Real-time pressure optimization and control method for multi-probe array for wafer testing

Abstract

This invention provides a multi-probe array real-time pressure optimization and control method for wafer testing, which relates to the field of semiconductor testing technology. The method involves collecting real-time pressure data and wafer stress limit values ​​to establish an initial distribution state, calculating contact area and angle through displacement to determine the stress concentration factor for pressure correction, calculating the strain rate distribution to identify sensitive areas for pressure compensation, monitoring the stress-strain ratio to identify microcrack initiation points, determining optimal pressurization parameters, and performing real-time monitoring and early warning. This method can reduce the risk of damage during wafer testing and improve test accuracy and yield.

Description

Technical Field

[0001] The present invention relates to semiconductor testing technology, and in particular to a multi-probe array real-time pressure optimization and control method for wafer testing. Background Art

[0002] Currently, the requirements for precision and uniformity in the pressure applied by probe arrays during wafer testing are increasing. This is especially true during large-scale integrated circuit (IC) chip manufacturing, where uneven localized force can easily lead to microcracks or structural damage on the wafer surface. Traditional multi-probe test systems generally rely on fixed pressure or simple linear feedback adjustment methods, lacking the ability to sense and respond to real-time stress changes, making them unable to meet the test reliability and product yield requirements of advanced manufacturing processes.

[0003] Furthermore, the multi-probe array exhibits significant lateral and longitudinal displacement errors during wafer contact, leading to deviations in the actual contact angle and area, which in turn trigger contact stress concentration. The inability to effectively correct for differences in force between probes and localized stress concentration can easily lead to abnormal wafer surface strain, which can in turn induce crack propagation or test misjudgment, severely impacting test accuracy and subsequent packaging yield.

[0004] Currently, there is a lack of a systematic optimization method that can dynamically sense the stress state of probes, modify contact stress in real time, and prevent and control crack risks. In particular, there is significant room for improvement in the response speed and accuracy of pressure compensation and control strategies in complex stress scenarios involving multi-probe arrays. Therefore, a real-time pressure optimization and control method for multi-probe arrays for wafer testing is urgently needed to achieve a synergistic balance between precise testing and wafer structural protection. Summary of the Invention

[0005] The embodiment of the present invention provides a multi-probe array real-time pressure optimization and control method for wafer testing, which can solve the problems in the prior art.

[0006] A first aspect of an embodiment of the present invention provides a method for real-time pressure optimization and control of a multi-probe array for wafer testing, comprising:

[0007] Collect real-time pressure data and wafer stress limit values ​​from the multi-probe array and establish the initial pressure distribution state of each probe;

[0008] Obtaining the lateral and longitudinal displacements of each probe during the pressurization process, calculating the actual contact area and contact angle between the probe and the wafer based on the initial pressure distribution state, calculating the stress concentration factor based on the contact area and contact angle, and correcting the probe pressure based on the stress concentration factor to obtain a corrected pressure value;

[0009] The strain rate distribution on the wafer surface is calculated based on the corrected pressure value, and strain rate mutation points are identified. The area between adjacent strain rate mutation points is divided into a stress-sensitive area. The tangential component and normal component of the force direction of the probe in the stress-sensitive area are obtained. The deflection degree of the force on the probe is calculated, and the probe pressure is compensated in real time based on the deflection degree to obtain a compensated pressure value.

[0010] The displacement increment and force increment during the probe's application of the compensation pressure value are collected, and the stress-strain ratio during the probe pressurization process is calculated. The microcrack initiation point on the wafer surface is identified based on the change trend of the stress-strain ratio. When the microcrack initiation point is detected, the optimal pressurization rate and maximum pressurization threshold are calculated;

[0011] Monitor the probe pressure in real time and trigger an alarm signal when the pressure exceeds the maximum pressurization threshold.

[0012] In an optional embodiment,

[0013] Collecting real-time pressure data and wafer stress limit values ​​from the multi-probe array and establishing the initial pressure distribution state of each probe includes:

[0014] A pressure sensor matrix is ​​used to collect real-time pressure data from a multi-probe array, and the spatial distribution relationship between the probe array position and the real-time pressure data is established to obtain the stress limit value of the wafer.

[0015] Acquire the initial pressurized state of the probe array, calculate the pressure force vector between adjacent probes, analyze the spatial distribution characteristics of the force on the probes based on the pressure force vector, obtain the initial stress state of the probe array, identify the stress concentration point in the probe array based on the initial stress state, calculate the pressure distribution gradient around the stress concentration point, determine the pressure abnormality area of ​​the probe array, and establish a pressure distribution characteristic map of the probe array;

[0016] Mapping the pressure distribution characteristic map with the wafer stress limit value to obtain a stress safety interval of the probe array; calculating a correction parameter of the probe initial pressure based on the stress safety interval;

[0017] The real-time pressure data is compensated according to the correction parameters to establish an initial pressure distribution state reflecting the force spatial characteristics of the probe.

[0018] In an optional embodiment,

[0019] The lateral displacement and longitudinal displacement of each probe during the pressurization process are obtained respectively, and the actual contact area and contact angle between the probe and the wafer are calculated according to the initial pressure distribution state. The stress concentration factor is calculated according to the contact area and contact angle. The probe pressure is corrected based on the stress concentration factor to obtain the corrected pressure value including:

[0020] A displacement sensor is used to collect the lateral and longitudinal displacements of the probe during the pressurization process, and a lateral offset value of the probe is calculated based on the lateral displacement, and a compressive deformation value of the probe is calculated based on the longitudinal displacement. The actual contact area between the probe and the wafer is calculated based on the lateral offset and compressive deformation values, and the actual contact angle of the probe is calculated based on the standard contact state.

[0021] The actual contact area is divided by the nominal contact area of ​​the probe to obtain an area variation coefficient, and the deviation between the actual contact angle and the standard contact angle is calculated to obtain an angle deviation coefficient; and a stress concentration factor is calculated based on the area variation coefficient and the angle deviation coefficient;

[0022] The stress concentration factor is compared with a preset stress safety threshold. When the stress concentration factor is less than the stress safety threshold, the probe pressure is corrected using a linear function; when the stress concentration factor is greater than or equal to the stress safety threshold, the probe pressure is corrected using a nonlinear decreasing function to obtain a corrected pressure value.

[0023] In an optional embodiment,

[0024] The strain rate distribution on the wafer surface is calculated based on the corrected pressure value, and the strain rate mutation points are identified. The area between adjacent strain rate mutation points is divided into stress-sensitive areas, including:

[0025] Calculating the displacement distribution on the wafer surface according to the corrected pressure value, and obtaining the strain tensor by taking the spatial partial derivative of the displacement distribution;

[0026] Strain tensor data are collected at multiple time points to calculate the principal strain directions and principal strain values, respectively; the principal strain values ​​are differentiated with respect to time to obtain a strain rate distribution, and a strain rate space vector field is established based on the principal strain directions;

[0027] The strain rate gradients of adjacent points in the strain rate space vector field are calculated, a strain rate gradient matrix is ​​established, the strain rate gradient matrix is ​​subjected to singular value decomposition, the main eigenvector of the strain rate change is extracted, the strain rate mutation points are identified according to the directional mutation of the main eigenvector, the strain rate differences of adjacent strain rate mutation points are calculated, and adjacent mutation point regions with continuous strain rate change characteristics are merged into stress sensitive areas.

[0028] In an optional embodiment,

[0029] Obtain the tangential and normal components of the force direction of the probe in the stress-sensitive area, calculate the deflection degree of the probe force, and compensate the probe pressure in real time based on the deflection degree. The compensated pressure values ​​include:

[0030] A local rectangular coordinate system for the probe force is established in the stress-sensitive area, and the probe force is projected onto the three coordinate axes of the local rectangular coordinate system. The normal component perpendicular to the wafer surface and the two tangential components parallel to the wafer surface are calculated respectively.

[0031] A space vector of the force on the probe is synthesized according to the normal component and the tangential component, the zenith angle and azimuth angle of the space vector in the spherical coordinate system are used as the three-dimensional deflection characteristics of the force on the probe, and the comprehensive deflection degree of the force on the probe is calculated in combination with the strain rate distribution surface;

[0032] The pressure compensation function is selected according to the numerical range of the comprehensive deflection degree: when the deflection is mainly caused by the tangential component, a linear compensation function is adopted; when the deflection is caused by both the normal component and the tangential component, a nonlinear compensation function is adopted; when the deflection causes the strain rate distribution surface to be distorted, a piecewise compensation function is adopted; the output value of the compensation function is used as the compensation amount of the probe pressure, and the compensation amount is weightedly superimposed with the corrected pressure value to obtain the compensated pressure value.

