A sample failure point pre-positioning and FIB coordinate mapping method

Abstract

This invention relates to the field of semiconductor failure analysis technology, and particularly to a method for pre-locating sample failure points and mapping FIB coordinates. The method includes: acquiring X-ray data of the sample under test for three-dimensional reconstruction, extracting an initial voxel density matrix, an ideal target cross-section matrix, and spatial reference features; establishing a spatial transformation relationship between X-rays and the FIB device based on these features, generating a mapped density matrix and a mapped cross-section matrix; constructing a sputtering prediction model based on the mapping matrix, and solving to generate an optimal residence time matrix; controlling the FIB device to mill according to this model and obtaining the current true physical morphology matrix; calculating the spatial residual between the true morphology and the theoretically predicted morphology, using this residual to inversely correct the mapped density matrix and iteratively iterating the prediction model until the physical morphology approximates the mapped cross-section. This invention achieves adaptive closed-loop control of the cutting depth through inverse residual correction, effectively avoiding the problem of overcutting damage to deeply buried failure points caused by open-loop blind cutting.

Description

Technical Field

[0001] This invention relates to the field of semiconductor failure analysis technology, and in particular to a method for pre-locating sample failure points and mapping FIB coordinates. Background Technology

[0002] In physical failure analysis of advanced 3D semiconductor packaging, focused ion beam (FIB) equipment is widely used to cut downwards and expose deeply buried micro- and nano-scale defects. Existing FIB sample preparation processes typically rely on open-loop trial-and-error cutting using 2D surface images. However, complex packaged samples often contain overlapping heterogeneous materials with vastly different sputtering yields. This extreme abrupt change in material physical properties makes it highly susceptible to nonlinear material stripping when the ion beam crosses the heterogeneous interface, resulting in a significant deviation of the actual cutting depth from the theoretically calculated value. Existing sample preparation mechanisms lack prior knowledge of the deeply buried 3D morphology and material hardness, often relying on post-hoc, single-step hysteresis feedback. This open-loop blind cutting operation, when encountering abrupt changes in internal material sputtering differences, easily induces severe morphology artifacts, directly causing irreversible overcutting damage to tiny failure points buried deep within the substrate before they are even observed, thus completely breaking the underlying evidence chain for physical failure analysis. Summary of the Invention

[0003] To overcome the above shortcomings, this invention provides a sample failure point pre-location and FIB coordinate mapping method, which aims to improve the problem that traditional FIB sample preparation mostly adopts open-loop blind cutting, which lacks prior prediction of internal material sputtering differences, thus causing deep-buried failure points to be easily overcut and damaged.

[0004] This invention provides the following technical solution: a method for pre-locating sample failure points and mapping FIB coordinates, comprising the following steps: S1. Obtain the X-ray projection data of the sample to be tested and perform three-dimensional reconstruction processing, pre-locate the target failure point, and extract the initial voxel density matrix, ideal target cross-section matrix and spatial reference features. S2. Based on the spatial reference features, establish the spatial transformation relationship between the X-ray coordinate system and the FIB equipment coordinate system, and transform the initial voxel density matrix and the ideal target cross section matrix to generate the mapping density matrix and the mapping cross section matrix. S3. Construct a sputtering prediction model based on the mapping density matrix and the mapping cross section matrix, and perform optimization to generate the optimal residence time matrix under the current control cycle; S4. Control the FIB device to perform physical ion milling operation according to the optimal residence time matrix, obtain the real-time cross-sectional image of the sample to be tested after milling and extract the real current physical morphology matrix. S5. Calculate the spatial residual between the current physical topography matrix and the theoretical predicted topography calculated based on the sputtering prediction model, use the spatial residual to inversely correct the mapping density matrix, and return to execute the step of constructing the sputtering prediction model until the current physical topography matrix approximates the mapping section matrix.

[0005] By adopting the above technical solution, a cross-device coordinate mapping is established and a sputtering prediction model with spatial residual inverse correction is constructed, thereby realizing closed-loop control of cutting depth. This improves the problem that traditional FIB sample preparation mostly adopts open-loop blind cutting, which lacks prior prediction of internal material sputtering differences, resulting in deep-buried failure points being easily damaged by overcutting.

[0006] The present invention has the following beneficial effects: 1. In this invention, by establishing cross-device coordinate mapping and constructing a sputtering prediction model with spatial residual inverse correction, closed-loop control of cutting depth is achieved, thereby improving the problem that traditional FIB sample preparation mostly adopts open-loop blind cutting, which lacks prior prediction of internal material sputtering differences, resulting in deep-buried failure points being easily damaged by overcutting.

