; Figure 4 This is a schematic diagram illustrating the determination of the sample force curve baseline and the integration of the main attraction interval in the application example; Figure 5 This is a single-peak fitting plot of the adhesion work characterization value of the sample in the application example; Figure 6 This is a multi-peak fitting graph of the adhesion work characterization values ​​of the sample in the application example; Figure 7This is a spatial distribution diagram of the peak categories of the adhesion work characterization values ​​for the sample in the application example; Figure 8 This is a two-dimensional distribution diagram of the adhesion work characterization values ​​of the sample in the application example. Detailed Implementation

[0020] This application provides a method for characterizing the statistical distribution of adhesion work on a wafer surface based on force-distance curves. It aims to address the technical problems in existing technologies, such as inaccurate baseline determination, unreasonable extraction of attraction intervals, and the inability to reveal the distribution characteristics of multi-component adhesion states in statistical analysis. The overall concept of this method is as follows: High-resolution force-distance curve data is acquired based on the interaction between a functionally modified probe and the wafer surface; an adaptive baseline identification algorithm and a main action interval screening strategy based on the maximum attraction depth are used to stably extract adhesion work characterization values ​​from each force curve; the dataset composed of adhesion work characterization values ​​from all measurement points is fitted with a single-peak or multi-peak Gaussian model to reveal the various adhesion states that may exist on the wafer surface and their statistical distribution patterns, thereby achieving an accurate assessment of the chemical state and uniformity of the wafer surface.

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Component models, methods, algorithms, and other features not explicitly described in this technical solution are considered common technical features disclosed in the prior art.

[0022] Example 1 This embodiment details a method for characterizing the statistical distribution of adhesion work on a wafer surface based on force-distance curves.

[0023] Before commencing measurement and analysis, a series of preparatory and calibration steps are performed to obtain reliable force-distance curve data. These include: The atomic force microscope probe was cleaned and then dried with an inert gas. The wafer sample was cut to the appropriate size and the surface was cleaned in sequence with organic solvents such as acetone and isopropanol and deionized water. Finally, the surface was dried with an inert gas.

[0024] The cleaned probe and wafer sample are placed on a support such as a glass slide, and then the support is placed in a plasma cleaner. Parameters such as activation time, power, and gas flow rate are set, and after evacuation, at least one reactive gas from nitrogen, oxygen, or argon is introduced for simultaneous plasma activation. This process constructs identical functional group modification layers on the probe and wafer sample surfaces, ensuring that the chemical interactions between the probe and sample are representative and targeted.

[0025] The activated probe underwent calibration of key mechanical parameters. Force curves were acquired on the surface of standard samples such as sapphire, and the bending sensitivity of the probe was calculated through the contact area. The probe dimensions were measured under an optical microscope, and the elastic modulus of the probe cantilever beam was calculated by combining the resonant frequency and quality factor. Subsequently, the morphology of the peak-shaped standard sample was scanned, and the morphology data of multiple characteristic tips were extracted. These data were processed using a three-dimensional convolution inversion algorithm and combined with the indentation depth data obtained from subsequent force curve measurements to calibrate the equivalent radius of curvature of the probe. The relative standard deviation of the calibration results was required to be within a preset range to ensure measurement accuracy.

[0026] In the specific implementation process, the calibration of the equivalent radius of curvature of the probe is not directly measured, but is achieved through an indirect inversion calculation: the probe to be calibrated is used to perform a high-resolution morphological scan on a special standard sample (such as the RS-12M peak sample) with multiple nanoscale sharp features, from which complete three-dimensional morphological data of at least 10 independent and clear feature tips are extracted. These data are physically the convolution result of the probe tip geometry and the true morphology of the standard sample; using the tip reconstruction module built into the atomic force microscope data processing software, based on the blind reconstruction algorithm or mature mathematical morphology three-dimensional convolution inversion algorithm such as Akhundov, the three-dimensional outer envelope contour of the probe tip is iteratively calculated, thereby initially determining its geometric radius of curvature; in order to make this geometric parameter more consistent with the actual measurement conditions, the indentation depth data obtained when collecting force-distance curves on the wafer sample is introduced to correlate and correct the geometric radius of curvature. Because in the non-contact or light contact attraction range involved in the adhesion work calculation, the force-sensitive area is not the tip of the probe, but the equivalent curvature range related to the indentation depth. By fitting the contact mechanics model (such as the DMT or JKR model) at different indentation depths with the probe profile obtained by inversion, the equivalent curvature radius that more realistically reflects the interface interaction area can be determined.