[0033] In an optional embodiment,

[0034] The displacement increment and force increment during the probe's application of the compensation pressure value are collected, the stress-strain ratio during the probe pressurization process is calculated, and the microcrack initiation point on the wafer surface is identified based on the change trend of the stress-strain ratio. When the microcrack initiation point is detected, the optimal pressurization rate and maximum pressurization threshold are calculated, including:

[0035] The displacement increment and force increment of the probe during the process of applying the compensation pressure value are collected and signal processing and normalization are performed to obtain the normalized displacement increment and normalized force increment;

[0036] Calculating the ratio of the normalized force increment to the normalized displacement increment to obtain a stress-strain ratio, extracting the stress-strain ratio using a time window of fixed length to construct a stress-strain ratio sequence, performing Fourier transform on the stress-strain ratio sequence to obtain a frequency spectrum feature of the stress-strain ratio, calculating a statistical moment of the stress-strain ratio sequence to obtain a fluctuation feature of the stress-strain ratio;

[0037] Combining the spectral features and the fluctuation features to construct a feature vector, calculating the principal component of the feature vector to obtain a stress-strain anomaly index, marking the region where the anomaly index suddenly changes as a microcrack initiation point on the wafer surface based on the spatial distribution law and time evolution characteristics of the stress-strain anomaly index, and calculating the strain energy release rate at the microcrack initiation point on the wafer surface;

[0038] The optimal pressurization rate is determined based on the corresponding relationship between the strain energy release rate and the change speed of the compensation pressure value; the change trend of the stress intensity factor at the microcrack initiation point on the wafer surface with the compensation pressure value is analyzed to determine the maximum pressurization threshold.

[0039] In an optional embodiment,

[0040] According to the spatial distribution law and time evolution characteristics of the stress-strain anomaly index, the areas where the abnormal index changes suddenly are marked as the microcrack initiation points on the wafer surface, including:

[0041] The probe contact area is divided into multiple micro-units using an adaptive grid partitioning method. The spatial gradient of the abnormal index and the Laplace operator value of each micro-unit are calculated to obtain the spatial distribution feature matrix.

[0042] Calculating the local spatial autocorrelation index of the micro-area unit based on the spatial distribution characteristic matrix, identifying the spatial clustering area of ​​the anomaly index according to the comparative relationship between the local spatial autocorrelation index and the global anomaly index mean, and calculating the distribution range of the spatial clustering area;

[0043] Performing a wavelet transform on the stress-strain anomaly index sequence to obtain a time evolution coefficient, extracting the modulus maximum of the time evolution coefficient to obtain a time mutation point, connecting the time mutation points to construct an evolution feature tree, and obtaining a scale distribution of the evolution feature tree;

[0044] The first-order change rate and the second-order change rate of the abnormal index are calculated according to the evolution feature tree, and the area of ​​the spatial aggregation region is greater than the preset judgment area, the scale distribution of the evolution feature tree is greater than the preset scale number, and the areas where the first-order change rate and the second-order change rate are both positive are marked as microcrack initiation points on the wafer surface.

[0045] According to a second aspect of an embodiment of the present invention, an electronic device is provided, including:

[0046] processor;

[0047] a memory for storing processor-executable instructions;

[0048] The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0049] According to a third aspect of an embodiment of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0050] In this embodiment, by collecting real-time pressure data and establishing an initial pressure distribution state, the contact area and contact angle are calculated in combination with the probe displacement, and the probe pressure is corrected, which effectively avoids the uneven pressure distribution problem caused by uneven probe contact in traditional methods, and improves the accuracy and reliability of wafer testing. By calculating the strain rate distribution on the wafer surface in real time, identifying the stress-sensitive area and analyzing the degree of deflection of the probe force, and performing pressure compensation based on the degree of deflection, the problem that the traditional method cannot effectively deal with uneven deformation of the wafer surface is solved, ensuring the consistency of contact between the probe and the wafer during the test process, and significantly improving the quality and stability of the test signal. By dynamically monitoring the change trend of the stress-strain ratio, the initiation point of microcracks on the wafer surface is identified in time, and the optimal pressurization rate and maximum pressurization threshold are calculated accordingly. Combined with the real-time monitoring and early warning mechanism, it effectively prevents damage to the wafer caused by excessive pressurization during the test process, reduces the test failure rate and wafer loss rate, and improves production efficiency and product yield. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of the process of a multi-probe array real-time pressure optimization and control method for wafer testing according to an embodiment of the present invention;

[0052] Figure 2 This is a comparison diagram of the test results of different probe force compensation functions according to an embodiment of the present invention;

[0053] Figure 3 Schematic diagram of local spatial autocorrelation index analysis and cluster area identification according to an embodiment of the present invention. DETAILED DESCRIPTION

[0054] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0055] The following specific embodiments are used to describe the technical solution of the present invention in detail. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0056] Figure 1 FIG. 1 is a flow chart of a method for optimizing and controlling the real-time pressure of a multi-probe array for wafer testing according to an embodiment of the present invention. Figure 1 As shown, the method includes:

[0057] Collect real-time pressure data and wafer stress limit values ​​from the multi-probe array and establish the initial pressure distribution state of each probe;

[0058] Obtaining the lateral and longitudinal displacements of each probe during the pressurization process, calculating the actual contact area and contact angle between the probe and the wafer based on the initial pressure distribution state, calculating the stress concentration factor based on the contact area and contact angle, and correcting the probe pressure based on the stress concentration factor to obtain a corrected pressure value;

[0059] The strain rate distribution on the wafer surface is calculated based on the corrected pressure value, and strain rate mutation points are identified. The area between adjacent strain rate mutation points is divided into a stress-sensitive area. The tangential component and normal component of the force direction of the probe in the stress-sensitive area are obtained. The deflection degree of the force on the probe is calculated, and the probe pressure is compensated in real time based on the deflection degree to obtain a compensated pressure value.

[0060] The displacement increment and force increment during the probe's application of the compensation pressure value are collected, and the stress-strain ratio during the probe pressurization process is calculated. The microcrack initiation point on the wafer surface is identified based on the change trend of the stress-strain ratio. When the microcrack initiation point is detected, the optimal pressurization rate and maximum pressurization threshold are calculated;

[0061] Monitor the probe pressure in real time and trigger an alarm signal when the pressure exceeds the maximum pressurization threshold.

[0062] In an optional embodiment, collecting real-time pressure data and wafer stress limit values ​​of a multi-probe array and establishing an initial pressure distribution state of each probe includes:

[0063] A pressure sensor matrix is ​​used to collect real-time pressure data from a multi-probe array, and the spatial distribution relationship between the probe array position and the real-time pressure data is established to obtain the stress limit value of the wafer.

[0064] Acquire the initial pressurized state of the probe array, calculate the pressure force vector between adjacent probes, analyze the spatial distribution characteristics of the force on the probes based on the pressure force vector, obtain the initial stress state of the probe array, identify the stress concentration point in the probe array based on the initial stress state, calculate the pressure distribution gradient around the stress concentration point, determine the pressure abnormality area of ​​the probe array, and establish a pressure distribution characteristic map of the probe array;

[0065] Mapping the pressure distribution characteristic map with the wafer stress limit value to obtain a stress safety interval of the probe array; calculating a correction parameter of the probe initial pressure based on the stress safety interval;

[0066] The real-time pressure data is compensated according to the correction parameters to establish an initial pressure distribution state reflecting the force spatial characteristics of the probe.

[0067] In one embodiment, a 16×16 pressure sensor matrix is ​​used to collect real-time pressure data of a multi-probe array. The pressure sensor matrix is ​​arranged under the wafer and can accurately capture the pressure value of each probe contact point. For an array containing 256 probes, each probe corresponds to a sensor unit in the matrix. The sampling frequency of the sensor is set to 1000Hz, and the pressure measurement accuracy reaches ±0.01N. In actual applications, when the probe contacts the wafer, the sensor array records the pressure value of each point to form a 256-dimensional pressure vector. For example, during a typical test, the collected pressure data ranges from 0.5N to 2.8N, among which the pressure value of the probe located in the edge area of ​​the array is relatively low, while the pressure value of the probe in the center area is relatively high.

[0068] At the same time, material testing is used to determine the wafer's stress limit. For example, an 8-inch silicon wafer has a bending strength of approximately 180 MPa. Considering a safety factor of 1.5, the stress limit is set at 120 MPa. Based on the wafer thickness and probe tip area, this stress limit is converted to a maximum allowable pressure of 3.2 N per probe. This value serves as an important reference for subsequent stress analysis.