[0007] 2. In this invention, by introducing spatial distance to generate adaptive weight coefficients for weighted matrix fitting, high-precision mapping and correction of local deformation is achieved, thereby improving the problem of cumulative offset in cross-device coordinate transformation caused by the traditional coordinate alignment, which mostly adopts global equal weight registration and ignores the micro-warping caused by sample stress.

[0008] 3. In this invention, by constructing a rolling optimization cost function that includes depth error and time increment penalty terms, the forward-looking smooth adjustment of the beam is achieved, thereby improving the problem that traditional material removal control mostly adopts single-step hysteresis feedback, which cannot detect the sudden change in hardness of the material interface in advance, thus causing the cross-section to easily produce curtain effect afterimages.

[0009] 4. In this invention, the state update gain matrix is ​​calculated based on the predicted covariance and measurement noise, thereby achieving accurate filtering and extraction of physical shape drift. This improves the problem that traditional error calculations mostly rely on directly reading the pixel difference of the cross section, which, due to the inclusion of random imaging white noise, easily causes erroneous divergence in closed-loop compensation. Attached Figure Description

[0010] Figure 1 This is a flowchart of a sample failure point pre-location and FIB coordinate mapping method proposed in this invention; Figure 2 This is a flowchart of the spatial coordinate mapping and data conversion process for a sample failure point pre-location and FIB coordinate mapping method proposed in this invention. Figure 3 This is a flowchart illustrating the sputtering prediction model construction and adaptive closed-loop correction of a sample failure point pre-location and FIB coordinate mapping method proposed in this invention. Detailed Implementation

[0011] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0012] Example 1: In a first embodiment of the present invention, the present invention provides a method for pre-locating sample failure points and mapping FIB coordinates, such as... Figure 1 As shown, it includes the following steps: S1. Obtain the X-ray projection data of the sample to be tested and perform three-dimensional reconstruction processing, pre-locate the target failure point, and extract the initial voxel density matrix, ideal target cross-section matrix and spatial reference features. Furthermore, in S1, the extraction of the initial voxel density matrix and spatial reference features includes: Filtered backprojection reconstruction of X-ray projection data is performed to construct a three-dimensional structural model that reflects the internal material distribution of the sample under test. Extract the 3D boundary contour of the heterogeneous encapsulation material from the 3D structural model, and mark the feature inflection points within the 3D boundary contour as spatial reference features. Extract the grayscale sequence of three-dimensional voxels located within the target processing area in the three-dimensional structural model, perform grayscale normalization mapping on the grayscale sequence of three-dimensional voxels, and generate an initial voxel density matrix.

[0013] In S1, the target failure point is pre-positioned, and the ideal target cross-section matrix is ​​extracted, including: In the constructed three-dimensional structural model, spatial density anomaly detection is performed, the set of anomalous voxels that have undergone density abrupt changes is extracted, and the three-dimensional spatial centroid of the anomalous voxel set is calculated as the target failure point. Construct a virtual plane that passes through the target failure point and whose normal vector is parallel to the preset electron beam observation angle of the FIB device; Extract the three-dimensional coordinate set of the three-dimensional structural model on the virtual plane, strip the material density properties of each node on the spatial plane, and extract only the Z-axis physical depth coordinates of each node corresponding to the processing downward direction. Define the two-dimensional depth array composed of the Z-axis physical depth coordinates as the ideal target section matrix characterizing the processing termination boundary.

[0014] Specifically, step S1 serves as the data supply source for the entire method chain. Its actual data interaction process is as follows: input the original X-ray projection data of the sample to be tested; through the underlying algorithm reconstruction and feature extraction mechanism, it finally outputs four core parameters that are directly called by subsequent modules: initial voxel density matrix, spatial reference features, three-dimensional coordinates of the target failure point, and ideal target cross-section matrix.

[0015] The system receives X-ray projection data and performs filtered backprojection reconstruction, restoring the multi-angle two-dimensional overlapping projection into a three-dimensional structural model that truly reflects the internal material distribution of the sample under test. For complex and advanced packaging structures, the system extracts the three-dimensional boundary contours of heterogeneous packaging materials and directly marks the feature inflection points within the three-dimensional boundary contours as spatial reference features.

[0016] This step utilizes the inherent physical contours of the heterogeneous material interface as natural landmarks, solving the technical challenge of the lack of artificial alignment marks for internal structures in a non-destructive observation environment. It provides a fixed anchor point for establishing the global spatial coordinate transformation relationship between the two heterogeneous physical devices, namely the X-ray microscope and the focused ion beam device.

[0017] The system extracts the grayscale sequence of three-dimensional voxels located within the target processing area of ​​the three-dimensional structural model and performs grayscale normalization processing using a linear mapping formula: ; in Represents the coordinates after normalization. The voxel density at that location is strictly limited to a value between 0 and 1; Represents the original 3D voxel grayscale value extracted from the 3D structural model; Represents the upper limit of the voxel grayscale value calibrated within the target processing area; This represents the lower limit of the voxel grayscale value calibrated within the target processing area.