[0027] After preprocessing and calibrating the probe and wafer sample, the core data for analysis can be obtained. Specifically, with appropriate scan rates and trigger thresholds set, force-distance curves are stably acquired at multiple measurement points on the wafer sample through the interaction between the functionally modified probe and the sample surface. After acquisition, each force-distance curve is subjected to baseline drift correction and noise suppression to eliminate the effects of thermal drift and random noise, forming effective force-distance curve data for subsequent analysis.

[0028] The core analysis and processing procedure is divided into two stages: feature extraction of a single force curve and global statistical analysis.

[0029] In the single force curve feature extraction stage, the goal is to accurately calculate the physical quantity representing the local interface adhesion state—the adhesion work—from each force-distance curve. The specific steps are as follows: The insertion branches of each force-distance curve are smoothed and their derivatives are calculated. A sudden change point is identified based on a preset quantile threshold. This sudden change point physically corresponds to the critical position where the probe tip begins to jump or bend due to the attractive or repulsive forces of atoms on the sample surface. The tail region after this sudden change point is extracted.

[0030] The tail section is assessed for stationarity. Statistical parameters (such as mean and standard deviation) and fluctuation amplitude are calculated for this tail section. When both statistical parameters and fluctuation amplitude fall within a preset threshold range, the tail section is considered stationary, meaning the probe has not yet effectively interacted with the sample surface within this distance and is in a zero-force or constant-force baseline region. In this case, a restricted least-squares fit is performed on the stationary tail section. Based on the physical constraints of the non-interaction region, the slope and intercept parameters of the fitted line are restricted, and the fitted intercept is used as the reference baseline to closely match the physical reality of the non-contact region and reduce interference from far-end noise. If the tail section is non-stationary, the force value at the abrupt change point is directly used as the reference baseline. This adaptive baseline determination scheme effectively solves the problem of inaccurate baseline estimation caused by tail drift of the force curve, thereby improving the stability of adhesion work extraction.

[0031] Identify and filter the primary attraction zone. Within the needle insertion branch, identify all attraction signal zones where the force value is below the reference baseline. These zones represent areas where the probe experiences attraction exceeding the baseline noise level. Since multiple discontinuous attraction valleys may exist on the force curve, to accurately extract the most representative interfacial attraction, these below-baseline signal zones are divided into multiple continuous sub-segments. Calculate the maximum attraction depth of each continuous sub-segment relative to the reference baseline. Select the continuous sub-segment with the largest maximum attraction depth as the primary attraction zone for calculation. This mechanism eliminates interference from secondary or non-representative minor attraction and shoulder signals, allowing the extracted attraction energy to more purely reflect the primary interfacial interaction mechanism.

[0032] Numerical integration is performed on the selected main attraction range. The integration range is from the starting point where the force value first falls below the reference baseline to the ending point where the force value finally rises above the reference baseline. The integrand (the difference between the reference baseline and the force curve) is integrated, and the integral value is the adhesion work characterization value corresponding to the measuring point.

[0033] After extracting the features of individual force curves at all measuring points, the process moves to the global statistical analysis stage. The goal is to provide a complete statistical description of the surface adhesion state of the entire measurement area. The specific steps are as follows: The adhesion work values ​​of all measuring points are compiled into a dataset. To eliminate the interference of outliers on the overall distribution, outlier removal is performed on the dataset beforehand.

[0034] The cleaned dataset is statistically analyzed to generate statistical histograms and density distribution curves.

[0035] Candidate peaks are identified based on local maxima of the density distribution curve, and these candidate peaks are used as initial mean parameters for fitting the Gaussian model. Single-peak and multi-peak Gaussian candidate models are used to fit the dataset, and the optimal model is selected from candidate models with different numbers of peaks based on goodness-of-fit indices (e.g., Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC)). This step automatically identifies several adhesive state components hidden behind the data.

[0036] Output the peak position, peak width, and weight parameters of each Gaussian component of the optimal model. These parameters characterize the typical adhesion work (central tendency), inconsistency (dispersion), and area proportion of the wafer surface under different adhesion states.