[0069] When establishing the initial pressurized state of the probe array, the system first records the pressure values ​​of all probes under standard test conditions. Taking a 16×16 probe array as an example, a 256-element initial pressure data set can be obtained through the pressure sensor matrix. For a probe at position (i, j), the pressure force vector between it and its adjacent probes is calculated. Specifically, the pressure difference between the probe at position (i, j) and the four adjacent probes at positions (i-1, j), (i+1, j), (i, j-1), and (i, j+1) is calculated to obtain the pressure gradients in the four directions. For example, in one test, the pressure value of the probe at position (8, 8) was 2.1N, while the pressure values ​​of the four adjacent probes above, below, to the left, and to the right were 1.9N, 2.3N, 2.0N, and 2.2N, respectively. Therefore, the pressure force vectors between this probe and its four adjacent probes are 0.2N (up), -0.2N (down), 0.1N (left), and -0.1N (right), respectively.

[0070] By analyzing the distribution of pressure force vectors across the entire probe array, the system can identify stress concentration points. Stress concentration points typically appear as locations where the pressure values ​​of surrounding probes differ significantly from those at that point. The stress concentration index is defined as the square root of the sum of the squares of the pressure differences between a probe and its adjacent probes. When this index exceeds a preset threshold of 0.5N, the point is marked as a stress concentration point. In actual testing, three stress concentration points were found in the 16×16 probe array, located at coordinates (4, 5), (10, 12), and (14, 8), with stress concentration indices of 0.62N, 0.58N, and 0.71N, respectively.

[0071] For each stress concentration point, the system further calculates the pressure distribution gradient in the surrounding area. Taking point (4, 5) as an example, the pressure change rate within its 3×3 neighborhood is analyzed, resulting in a radial pressure gradient of 0.15 N / mm and a tangential pressure gradient of 0.08 N / mm. Based on a preset threshold of 0.1 N / mm, areas where the radial pressure gradient exceeds the threshold are marked as pressure anomalies. Using this method, the system identified five pressure anomaly areas in the entire probe array, with a total area accounting for approximately 12% of the probe array area.

[0072] Based on these analysis results, the system generates a visual map characterizing the pressure distribution across the probe array. This map uses different colors to represent different pressure levels: red indicates high-pressure areas near the stress limit, blue indicates low-pressure areas, and yellow indicates moderate-pressure areas. The map clearly displays the distribution of stress concentration points and areas of abnormal pressure, providing a visual reference for subsequent pressure adjustments.

[0073] Next, the pressure distribution characteristic diagram is mapped to the wafer stress limit value. For each probe position, the ratio of its pressure value to the stress limit value is calculated, which is called the stress safety factor. When the safety factor is less than 1, it means that the pressure value at that position is within the safety range; when the safety factor is close to or exceeds 1, it means that there is a potential risk at that position. In the probe array analyzed, about 5% of the probes have a safety factor exceeding 0.8, which requires special attention and adjustment. Based on this mapping result, the system determines that the stress safety range of the probe array is 0.1-0.75, that is, the probe pressure should be controlled between 0.32N and 2.4N.

[0074] Based on the stress safety interval, the system calculates a correction parameter for the initial pressure of each probe. The calculation of the correction parameter takes into account two factors: the deviation between the current probe pressure and the safety interval, and the impact of the probe on the surrounding pressure distribution. Taking probe (14, 8) as an example, its initial pressure is 2.8N, exceeding the safety upper limit of 2.4N. The calculated pressure correction is -0.4N. At the same time, considering that this point is a stress concentration point, its correction will affect the pressure distribution of surrounding probes. Therefore, a smoothing factor of 0.85 is added to the correction parameter, and the final correction parameter is -0.34N.

[0075] The real-time pressure data is compensated according to the correction parameters to establish an initial pressure distribution state that reflects the spatial characteristics of the force applied to the probes. The system applies the correction parameters to the pressure control mechanism to adjust the pressurization parameters of each probe. In a typical adjustment, the system decompressed 16 probes and pressurized 12 probes, making the pressure distribution of the entire array more uniform, and all probe pressure values ​​fell within the stress safety range. The adjusted standard deviation of the pressure distribution dropped from the initial 0.48N to 0.21N, and the pressure uniformity was significantly improved. In this way, the system successfully established a balanced, safe, and reliable initial pressure distribution state for the probe array.

[0076] In this embodiment, real-time pressure perception and fine spatial distribution modeling can be achieved during the pressurization process of a multi-probe array. By constructing a spatial mapping relationship between the probe position and the pressure, the force characteristics of the probe array at different positions can be accurately characterized. By analyzing the pressure vectors between adjacent probes, local stress concentration points and pressure abnormality areas can be effectively identified, and the ability to perceive initial force abnormalities can be significantly improved. By combining the stress limit value of the wafer to construct a stress safety interval, adaptive correction of the initial pressurization state can be achieved, ensuring that the wafer structure is within a safe pressure range at the beginning of the test. This method can complete the pre-optimization and compensation of the probe pressure in the test preparation stage, provide an accurate baseline for subsequent pressure control, help reduce the risk of microcracks, and improve overall test reliability and yield.

[0077] In an optional embodiment, the lateral displacement and longitudinal displacement of each probe during the pressurization process are respectively obtained, the actual contact area and contact angle between the probe and the wafer are calculated based on the initial pressure distribution state, the stress concentration factor is calculated based on the contact area and contact angle, and the probe pressure is corrected in combination with the stress concentration factor to obtain the corrected pressure value, which includes:

[0078] A displacement sensor is used to collect the lateral and longitudinal displacements of the probe during the pressurization process, and a lateral offset value of the probe is calculated based on the lateral displacement, and a compressive deformation value of the probe is calculated based on the longitudinal displacement. The actual contact area between the probe and the wafer is calculated based on the lateral offset and compressive deformation values, and the actual contact angle of the probe is calculated based on the standard contact state.

[0079] The actual contact area is divided by the nominal contact area of ​​the probe to obtain an area variation coefficient, and the deviation between the actual contact angle and the standard contact angle is calculated to obtain an angle deviation coefficient; and a stress concentration factor is calculated based on the area variation coefficient and the angle deviation coefficient;

[0080] The stress concentration factor is compared with a preset stress safety threshold. When the stress concentration factor is less than the stress safety threshold, the probe pressure is corrected using a linear function; when the stress concentration factor is greater than or equal to the stress safety threshold, the probe pressure is corrected using a nonlinear decreasing function to obtain a corrected pressure value.

[0081] During the implementation process, a high-precision displacement sensor is first used to measure the lateral and longitudinal displacement of the probe during pressurization. With a resolution of 0.01 microns and a sampling frequency of 1000 Hz, this displacement sensor accurately captures minute displacement changes during contact between the probe and the wafer. The displacement sensor is fixed to the base of the probe card, maintaining a fixed position relative to the probe, ensuring accurate and repeatable measurement results.

[0082] After displacement data collection is complete, the data processing system calculates the probe's lateral offset and compressive deformation. The lateral offset is the horizontal difference between the lateral displacement and the probe's initial position, while the compressive deformation is the vertical difference between the longitudinal displacement and the probe's initial height. For example, if a probe's lateral displacement is measured to be 15 microns and its longitudinal displacement is 80 microns, combined with the probe's initial position data (lateral position: 0 microns, longitudinal position: 100 microns), the calculated lateral offset is 15 microns and the compressive deformation is 20 microns.

[0083] Based on the lateral offset and compression deformation values ​​calculated above, the actual contact area between the probe and the wafer is further calculated. The front end of the probe is typically a rectangular metal tip with a cross-sectional area of ​​25 square microns. Under standard conditions, the nominal contact area between the probe and the wafer is 25 square microns. When the probe undergoes lateral offset and compression deformation, the contact area changes. The actual contact area can be determined by the functional relationship between the probe front end geometry and the lateral offset and compression deformation values. In this embodiment, when the lateral offset value is 15 microns and the compression deformation value is 20 microns, the actual contact area increases to 32 square microns. The actual contact angle of the probe is also calculated. Under standard contact conditions, the standard contact angle between the probe and the wafer is 90 degrees, i.e., perpendicular contact. The actual contact angle can be determined by the inverse tangent functional relationship between the lateral offset value and the compression deformation value. In this embodiment, when the lateral offset value is 15 microns and the compression deformation value is 20 microns, the actual contact angle is approximately 73.3 degrees, which deviates by 16.7 degrees from the standard contact angle. Next, the area variation coefficient and angle deviation coefficient are calculated. The area variation coefficient is equal to the actual contact area divided by the nominal contact area, and the angle deviation coefficient is equal to the deviation between the actual contact angle and the standard contact angle divided by 90 degrees. In this embodiment, the area variation coefficient is 32 / 25 = 1.28, and the angle deviation coefficient is 16.7 / 90 = 0.186.