[0037] As a preferred implementation, after the initial fitting, the results need to be screened and corrected for physical rationality. Specifically, based on the peak spacing, peak width, and weight ratio of each Gaussian component obtained from the fitting, closely spaced peaks are merged, and spurious peaks with too low weight caused by statistical fluctuations or noise are removed. Then, the weights of the remaining Gaussian components are normalized, ultimately outputting peak positions, peak widths, and weight parameters that accurately and reasonably reflect the physicochemical state. This series of post-processing steps ensures the correspondence between the statistical model conclusions and the physical world, improving the robustness and interpretability of the results. Thus, the statistical distribution characteristics of the adhesion state on the wafer surface are obtained.

[0038] Example 2 This embodiment is a further optimization based on Embodiment 1, and provides a specific method for characterizing the spatial distribution of adhesion states.

[0039] After outputting the peak position, peak width, and weight parameters of each Gaussian component based on the optimal Gaussian model, this method also includes the subsequent step of spatial mapping analysis: The adhesion work characterization value of each measurement point in the dataset is correlated with its spatial coordinates (X, Y) on the wafer surface, and a two-dimensional spatial distribution map of the adhesion work characterization value is generated using data visualization methods.

[0040] Based on the Gaussian components obtained from the Gaussian model fitting, a category label is assigned to each measurement point. This label corresponds to the Gaussian component to which its adhesion work characterization value most likely belongs. Based on these labels and the spatial coordinates of the measurement points, a peak category spatial distribution map is generated.

[0041] Two-dimensional spatial distribution maps of adhesion work values ​​and peak category spatial distribution maps are used together to evaluate the spatial uniformity of adhesion states on the wafer surface. The two-dimensional distribution map of adhesion work values ​​visually displays the fluctuations of the adhesion work index across the entire measurement area, while the peak category spatial distribution map clearly reveals the specific geographical distribution of micro-regions of different adhesion states. For example, it can qualitatively determine whether a strong or weak bonding state is distributed in an island-like pattern or uniformly dispersed. Combining statistical and spatial distribution characteristics, this method can provide process engineers with comprehensive and quantitative information on wafer surface states, enabling precise location of process defects and optimization of activation parameters, thereby improving the overall yield of hybrid bonding.

[0042] Application Example 1 This application example uses a statistical distribution characterization method for adhesion work on wafer surfaces based on force-distance curves. (See [link to relevant documentation]). Figure 1 Specifically, it includes the following steps: Step 1: Surface pretreatment of the atomic force microscope probe and the SiO2 sample; Step one includes: At room temperature, the probe is immersed in deionized water for 20 seconds and then dried with nitrogen gas. The SiO2 sample was cut to a size of 1.5 × 1.5 cm. 2 The sample was cleaned in sequence with acetone, isopropanol and deionized water, and finally dried with nitrogen.

[0043] Step 2: The probe and the SiO2 sample are activated by plasma to construct the same functional group modification layer. The probe and SiO2 sample are simultaneously activated in a plasma cleaner to ensure that the probe surface and the SiO2 sample surface have the same chemical groups. The steps include: placing the probe and SiO2 sample treated in step one onto a glass slide, placing the glass slide into the plasma cleaner, setting the time, gas, power, and flow rate, turning on the vacuum pump to evacuate the environment of the plasma cleaner to a vacuum, starting the cleaning process, and introducing the reaction gas.

[0044] Step 3: Calibrate the probe's bending sensitivity, elastic coefficient, and equivalent radius of curvature. The bending sensitivity calibration of the processed probe includes the following steps: collecting 5 sets of force curves on the surface of a sapphire standard sample, selecting the contact area between the probe and the sample on the force curve in the atomic force microscopy data processing software, and calculating the bending sensitivity of the probe.

[0045] The calibration of the elastic coefficient K of the processed probe includes the following steps: measuring the length and width of the probe under an optical microscope using a standard grating as a scale; fitting the resonance peak in the atomic force microscopy data processing software to obtain the resonance frequency and quality factor of the probe; calculating the elastic coefficient K of the probe cantilever beam and filling it into the atomic force microscopy data processing software.

[0046] like Figure 2 As shown, the equivalent radius of curvature of the sample calibration probe was determined using the RS-12M sample calibration probe equipped with a Bruker atomic force microscope. The specific steps included: setting the resolution to 512×512 and the scanning range to 1.2×1.2μm. 2 At least 10 feature tip morphology data were extracted, and three-dimensional convolution inversion calculations were automatically performed using the tip processing module in the atomic force microscope data processing software. The radius of curvature was obtained by combining the indentation depth data obtained from the subsequent force curve, with a relative standard deviation of ≤5%.