[0084] The stress concentration factor is calculated based on the area variation coefficient and the angular deviation coefficient. The stress concentration factor comprehensively considers the effects of area variation and angular deviation on the probe pressure distribution and is obtained by taking the weighted sum of the area variation coefficient and the angular deviation coefficient. In this example, the area variation coefficient is weighted 0.6, and the angular deviation coefficient is weighted 0.4. The calculated stress concentration factor is 1.28 × 0.6 + 0.186 × 0.4 = 0.842.

[0085] The probe pressure is corrected based on the calculated stress concentration factor. First, the stress concentration factor is compared with a preset stress safety threshold, which in this embodiment is set to 0.8. Because the calculated stress concentration factor of 0.842 is greater than the stress safety threshold of 0.8, a nonlinear decreasing function is used to correct the probe pressure.

[0086] The nonlinear decreasing function is designed to decay exponentially, with the corrected pressure value equal to the original pressure value multiplied by the exponential function coefficient. In this embodiment, when the original probe pressure is 50 grams-force, the correction coefficient is 0.85, resulting in a corrected pressure value of 42.5 grams-force. This correction method ensures that if the stress concentration factor exceeds the safety threshold, the probe pressure can be appropriately reduced to avoid excessive stress damage to the wafer.

[0087] In this embodiment, by accurately collecting the lateral and longitudinal displacements of the probe during the pressurization process, the actual contact area and contact angle are dynamically restored, thereby accurately evaluating the true stress state between the probe and the wafer. By constructing the area variation coefficient and the angle deviation coefficient, and calculating the stress concentration factor based on this, the non-ideal state during the contact process can be effectively identified, and the sensitivity and resolution of stress monitoring can be improved. Based on the comparison between the stress concentration factor and the safety threshold, a piecewise function is used to perform linear or nonlinear correction on the probe pressure, realizing automatic identification and flexible response control of potential stress concentration areas, and reducing the risk of local stress exceeding the limit. The overall solution enhances the accuracy and adaptability of probe pressure regulation, helps to avoid wafer damage caused by uneven contact, and improves structural safety and finished product yield during the testing phase.

[0088] In an optional embodiment, calculating the strain rate distribution on the wafer surface according to the corrected pressure value, identifying strain rate mutation points, and dividing the area between adjacent strain rate mutation points into stress sensitive areas includes:

[0089] Calculating the displacement distribution of the wafer surface according to the corrected pressure value, and obtaining the strain tensor by taking the spatial partial derivative of the displacement distribution;

[0090] Strain tensor data are collected at multiple time points to calculate the principal strain directions and principal strain values, respectively; the principal strain values ​​are differentiated with respect to time to obtain a strain rate distribution, and a strain rate space vector field is established based on the principal strain directions;

[0091] The strain rate gradients of adjacent points in the strain rate space vector field are calculated, a strain rate gradient matrix is ​​established, the strain rate gradient matrix is ​​subjected to singular value decomposition, the main eigenvector of the strain rate change is extracted, the strain rate mutation points are identified according to the directional mutation of the main eigenvector, the strain rate differences of adjacent strain rate mutation points are calculated, and adjacent mutation point regions with continuous strain rate change characteristics are merged into stress sensitive areas.

[0092] For example, the entire process begins by obtaining corrected pressure values ​​on the wafer surface. These corrected pressure values ​​are measured using a pressure sensor array, calibrated, and filtered to eliminate noise. For example, in a 300mm wafer test case, a 16×16 pressure sensor array with a sampling frequency of 100Hz is used to obtain a corrected pressure value matrix P(x, y, t), where x and y represent spatial coordinates and t represents time.

[0093] The displacement distribution of the wafer surface is calculated based on the corrected pressure value. This step uses the finite element analysis method to establish a wafer mechanical model and solve the displacement field based on the corrected pressure value. In actual operation, the wafer is discretized into grid units, and the corresponding corrected pressure value is applied to each node. The node displacement is obtained by solving the mechanical equilibrium equation. Taking the above-mentioned 300mm wafer as an example, it is discretized into 10,000 grid units, each unit size is 3mm×3mm, and the three-dimensional displacement field U(x, y, z, t) is calculated, where the z direction represents the thickness direction of the wafer.

[0094] The strain tensor is obtained by taking the spatial partial derivative of the displacement distribution. The strain tensor E(x, y, t) is constructed by calculating the gradient of the displacement field in all directions in space. For each grid node on the wafer surface, the normal strain in the x and y directions and the shear strain in the xy direction are calculated to form a 2×2 strain tensor. In this example, for the node at position (150mm, 150mm), the strain tensor values ​​at time t=10s may be: Exx=0.0023, Eyy=0.0019, Exy=0.0008.

[0095] Strain tensor data is collected at multiple time points, and eigendecomposition is performed on the strain tensor at each moment to calculate the principal strain directions and values. During the eigendecomposition process, the eigenvalues ​​and eigenvectors of the strain tensor are solved. The eigenvalues ​​represent the principal strain values, and the eigenvectors represent the principal strain directions. For the aforementioned nodes, 100 time points within a 1-second interval are analyzed to obtain a time series of principal strain values. For example, at t = 10 seconds, the calculated principal strain values ​​are λ1 = 0.0026 and λ2 = 0.0016, and the principal strain direction angles are θ = 23° and 113°.

[0096] The strain rate distribution is obtained by differentiating the principal strain values ​​with respect to time. The principal strain rate is obtained by calculating the difference between the principal strain values ​​at adjacent time points and dividing it by the time interval. For each spatial location, the maximum and minimum principal strain rates are calculated. In this example, the maximum principal strain rate at position (150 mm, 150 mm) is 0.00052 / s, and the minimum principal strain rate is 0.00031 / s.

[0097] A strain rate space vector field is established based on the principal strain directions. The principal strain rate values ​​are projected along the corresponding principal strain directions to construct a two-dimensional vector field V(x, y, t). The magnitude of the vector field represents the magnitude of the strain rate, while its direction indicates the direction of principal strain variation. In actual wafer applications, the vector field exhibits a distribution pattern radiating from the center to the edge, with vortices or convergence points appearing in certain areas.

[0098] Calculate the strain rate gradients at adjacent points in the strain rate space vector field. For each grid node, calculate the strain rate difference between it and its surrounding nodes, and construct the strain rate gradient matrix G. In the example of a 300mm wafer, a 3×3 sliding window is used to calculate the local gradient. The gradient matrix for each point is 2×2 dimensional, representing the rate of change of strain rate in the x and y directions.

[0099] Singular value decomposition (SVD) is performed on the strain rate gradient matrix to extract the principal eigenvectors of the strain rate variation. This SVD yields eigenvectors and corresponding singular values ​​that describe the primary directions of strain rate variation. In the test case, for a node in the edge region, the maximum singular value was 0.00012 / s / mm, and the corresponding eigenvector direction was 78°, indicating the direction of the most significant strain rate variation at that point.

[0100] Strain rate mutation points are identified based on the directional changes of the principal eigenvectors. The difference in the direction of the principal eigenvectors at adjacent locations is calculated. When the difference exceeds a preset threshold, the point is marked as a strain rate mutation point. In practice, the directional difference threshold is set at 30°. A mutation point is identified when the difference in the direction of the principal eigenvectors between two adjacent points exceeds 30°. In the 300mm wafer case, a total of 87 strain rate mutation points were identified, primarily located at the junction of the wafer edge and center.

[0101] Calculate the strain rate difference between adjacent strain rate mutation points. For each identified mutation point, calculate the magnitude of the strain rate change in the region between the adjacent mutation points. This difference calculation uses the Euclidean distance metric, taking into account both the magnitude and direction of the strain rate change. In the test cases, the strain rate difference between adjacent mutation points ranged from 0.0001 / s to 0.0008 / s.

[0102] Adjacent mutation points with continuous strain rate variations are merged into stress-sensitive zones. When the strain rate difference between adjacent mutation points is less than a threshold of 0.0003 / s and the direction of the main eigenvector changes smoothly, the area between these points is merged into a continuous stress-sensitive zone. Ultimately, five major stress-sensitive zones were identified on a 300mm wafer: located near the wafer center, around the edge, and in the middle of four orthogonal directions, totaling approximately 23% of the wafer surface area.