[0047] Step 4: Utilize the interaction between the functional group-modified probe and the SiO2 sample surface, set appropriate scanning parameters, stabilize the force-distance curve acquisition, and perform preprocessing and analysis. like Figure 3 As shown, a functionally modified and activated probe was used to measure the force-distance curves of a SiO2 sample after simultaneous activation treatment. Specific steps included setting parameters such as scan rate, trigger threshold, and number of sampling points; acquiring at least five effective force curves for each measurement point; and performing baseline drift correction on the measured curves to reduce the influence of thermal drift. By analyzing the indentation and withdrawal branches in the force curves, information related to probe indentation depth and sample surface adhesion was obtained for subsequent calculation of adhesion work characterization values.

[0048] Force curves at multiple points on the sample under test were measured using a probe, with a sampling point count of 64×64 and a scanning range of 500×500 nm. 2 We extracted all 4096 force curves to form a dataset for processing and analysis.

[0049] Step 5: Based on the force-distance curve, adaptively determine the reference baseline for the needle insertion branch, identify the main attraction zone below the reference baseline, and perform integration calculations on the main attraction zone (see...). Figure 4 ), and obtain the adhesion work characterization value.

[0050] Specifically, determining the reference baseline includes: smoothing the needle insertion force-distance curve and calculating its derivative; determining abrupt change points based on preset quantile thresholds; extracting the tail interval after the abrupt change point and determining whether it is a stable interval based on the parameters and fluctuation amplitude of the tail interval; when the tail interval is a stable interval, performing a restricted least-squares fit on the tail interval and taking the fit intercept as the reference baseline to conform to the actual physical meaning; when the tail interval is a non-stationary interval, taking the force value at the abrupt change point as the reference baseline.

[0051] Furthermore, the force-distance curves obtained from each measurement point of the wafer sample under test are processed, the needle insertion branches are extracted and the reference baseline is determined, the attraction signal intervals below the reference baseline in the needle insertion branches are identified, and the continuous sub-segments corresponding to the maximum attraction depth are determined as the main attraction range. The main attraction range is numerically integrated to obtain the adhesion work characterization value corresponding to each force-distance curve.

[0052] Step six: The adhesion work characterization values ​​of all measurement points obtained in step five are used to form an adhesion work characterization value dataset. The adhesion work characterization value dataset is fitted, filtered and spatially mapped based on a single-peak or multi-peak Gaussian model to obtain the peak position, peak width and weight parameters of the Gaussian component, and to obtain the statistical distribution characteristics and spatial distribution characteristics of the adhesion state on the wafer surface.

[0053] In this application example, the adhesion work characterization dataset is statistically analyzed to generate histograms and density distribution curves. Candidate peak positions are identified based on data distribution characteristics and used as initial parameters for Gaussian model fitting. A single-peak or multi-peak Gaussian model is used to fit the adhesion work characterization dataset, and candidate models with different numbers of peaks are compared to determine the fitted model. The peak positions, peak widths, and weight parameters of the Gaussian components are output (see [link to relevant documentation]). Figure 5 , Figure 6 Furthermore, based on the peak spacing, peak width, and weight ratio of the Gaussian components, the fitting results are filtered, merged, or corrected, and the weights of the filtered Gaussian components are normalized. If the fitting result is a multi-peak distribution, the measurement points are classified according to the Gaussian component categories obtained from the Gaussian model fitting, resulting in a peak category distribution map (see...). Figure 7 Simultaneously, the adhesion work characterization values ​​at each measuring point are mapped according to the spatial location of the measuring points to generate a two-dimensional distribution map of the adhesion work characterization values ​​(see [link]). Figure 8 ( ), to evaluate the statistical distribution characteristics, spatial distribution characteristics and spatial uniformity of the measurement area.

[0054] Comparative Example 1 Patent document CN120721574A discloses a method for measuring wafer surface energy in mixed bonding based on a chemically modified probe. This method involves modifying the probe and the wafer sample with the same functional groups, collecting force-distance curves, calculating the initial adhesion work based on the formula W=F / 2πR, correcting the initial adhesion work for errors using the surface energy measured by the contact angle method of a standard wafer sample, and establishing a quantitative mapping relationship between the corrected adhesion work and the bonding strength. However, the fundamental flaw of this method lies in the fact that the determination of its reference baseline still relies on conventional adaptive baseline correction algorithms. It does not disclose how to judge and constrain the baseline stability and physical rationality for possible drift, noise disturbances, or non-stationary signals in the needle branch. This leads to the baseline estimation being prone to deviating from the true non-contact zero-force state when there are severe fluctuations in the tail section, affecting the accuracy and repeatability of the adhesion work extraction at a single measurement point. On the other hand, this scheme only focuses on the single-point numerical measurement of adhesion work and macroscopic error correction through the compensation coefficient α. Its data analysis endpoint is to establish a single linear mapping relationship between the corrected adhesion work and the bonding strength. It does not conduct statistical distribution mining of adhesion work data at a large number of measurement points on the same wafer surface. Therefore, it is difficult to reveal the multi-component distribution characteristics of the adhesion state caused by various surface chemical states, functional group distribution differences, or local uneven processing that may exist in the measurement area.

[0055] This invention employs a completely different data processing and statistical characterization approach within the same technical field. Instead of relying on the contact angle method for external error correction to indirectly estimate surface energy, this invention focuses on extracting interfacial attraction information from the microscopic force curve itself and directly revealing the distribution pattern of the adhesion state through a multi-peak Gaussian statistical model. Specifically, in the force curve processing stage, this invention introduces an adaptive reference baseline determination mechanism based on the stability condition of the tail interval: statistical parameters and fluctuation amplitudes are calculated for the tail interval after the abrupt change point; restricted least squares fitting is performed only when the stability condition is met, and the intercept is taken as the reference baseline; otherwise, the force value at the abrupt change point is directly used as the baseline, greatly reducing the impact of baseline estimation instability caused by thermal drift or noise. In attracting interval identification, this invention does not simply select all intervals below the baseline, but divides the signal interval below the baseline into multiple continuous sub-segments, selecting the sub-segment corresponding to the maximum attracting depth as the main attracting interval for integration, thus eliminating interference from non-representative attracting valleys or peaks.

[0056] This invention constructs a dataset from the adhesion work values ​​extracted from all measurement points, then fits it using a single-peak or multi-peak Gaussian model, outputting the peak position, peak width, and weight parameters of each Gaussian component. This allows the invention to statistically distinguish multiple adhesion states that may coexist on the wafer surface (e.g., different hydrophilic regions), quantitatively providing the average adhesion work level, dispersion, and area proportion of each state. Furthermore, it generates a peak category distribution map through spatial mapping to assess the uniformity of the surface chemical state. This is a technical capability that the single compensation coefficient correction and linear mapping methods disclosed in the prior art completely lack. The solution of this invention provides more comprehensive data support for the refined screening of surface activation parameters and the pre-evaluation of interface states in hybrid bonding processes.

[0057] The above description of the embodiments is provided to enable those skilled in the art to understand and use the invention. It will be apparent to those skilled in the art that various modifications can be made to these embodiments, and the general principles described herein can be applied to other embodiments without inventive effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made by those skilled in the art based on the disclosure of the present invention without departing from the scope of the invention should be within the protection scope of the present invention.

Claims

1. A method for characterizing the statistical distribution of adhesion work on a wafer surface based on force-distance curves, characterized in that, include: Force-distance curve data collected at multiple measurement points are acquired, the force-distance curve data being collected based on the interaction between a functional group-modified atomic force microscope probe and the surface of a wafer sample; The needle insertion branches of each force-distance curve are smoothed and their derivatives are calculated. Abrupt change points are identified based on a preset quantile threshold, and the tail interval after the abrupt change point is extracted. When the tail interval satisfies the stationarity condition, a restricted least squares fit is performed on the tail interval, and the fitting intercept is taken as the reference baseline; otherwise, the force value at the abrupt change point is taken as the reference baseline. Identify the attraction signal interval below the reference baseline in the needle insertion branch, take the continuous sub-segment corresponding to the maximum attraction depth as the main attraction range, and perform numerical integration on the main attraction range to obtain the adhesion work characterization value of each measuring point. The dataset is constructed based on the adhesion work values ​​of all measurement points. A single-peak or multi-peak Gaussian model is used for fitting, and the peak position, peak width and weight parameters of each Gaussian component are output to characterize the statistical distribution characteristics of the adhesion state on the wafer surface.