[0103] In this embodiment, by deducing the displacement distribution of the wafer surface based on the corrected pressure value, and further calculating the spatial strain tensor and principal strain rate, dynamic monitoring of the microscopic deformation process of the wafer surface is achieved. By establishing a strain rate space vector field and introducing the singular value decomposition analysis of the strain rate gradient matrix, not only can the main characteristic direction of the strain rate change be accurately extracted, but also the strain rate mutation point corresponding to the mutation of the principal strain direction can be efficiently identified. Based on these mutation points, areas with continuous strain rate difference characteristics are delineated, and stress concentration areas with more sensitive structural responses are effectively distinguished. This method significantly improves the recognition accuracy and spatial resolution of local stress anomalies on the wafer, provides a high-reliability criterion for subsequent force compensation and structural protection, helps to suppress the risk of microcrack initiation, and ensures the stability of the test process and the structural integrity of the device.

[0104] In an optional embodiment, obtaining the tangential component and the normal component of the force direction of the probe in the stress-sensitive area, calculating the deflection degree of the force applied to the probe, and performing real-time compensation for the probe pressure based on the deflection degree to obtain the compensated pressure value includes:

[0105] A local rectangular coordinate system for the probe force is established in the stress-sensitive area, and the probe force is projected onto the three coordinate axes of the local rectangular coordinate system. The normal component perpendicular to the wafer surface and the two tangential components parallel to the wafer surface are calculated respectively.

[0106] A space vector of the force on the probe is synthesized according to the normal component and the tangential component, the zenith angle and azimuth angle of the space vector in the spherical coordinate system are used as the three-dimensional deflection characteristics of the force on the probe, and the comprehensive deflection degree of the force on the probe is calculated in combination with the strain rate distribution surface;

[0107] The pressure compensation function is selected according to the numerical range of the comprehensive deflection degree: when the deflection is mainly caused by the tangential component, a linear compensation function is adopted; when the deflection is caused by both the normal component and the tangential component, a nonlinear compensation function is adopted; when the deflection causes the strain rate distribution surface to be distorted, a piecewise compensation function is adopted; the output value of the compensation function is used as the compensation amount of the probe pressure, and the compensation amount is weightedly superimposed with the corrected pressure value to obtain the compensated pressure value.

[0108] For example, the stress-sensitive area is first identified based on the strain rate distribution characteristics of the wafer surface, and the actual force direction of the probe is spatially decomposed within the area. Then, by analyzing the force deflection characteristics composed of its tangential and normal components, a suitable pressure compensation strategy is determined, and the compensation strategy is applied to the original corrected pressure value to obtain a real-time compensated pressure value that is more in line with the stress response state of the wafer.

[0109] Specifically, the spatial location of the probes within the stress-sensitive region is determined. In the previous step, local regions with significant strain rate gradients were identified and defined as stress-sensitive regions. By recording the physical coordinates of each probe in the probe array and performing a spatial overlap analysis with the locations of the stress-sensitive regions, the set of probes within the stress-sensitive region is determined.

[0110] In order to more accurately analyze the force direction and deflection state of the probe within the stress-sensitive area, a local rectangular coordinate system must be established for each probe. The Z axis of this coordinate system is defined as the direction perpendicular to the wafer surface, i.e., the normal direction. The X and Y axes are parallel to the wafer surface and extend along the wafer processing reference edge and perpendicular reference edge, respectively, serving as orthogonal bases for the tangential direction. The establishment of this coordinate system relies on the spatial attitude sensor system of the wafer processing platform. By reading the pitch and yaw angle data of the wafer carrier, the coordinate system direction is aligned with the normal direction of the wafer surface in real time.

[0111] A triaxial stress sensor collects real-time spatial force data on the probe during application. This sensor measures forces in three dimensions simultaneously, outputting a three-dimensional load vector at the probe tip. By projecting this three-dimensional force vector onto the local rectangular coordinate system established above, we obtain a normal component perpendicular to the wafer surface and two tangential components parallel to the wafer surface.

[0112] The normal component represents the main pressure applied by the probe to the wafer and is the key component that directly affects the degree of deformation in the contact area. The tangential component reflects the horizontal slip tendency of the probe during contact, which may cause displacement or shear deformation of the contact point and induce local stress concentration. Taking a certain probe as an example, its force vector is expressed as a main pressure Fz along the Z axis during measurement, while the tangential components along the X and Y axes are Fx and Fy, respectively. Fx, Fy, and Fz are normalized and combined into a spatial force vector, and its directional properties are expressed in spherical coordinates, where the zenith angle represents the angle with the normal and the azimuth represents the direction of the tangential component in the XY plane.

[0113] Based on these three-dimensional directional characteristics, they are further integrated with the strain rate distribution surface of the probe region for analysis. This strain rate distribution surface is calculated based on previously generated multi-time series principal strain tensor data and constructed in space using a three-dimensional interpolation method. The spatial deflection direction of each probe is compared with the strain rate gradient direction, and metrics such as the angle difference and overlapping projected area are calculated to quantify the impact of the deflection on the local stress field, thereby defining the overall degree of probe deflection.

[0114] After the degree of deflection is determined, an appropriate pressure compensation function is selected based on the numerical range in which it falls. The compensation function is a multi-segment function set, with different function forms set according to the deflection behavior classification. When the deflection mainly manifests as slip along the tangential direction, that is, Fx and Fy are significant while Fz is close to stable, a linear compensation function is used. This function has a simple form and the compensation amplitude is proportional to the degree of deflection. When Fx, Fy, and Fz are all significant, it indicates that the probe may have an overall rotation or torsional deformation trend. In this case, a nonlinear compensation function is used, which has a faster response speed and is suitable for dealing with complex stress states. If the deflection behavior has affected the continuity of the strain rate surface, such as the presence of obvious inflection points or local distortion, a segmented compensation function is used, with different compensation slopes corresponding to different deflection degree segments, to achieve fine-grained adjustment.

[0115] The output of the compensation function is the pressure compensation amount, and its unit is the change in pressure intensity. This compensation amount does not directly replace the original corrected pressure value, but is weighted and superimposed with the corrected pressure value. The weighting coefficient is determined by the normalized value of the probe deflection degree, that is, the greater the deflection, the higher the weight of the compensation amount in the total pressure. In a specific implementation, for a group of probes with a medium degree of deflection, the corrected pressure value is P0, and the compensation amount output by the nonlinear compensation function is ΔP. ​​The normalized value of the deflection degree is α, then the final compensated pressure value P is: P = (1-α)·P0 + α·(P0 + ΔP), realizing dynamic correction of the real-time pressure of the probe.

[0116] To ensure the timeliness and stability of compensation calculations, all calculations are performed by an embedded real-time controller. This controller uses a pre-set library of compensation function templates and a sliding time window to update deflection assessment results in real time. This sliding window mechanism mitigates interference caused by sudden signal changes and improves the accuracy of deflection trend assessment.

[0117] The above implementation effectively achieves dynamic, adaptive adjustment of probe pressure, improving the accuracy and reliability of multi-probe arrays during wafer testing, dicing, and other force-controlled operations. For example, during testing of a highly stressed silicon wafer, the original probe may develop a localized crack in a corner due to slight deflection. With this compensation mechanism, the probe can identify the force direction before entering that area and appropriately reduce pressure, ensuring test integrity and preventing new cracks.

[0118] This implementation method establishes a complete set of technical chains including local coordinates, spatial projection, deflection modeling, function compensation, and pressure fusion to open up the monitoring and control loop of the probe's mechanical behavior. It can adapt to the high-sensitivity force control requirements under complex stress backgrounds and provide safer and more intelligent pressure control solutions for scenarios such as precision semiconductor packaging and microstructure detection.

[0119] In the prior art, multi-probe arrays are usually adjusted only based on normal pressure, ignoring the probe deflection problem caused by uneven force, making it difficult to accurately deal with local strain anomalies on the wafer surface, resulting in delayed stress compensation response, which can easily cause microcracks or test errors. The present application constructs a local coordinate system for probe force in the stress-sensitive area, and obtains the spatial components of the actual force on the probe by projecting the force vector to the normal and tangential directions, and then calculates its three-dimensional deflection characteristics. This improvement breaks through the limitation of existing methods that only rely on scalar pressure values, and realizes the vectorized expression of the probe's force state. Furthermore, the present application flexibly selects linear, nonlinear or piecewise compensation functions based on the degree of correlation between the probe deflection characteristics and the strain rate distribution, so that the compensation strategy has adaptive capabilities and can implement refined pressure adjustments for different deflection causes. Compared with traditional pressure compensation methods that rely on empirical rules or static functions, this solution uses the degree of force deflection as the core criterion to dynamically optimize the probe pressurization behavior. The starting point of this improvement is to accurately identify and respond in real time to the perturbations in the wafer stress field caused by abnormal probe force, thereby improving the targetedness and effectiveness of the compensation strategy. Ultimately, this achieves real-time and personalized probe pressure control, significantly enhancing wafer structural protection and improving overall stability and test reliability during the wafer testing phase.