2. The method for characterizing the statistical distribution of adhesion work on a wafer surface based on a force-distance curve according to claim 1, characterized in that, The tail interval satisfies the stationarity condition, specifically by calculating the statistical parameters and fluctuation amplitude of the tail interval. When both the statistical parameters and fluctuation amplitude fall within a preset threshold range, the tail interval is determined to be a stationary interval.

3. The method for characterizing the statistical distribution of adhesion work on a wafer surface based on a force-distance curve according to claim 1, characterized in that, The continuous sub-segment corresponding to the maximum attraction depth is taken as the main attraction zone, including: The signal interval in the needle insertion branch that is below the reference baseline is divided into multiple continuous sub-segments; Calculate the maximum attraction depth of each continuous sub-segment relative to the reference baseline; The continuous sub-segment with the largest maximum attraction depth is defined as the main attraction zone.

4. The method for characterizing the statistical distribution of adhesion work on a wafer surface based on a force-distance curve according to claim 1, characterized in that, A dataset is constructed based on the adhesion work characterization values ​​of all measurement points, and fitted using a single-peak or multi-peak Gaussian model, including: Outlier removal is performed on the adhesion work characterization dataset, and statistical histograms and density distribution curves are generated. Candidate peak positions are identified based on the local maxima of the density distribution curve, and these candidate peak positions are used as the initial mean parameters for fitting the Gaussian model. The dataset was fitted using both unimodal and multimodal Gaussian candidate models, and the optimal model was selected as the fitted model based on the goodness-of-fit index.

5. The method for characterizing the statistical distribution of adhesion work on a wafer surface based on a force-distance curve according to claim 4, characterized in that, After fitting the dataset with unimodal and multimodal Gaussian candidate models respectively, the process further includes: Based on the peak spacing, peak width and weight ratio of each Gaussian component obtained by fitting, similar peaks are merged and spurious peaks caused by noise are removed. The weights of the filtered Gaussian components are normalized, and the final peak position, peak width, and weight parameters are output.

6. The method for characterizing the statistical distribution of adhesion work on a wafer surface based on a force-distance curve according to claim 1, characterized in that, After outputting the peak position, peak width, and weight parameters of each Gaussian component, the following is also included: By associating the adhesion work characterization value of each measuring point with its spatial location coordinates, a two-dimensional spatial distribution map of the adhesion work characterization value is generated. Based on the categories of each Gaussian component obtained by fitting the Gaussian model, each measurement point is classified to generate a peak category spatial distribution map, which is used to evaluate the spatial uniformity of the adhesion state on the wafer surface.

7. The method for characterizing the statistical distribution of adhesion work on a wafer surface based on a force-distance curve according to claim 1, characterized in that, Before acquiring force-distance curve data collected from multiple measuring points, the following steps are also included: Surface cleaning pretreatment was performed on the atomic force microscope probe and the wafer sample; The pretreated probe and wafer sample were placed in a plasma cleaner and a reaction gas was introduced for simultaneous plasma activation treatment to build the same functional group modification layer on the surface of the probe and wafer sample. The activated probe is then calibrated for bending sensitivity, elastic coefficient, and equivalent radius of curvature.

8. The method for characterizing the statistical distribution of adhesion work on a wafer surface based on a force-distance curve according to claim 7, characterized in that, The equivalent radius of curvature calibration includes: Scan the morphology of standard samples and extract morphology data of multiple feature tips; The topography data is processed using a three-dimensional convolution inversion algorithm, and the equivalent radius of curvature of the probe is calibrated by combining the indentation depth data in the force curve.

9. The method for characterizing the statistical distribution of adhesion work on a wafer surface based on a force-distance curve according to claim 1, characterized in that, Before smoothing the needle insertion branches of each force-distance curve and calculating the derivative, the following steps are also included: Baseline drift correction and noise suppression were performed on the acquired force-distance curves.

10. The method for characterizing the statistical distribution of adhesion work on a wafer surface based on a force-distance curve according to claim 1, characterized in that, The restricted least squares fitting is: during the fitting process, the least squares fitting applies a range restriction to the fitting parameters based on the physical constraints of the tail interval in the non-interacting region.

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