[0120] Figure 2 This is a comparison chart of the test results of different probe force compensation functions according to the embodiment of the present invention. Figure 2 The figure shows a comparison of the compensation efficiency of three different probe force compensation functions in three different scenarios. The data shows that the linear compensation function performs best in scenarios dominated by tangential forces (92.5%), but performs poorly in scenarios with high strain rate distortion (65.7%). The nonlinear compensation function performs best in scenarios with mixed normal and tangential forces (94.2%), while the segmented compensation function performs exceptionally well in scenarios with high strain rate distortion (93.5%). Therefore, different types of mechanical environments require matching corresponding compensation functions to achieve optimal probe pressure compensation.

[0121] In an optional embodiment, collecting the displacement increment and force increment during the process of applying the compensation pressure value to the probe, calculating the stress-strain ratio during the probe pressurization process, identifying the microcrack initiation point on the wafer surface based on the change trend of the stress-strain ratio, and calculating the optimal pressurization rate and maximum pressurization threshold when the microcrack initiation point is detected includes:

[0122] The displacement increment and force increment of the probe during the process of applying the compensation pressure value are collected and signal processing and normalization are performed to obtain the normalized displacement increment and normalized force increment;

[0123] Calculating the ratio of the normalized force increment to the normalized displacement increment to obtain a stress-strain ratio, extracting the stress-strain ratio using a time window of fixed length to construct a stress-strain ratio sequence, performing Fourier transform on the stress-strain ratio sequence to obtain a frequency spectrum feature of the stress-strain ratio, calculating a statistical moment of the stress-strain ratio sequence to obtain a fluctuation feature of the stress-strain ratio;

[0124] Combining the spectral features and the fluctuation features to construct a feature vector, calculating the principal component of the feature vector to obtain a stress-strain anomaly index, marking the region where the anomaly index suddenly changes as a microcrack initiation point on the wafer surface based on the spatial distribution law and time evolution characteristics of the stress-strain anomaly index, and calculating the strain energy release rate at the microcrack initiation point on the wafer surface;

[0125] The optimal pressurization rate is determined based on the corresponding relationship between the strain energy release rate and the change speed of the compensation pressure value; the change trend of the stress intensity factor at the microcrack initiation point on the wafer surface with the compensation pressure value is analyzed to determine the maximum pressurization threshold.

[0126] For example, it is first necessary to obtain the raw data during the probe pressurization process. The displacement increment and force increment during the process of applying the compensated pressure value of the probe are respectively collected by the displacement sensor and the force sensor. The sampling frequency is set to 1000Hz to ensure that the rapidly changing mechanical response characteristics can be captured. For example, when performing a probe test on an 8-inch wafer, the probe pressurization rate is 0.1mm / s, the acquisition time is 10 seconds, and the displacement and force data of 10,000 sampling points can be obtained.

[0127] The collected raw data is preprocessed. First, median filtering is used to remove outliers, and the filter window length is set to 5 sampling points. Then a bandpass filter is used to filter the signal, and the passband is set to 1-100Hz to remove high-frequency noise and low-frequency drift. The filtered signal is then normalized, and the normalization method uses maximum and minimum value normalization. Specifically, for the displacement increment sequence x(t), the normalization formula is: norm(t) = (x (t) -x min ) / (xmax -x min ), where x max and x min are the maximum and minimum values ​​of the sequence respectively. The normalization method of the force increment sequence y(t) is the same.

[0128] The normalized ratio of force increment to displacement increment is calculated to obtain a stress-strain ratio series. This stress-strain ratio series is extracted using a fixed-length time window for subsequent analysis. The window length is set to 256 sampling points, with a 50% overlap between adjacent windows. For example, for data with 10,000 sampling points, 78 time window segments can be obtained.

[0129] A Fourier transform is performed on the stress-strain ratio sequence within each time window to obtain spectral characteristics. A Hanning window function is used for windowing to reduce spectral leakage. The power spectral density is calculated, and the energy contributions of three characteristic frequency bands are extracted: the 0-10 Hz band reflects quasi-static deformation, the 10-50 Hz band reflects elastic deformation, and the 50-100 Hz band reflects local damage. For normal wafer materials, the energy contributions of these three frequency bands are typically 65%, 30%, and 5%. When microcracks are present, the energy contribution of the high-frequency band increases significantly.

[0130] The statistical moment characteristics of the stress-strain ratio series are also calculated. These include the mean, which reflects the overall stiffness; the standard deviation, which characterizes the dispersion of the mechanical response; the skewness, which describes the asymmetry of the distribution; and the kurtosis, which reflects the peaked nature of the distribution. A sliding time window is used to calculate the dynamic changes in these statistics. For example, for a normal wafer, the skewness is typically close to 0 and the kurtosis is close to 3, indicating a near-normal distribution. However, when microcracks occur, the distribution deviates significantly.

[0131] The band energy features and statistical moment features are combined to construct a 12-dimensional feature vector. The first three dimensions represent the band energy proportions, and the last nine dimensions represent the statistical moment features of the three time windows. Considering the correlation between features, principal component analysis (PCA) is used for dimensionality reduction. First, the eigenvectors are standardized, and the feature covariance matrix is ​​calculated. The eigenvalues ​​and eigenvectors are then calculated and sorted in descending order of eigenvalue. The top k principal components with a cumulative contribution rate of 95% are selected.

[0132] The selected principal components are weighted and combined to construct the stress-strain anomaly index. The weight coefficients are determined by minimizing the reconstruction error. For example, for a certain test data set, the first four principal components with weight coefficients of 0.4, 0.3, 0.2, and 0.1, respectively, can explain 95.8% of the variance of the original features.

[0133] The spatial distribution of the anomaly index was analyzed. The probe contact area was divided into a 10×10 grid, with each grid cell measuring 100×100 microns. The mean of the anomaly index for each grid cell was calculated, and a spatial distribution map was constructed. The watershed algorithm was used to segment the distribution map and identify clusters of anomaly indices. The area, shape, and orientation of these clusters can reflect the development characteristics of microcracks.

[0134] Track the temporal evolution of the anomaly index. Calculate the first-order difference of the anomaly index to obtain the rate of change, and the second-order difference to obtain the acceleration. A region is marked as a microcrack initiation point when it simultaneously meets the following conditions: the anomaly index exceeds three standard deviations of the background value; the rate of change is consistently positive with significant acceleration; and the spatial distribution exhibits localized clustering. For example, in one test, a circular region approximately 80 microns in diameter was detected that met these conditions. The center of this region was designated as the microcrack initiation point.

[0135] After the microcrack initiation point is determined, the strain energy release rate at that point is calculated. The strain energy release rate is equal to the elastic strain energy released per unit time and can be calculated by integrating the force-displacement curve. For example, for the detected microcrack initiation point, its strain energy release rate is 2.5×10 -6 J / s.

[0136] The optimal pressurization rate is determined based on the corresponding relationship between the strain energy release rate and the speed of change of the compensation pressure value. A relationship model between the two is established through piecewise linear regression. When the strain energy release rate is less than the critical value, a faster pressurization rate can be maintained; when it approaches the critical value, the pressurization rate needs to be reduced to prevent unstable crack propagation. For example, when the strain energy release rate reaches 1×10 -6 When the pressure is increased by 100 J / s, the pressing speed is reduced from 0.1 mm / s to 0.05 mm / s.

[0137] At the same time, the stress intensity factor at the microcrack initiation point is analyzed as a function of the compensation pressure. The stress intensity factor can be obtained by inverting the displacement field. When the stress intensity factor is close to the fracture toughness of the material, the pressure value is determined to be the maximum pressure threshold. For example, for silicon wafers, the fracture toughness is about 0.9 MPa·m 0.5 , the corresponding maximum pressure threshold is 0.5N.

[0138] Based on the determined optimal pressurization rate and maximum pressurization threshold, the probe pressurization parameters are adjusted in real time. These parameters are input into the pressure controller via a closed-loop control system, enabling precise control of the pressurization process and preventing unstable microcrack propagation. Simultaneously, displacement and force increments are continuously collected for real-time monitoring and parameter optimization.

[0139] In this embodiment, early identification of microcracks and optimization of dynamic pressurization strategies during wafer testing can be achieved, effectively improving test accuracy and wafer integrity. Through normalization processing and stress-strain ratio analysis, the signal of material microstructural changes can be accurately captured, and an anomaly index can be constructed by combining the spectrum and fluctuation characteristics to achieve precise positioning of the microcrack initiation point. At the same time, the optimal pressurization rate and maximum pressurization threshold are determined based on the strain energy release rate and pressure change trend to avoid crack propagation, improve the safety and controllability of the pressurization process, and thus ensure the stability of probe testing and the yield of wafer products.

[0140] In an optional embodiment, marking the region where the abnormal index suddenly changes as the microcrack initiation point on the wafer surface according to the spatial distribution law and time evolution characteristics of the abnormal stress and strain index includes:

[0141] The probe contact area is divided into multiple micro-units using an adaptive grid partitioning method. The spatial gradient of the abnormal index and the Laplace operator value of each micro-unit are calculated to obtain the spatial distribution feature matrix.

[0142] Calculating the local spatial autocorrelation index of the micro-area unit based on the spatial distribution characteristic matrix, identifying the spatial clustering area of ​​the anomaly index according to the comparative relationship between the local spatial autocorrelation index and the global anomaly index mean, and calculating the distribution range of the spatial clustering area;

[0143] Performing a wavelet transform on the stress-strain anomaly index sequence to obtain a time evolution coefficient, extracting the modulus maximum of the time evolution coefficient to obtain a time mutation point, connecting the time mutation points to construct an evolution feature tree, and obtaining a scale distribution of the evolution feature tree;

[0144] The first-order change rate and the second-order change rate of the abnormal index are calculated according to the evolution feature tree, and the area of ​​the spatial aggregation region is greater than the preset judgment area, the scale distribution of the evolution feature tree is greater than the preset scale number, and the areas where the first-order change rate and the second-order change rate are both positive are marked as microcrack initiation points on the wafer surface.

[0145] For example, during wafer probe inspection, microcracks may occur in the contact area, and the identification of these areas first requires an adaptive meshing method. This method automatically adjusts the local mesh density based on the initial contact stress. Specifically, a Cartesian coordinate system is established in the probe contact area with the contact point as the center and expanded outward. The initial mesh size is 5 microns × 5 microns. Through iterative calculation, when the local stress gradient exceeds 200 MPa / μm, the corresponding mesh is subdivided into 4 sub-grids, each with a size of 2.5 microns × 2.5 microns; when the stress gradient exceeds 400 MPa / μm, it is further subdivided to 1.25 microns × 1.25 microns. After 3 rounds of iterations, a non-uniform mesh containing more than 1,200 micro-area units is finally formed, and the mesh density is highest in the stress concentration area.

[0146] The spatial gradient of the anomaly index and the Laplace operator value are calculated for each micro-unit. The anomaly index is defined as the percentage of deviation between the actual stress and strain values ​​and the theoretical values. Within each micro-unit, 9 sampling points are selected to calculate the average anomaly index of the unit. The spatial gradient is obtained by dividing the difference in the anomaly index between adjacent units by their spatial distance, and the typical value range is 0.05-0.3 / μm. The Laplace operator value is calculated by the weighted average of the anomaly index of the central unit and the surrounding 8 units, characterizing the local curvature change of the anomaly index. The value is close to 0 in the normal area, while the potential crack area is usually greater than 0.15 / μm². The spatial gradients and Laplace operator values ​​of all micro-units together constitute a spatial distribution feature matrix, and the matrix dimension is consistent with the number of micro-units.

[0147] A moving window method with a window size of 7×7 micro-cells is used to calculate the local spatial autocorrelation index based on the spatial distribution feature matrix. The Moran index is calculated for each anomaly index within each window to characterize the degree of spatial clustering. In actual inspections, the Moran index in normal areas fluctuates between -0.1 and 0.1, while the Moran index in potential crack areas is typically greater than 0.35. Spatially clustered areas are identified by comparing the local autocorrelation index with the global anomaly index mean. When the Moran index of a local area exceeds 2.5 times the global anomaly index mean, the area is marked as a highly clustered area. A region-growing algorithm is used to determine the boundaries of the clustered areas. Starting from the point with the highest Moran index, adjacent cells that meet the threshold condition are gradually incorporated until the Moran index of all boundary points drops below 40% of the peak value. Ultimately, the precise distribution range of the clustered areas is determined.

[0148] The time evolution characteristics of the stress-strain anomaly index series are analyzed using the wavelet transform method. In practical applications, the Morlet wavelet function is used to transform the anomaly index time series of each micro-unit. The time series contains 240 sampling points with a sampling interval of 50 microseconds. After the wavelet transform, a coefficient matrix on the time-scale plane is obtained, and each coefficient represents the intensity of the anomaly index change at a specific time and scale. The coefficient matrix is ​​searched for modulus maxima points, which correspond to the locations of sudden changes in the anomaly index. In the case detection, a total of 12 modulus maxima points at time scales were identified, forming an evolutionary feature tree. The feature tree of normal areas is usually less than 3 scales, while the feature tree of crack initiation areas can contain more than 7 scales, indicating the presence of abnormal changes at multiple scales.

[0149] The rate of change of the anomaly index is calculated based on the evolutionary feature tree. The first-order rate of change indicates the rate of change of the anomaly index over time and is calculated by dividing the difference in the anomaly index between adjacent time points by the time interval. The second-order rate of change indicates the rate of change of the first-order rate of change and reflects the degree of acceleration of the anomaly index change. On the wafer surface tested in the example, the first-order rate of change at the microcrack initiation point was typically 0.15-0.32 / ms, and the second-order rate was 0.4-0.9 / ms². Both positive values ​​indicate that the stress anomaly is continuing to intensify.

[0150] To ultimately determine the initiation point of microcracks on the wafer surface, three conditions must be met simultaneously: the area of ​​the spatial clustering region is larger than the preset judgment area, the scale distribution of the evolutionary feature tree is larger than the preset number of scales, and both the first-order and second-order rates of change are positive. In actual applications, the preset judgment area is set to 25μm², and the preset number of scales is set to 6. In a certain test, a total of 5 regions were found to meet the spatial clustering area condition, of which the scale distribution of the evolutionary feature tree of 3 regions exceeded the preset value. Ultimately, only 2 regions had both the first-order and second-order rates of change as positive values ​​and were successfully marked as microcrack initiation points on the wafer surface. Subsequent electron microscopy tests confirmed that micron-scale cracks did appear in these 2 regions, verifying the effectiveness of this method.

[0151] In this embodiment, by introducing adaptive grid division and spatial statistical analysis methods, high-precision identification of microcrack initiation points on the wafer surface is achieved. Compared with existing technologies that rely primarily on single-point stress monitoring or threshold judgment, which makes it difficult to accurately capture early signs of microcrack evolution, this solution integrates spatial distribution characteristics with temporal variation trends, cross-validating the physical evolution behavior of abnormal points from multiple dimensions. In the spatial dimension, the Laplace operator and the local spatial autocorrelation index are used to mine abnormal clusters, improving the spatial resolution of crack nucleation point detection. In the temporal dimension, an evolutionary feature tree is constructed in conjunction with wavelet transforms to quantify the mutation patterns during the abnormal development process, enhancing the ability to perceive microcrack evolution trends. By constructing judgment conditions for first-order and second-order change rates and integrating scale distribution and spatial aggregation to form a judgment rule, the high misjudgment rate and detection lag problems of existing methods are effectively avoided, improving the accuracy and stability of online wafer monitoring, and providing more reliable judgment support for subsequent pressure strategy adjustments.

[0152] Figure 3 Schematic diagram of local spatial autocorrelation index analysis and cluster area identification according to an embodiment of the present invention. Figure 3 As shown in the figure, the LSAI value detected by this technical solution at the radial position of 125-135mm is as high as 0.875, which is significantly higher than the global anomaly index average of 0.312, indicating that there is obvious spatial aggregation in this area. The traditional Moran's I method only detects a maximum value of 0.537, while the maximum value detected by the distance-weighted G* statistical method is 0.623. The figure also shows the spatial aggregation area recognition results of the three methods. The area of ​​the clustered area identified by this technical solution is 3.25mm 2 , while the traditional method can only identify 1.87mm 2 and 2.13mm 2 Data shows that under the condition of a spatial aggregation intensity threshold of 0.65, the recognition accuracy of this technical solution reaches 94.3%, which is 23.7% higher than the traditional method. It can also effectively identify microcracks as small as 2.5μm, which is 42% of the detection limit of traditional methods (6μm).

[0153] According to a second aspect of an embodiment of the present invention, an electronic device is provided, including:

[0154] processor;

[0155] a memory for storing processor-executable instructions;

[0156] The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0157] According to a third aspect of an embodiment of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0158] The present invention may be a method, an apparatus, a system and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for executing various aspects of the present invention.

[0159] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-probe array real-time pressure optimization and control method for wafer testing, characterized in that: include: Collect real-time pressure data and wafer stress limit values ​​from the multi-probe array and establish the initial pressure distribution state of each probe; Obtaining the lateral and longitudinal displacements of each probe during the pressurization process, calculating the actual contact area and contact angle between the probe and the wafer based on the initial pressure distribution state, calculating the stress concentration factor based on the contact area and contact angle, and correcting the probe pressure based on the stress concentration factor to obtain a corrected pressure value; The strain rate distribution on the wafer surface is calculated based on the corrected pressure value, and strain rate mutation points are identified. The area between adjacent strain rate mutation points is divided into a stress-sensitive area. The tangential component and normal component of the force direction of the probe in the stress-sensitive area are obtained. The deflection degree of the force on the probe is calculated, and the probe pressure is compensated in real time based on the deflection degree to obtain a compensated pressure value. The displacement increment and force increment during the probe's application of the compensation pressure value are collected, and the stress-strain ratio during the probe pressurization process is calculated. The microcrack initiation point on the wafer surface is identified based on the change trend of the stress-strain ratio. When the microcrack initiation point is detected, the optimal pressurization rate and maximum pressurization threshold are calculated; Monitor the probe pressure in real time and trigger an alarm signal when the pressure exceeds the maximum pressurization threshold.

2. The method according to claim 1, characterized in that Collecting real-time pressure data and wafer stress limit values ​​from the multi-probe array and establishing the initial pressure distribution state of each probe includes: A pressure sensor matrix is ​​used to collect real-time pressure data from a multi-probe array, and the spatial distribution relationship between the probe array position and the real-time pressure data is established to obtain the stress limit value of the wafer. Acquire the initial pressurized state of the probe array, calculate the pressure force vector between adjacent probes, analyze the spatial distribution characteristics of the force on the probes based on the pressure force vector, obtain the initial stress state of the probe array, identify the stress concentration point in the probe array based on the initial stress state, calculate the pressure distribution gradient around the stress concentration point, determine the pressure abnormality area of ​​the probe array, and establish a pressure distribution characteristic map of the probe array; Mapping the pressure distribution characteristic map with the wafer stress limit value to obtain a stress safety interval of the probe array; calculating a correction parameter of the probe initial pressure based on the stress safety interval; The real-time pressure data is compensated according to the correction parameters to establish an initial pressure distribution state reflecting the force spatial characteristics of the probe.

3. The method according to claim 1, characterized in that The lateral displacement and longitudinal displacement of each probe during the pressurization process are obtained respectively, and the actual contact area and contact angle between the probe and the wafer are calculated according to the initial pressure distribution state. The stress concentration factor is calculated according to the contact area and contact angle. The probe pressure is corrected based on the stress concentration factor to obtain the corrected pressure value including: A displacement sensor is used to collect the lateral and longitudinal displacements of the probe during the pressurization process, and a lateral offset value of the probe is calculated based on the lateral displacement, and a compressive deformation value of the probe is calculated based on the longitudinal displacement. The actual contact area between the probe and the wafer is calculated based on the lateral offset and compressive deformation values, and the actual contact angle of the probe is calculated based on the standard contact state. The actual contact area is divided by the nominal contact area of ​​the probe to obtain an area variation coefficient, and the deviation between the actual contact angle and the standard contact angle is calculated to obtain an angle deviation coefficient; and a stress concentration factor is calculated based on the area variation coefficient and the angle deviation coefficient; The stress concentration factor is compared with a preset stress safety threshold. When the stress concentration factor is less than the stress safety threshold, the probe pressure is corrected using a linear function; when the stress concentration factor is greater than or equal to the stress safety threshold, the probe pressure is corrected using a nonlinear decreasing function to obtain a corrected pressure value.

4. The method according to claim 1, wherein The strain rate distribution on the wafer surface is calculated based on the corrected pressure value, and the strain rate mutation points are identified. The area between adjacent strain rate mutation points is divided into stress-sensitive areas, including: Calculating the displacement distribution on the wafer surface according to the corrected pressure value, and obtaining the strain tensor by taking the spatial partial derivative of the displacement distribution; Strain tensor data are collected at multiple time points to calculate the principal strain directions and principal strain values, respectively; the principal strain values ​​are differentiated with respect to time to obtain a strain rate distribution, and a strain rate space vector field is established based on the principal strain directions; The strain rate gradients of adjacent points in the strain rate space vector field are calculated, a strain rate gradient matrix is ​​established, the strain rate gradient matrix is ​​subjected to singular value decomposition, the main eigenvector of the strain rate change is extracted, the strain rate mutation points are identified according to the directional mutation of the main eigenvector, the strain rate differences of adjacent strain rate mutation points are calculated, and adjacent mutation point regions with continuous strain rate change characteristics are merged into stress sensitive areas.

5. The method according to claim 1, wherein Obtain the tangential and normal components of the force direction of the probe in the stress-sensitive area, calculate the deflection degree of the probe force, and compensate the probe pressure in real time based on the deflection degree. The compensated pressure values ​​include: A local rectangular coordinate system for the probe force is established in the stress-sensitive area, and the probe force is projected onto the three coordinate axes of the local rectangular coordinate system. The normal component perpendicular to the wafer surface and the two tangential components parallel to the wafer surface are calculated respectively. A space vector of the probe force is synthesized according to the normal component and the tangential component, and the zenith angle and azimuth angle of the space vector in the spherical coordinate system are used as the three-dimensional deflection characteristics of the probe force, and the comprehensive deflection degree of the probe force is calculated in combination with the strain rate distribution surface; The pressure compensation function is selected according to the numerical range of the comprehensive deflection degree: when the deflection is mainly caused by the tangential component, a linear compensation function is adopted; when the deflection is caused by both the normal component and the tangential component, a nonlinear compensation function is adopted; when the deflection causes the strain rate distribution surface to be distorted, a piecewise compensation function is adopted; the output value of the compensation function is used as the compensation amount of the probe pressure, and the compensation amount is weightedly superimposed with the corrected pressure value to obtain the compensated pressure value.

6. The method according to claim 1, characterized in that The displacement increment and force increment during the probe's application of the compensation pressure value are collected, the stress-strain ratio during the probe pressurization process is calculated, and the microcrack initiation point on the wafer surface is identified based on the change trend of the stress-strain ratio. When the microcrack initiation point is detected, the optimal pressurization rate and maximum pressurization threshold are calculated, including: The displacement increment and force increment of the probe during the process of applying the compensation pressure value are collected and signal processing and normalization are performed to obtain the normalized displacement increment and normalized force increment; Calculating the ratio of the normalized force increment to the normalized displacement increment to obtain a stress-strain ratio, extracting the stress-strain ratio using a time window of fixed length to construct a stress-strain ratio sequence, performing Fourier transform on the stress-strain ratio sequence to obtain a frequency spectrum feature of the stress-strain ratio, calculating a statistical moment of the stress-strain ratio sequence to obtain a fluctuation feature of the stress-strain ratio; Combining the spectral features and the fluctuation features to construct a feature vector, calculating the principal component of the feature vector to obtain a stress-strain anomaly index, marking the region where the anomaly index suddenly changes as a microcrack initiation point on the wafer surface based on the spatial distribution law and time evolution characteristics of the stress-strain anomaly index, and calculating the strain energy release rate at the microcrack initiation point on the wafer surface; The optimal pressurization rate is determined based on the corresponding relationship between the strain energy release rate and the change speed of the compensation pressure value; the change trend of the stress intensity factor at the microcrack initiation point on the wafer surface with the compensation pressure value is analyzed to determine the maximum pressurization threshold.

7. The method according to claim 6, characterized in that According to the spatial distribution law and time evolution characteristics of the stress-strain anomaly index, the areas where the abnormal index changes suddenly are marked as the microcrack initiation points on the wafer surface, including: The probe contact area is divided into multiple micro-units using an adaptive grid partitioning method. The spatial gradient of the abnormal index and the Laplace operator value of each micro-unit are calculated to obtain the spatial distribution feature matrix. Calculating the local spatial autocorrelation index of the micro-area unit based on the spatial distribution characteristic matrix, identifying the spatial clustering area of ​​the anomaly index according to the comparative relationship between the local spatial autocorrelation index and the global anomaly index mean, and calculating the distribution range of the spatial clustering area; Performing a wavelet transform on the stress-strain anomaly index sequence to obtain a time evolution coefficient, extracting the modulus maximum of the time evolution coefficient to obtain a time mutation point, connecting the time mutation points to construct an evolution feature tree, and obtaining a scale distribution of the evolution feature tree; The first-order change rate and the second-order change rate of the abnormal index are calculated according to the evolution feature tree, and the area of ​​the spatial aggregation region is greater than the preset judgment area, the scale distribution of the evolution feature tree is greater than the preset scale number, and the areas where the first-order change rate and the second-order change rate are both positive are marked as microcrack initiation points on the wafer surface.

8. An electronic device, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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