[0018] The original X-ray grayscale is easily affected by fluctuations in equipment tube voltage and exposure time. The above normalization formula is used to generate an initial voxel density matrix, which removes the imaging differences at the equipment level and transforms the simple image grayscale into a standard scale that characterizes the physical hardness properties of local materials. This scale is then directly used as the basic input parameter for constructing a sputtering evolution prediction model for heterogeneous materials.

[0019] The system performs spatial density anomaly detection in the 3D structural model, extracts anomalous voxel sets with abrupt density changes such as holes or inclusions, and calls the spatial centroid algorithm to calculate the 3D physical center of the anomalous voxel sets: ; in The three-dimensional spatial coordinate vector representing the calculated target failure point; Represents the total number of voxels contained in the extracted abnormal voxel set, and its value is a positive integer greater than 1; Represents the first in the set of abnormal voxels The absolute spatial coordinate vector of an anomalous voxel.

[0020] By quantitatively solving the centroid of the abnormal voxel as the target failure point, the traditional method of manually estimating the defect location by visual estimation is replaced. This improves the defect location of deeply buried micro-defects, which are prone to geometric deviations, and thus avoids the problem of the ion milling process deviating from the actual source of the fault.

[0021] After locating the target failure point, the system constructs a virtual plane in virtual space that absolutely passes through the target failure point and whose normal vector is strictly parallel to the preset electron beam observation angle of the focused ion beam equipment. Then, a two-dimensional voxel distribution array of the three-dimensional structural model is extracted on the virtual plane to generate the ideal target cross-section matrix.

[0022] Since focused ion beam milling is a destructive unidirectional machining process, the introduction of a virtual plane predefines the absolute physical cutting termination boundary in three-dimensional space. The generated ideal target section matrix serves as a target reference template for subsequent error closed-loop comparison, providing a rigorous endpoint judgment condition for the system to determine whether the current physical morphology state matrix is ​​close to the tolerance range.

[0023] like Figure 2 As shown, S2, based on the spatial reference features, establish the spatial transformation relationship between the X-ray coordinate system and the FIB equipment coordinate system, and transform the initial voxel density matrix and the ideal target cross section matrix to generate the mapped density matrix and the mapped cross section matrix. Furthermore, in S2, the spatial transformation relationship between the X-ray coordinate system and the focused ion beam (FIB) equipment coordinate system, established based on spatial reference features, includes: Obtain the actual physical measurement coordinates of the spatial reference features in the FIB device coordinate system; Calculate the Euclidean spatial distance between each spatial reference feature and the target failure point, and generate an adaptive distance weight coefficient corresponding to each spatial reference feature based on the Euclidean spatial distance; By substituting the real physical measurement coordinates and adaptive distance weighting coefficients into the affine transformation model, a weighted matrix fitting is performed to calculate the spatial transformation relationship that includes the three-dimensional rotation matrix and the three-dimensional translation vector.

[0024] In S2, the initial voxel density matrix and the ideal target cross-section matrix are transformed to generate the mapped density matrix and the mapped cross-section matrix, including: The initial voxel density matrix is ​​resampled and aligned to the three-dimensional spatial coordinate system using spatial transformation relationships to generate a mapped density matrix aligned with the coordinate axes of the FIB device coordinate system. By performing normal vector rotation and origin translation transformations on the ideal target cross-section matrix using spatial transformation relationships, a mapped cross-section matrix aligned with the observation viewpoint of the FIB device is generated.

[0025] Specifically, step S2, as the core hub of cross-device data bridging, has the following actual data interaction process: input the initial voxel density matrix, ideal target cross section matrix, and three-dimensional coordinates of spatial reference features extracted from the previous step, as well as the real physical measurement coordinates of the corresponding features obtained in real time through the focused ion beam device; after weighted affine transformation and mesh resampling operation, the final output is two parameters directly aligned with the underlying hardware: the mapping density matrix and the mapping cross section matrix.

[0026] The system first instructs the focused ion beam (FIB) device to scan the sample surface or shallow layer, obtaining the actual physical measurement coordinates of the spatial reference features in the FIB device coordinate system. To address the issue of localized physical warping caused by thermal or mechanical stress in complex packaged samples, the system introduces an Euclidean spatial distance calculation mechanism: ; in Representing the The Euclidean spatial distance between a spatial reference feature and the target failure point; , , Representing the Three-dimensional spatial coordinates of a spatial reference feature; , , The three-dimensional spatial coordinates representing the target failure point.

[0027] Subsequently, the system generates adaptive distance weighting coefficients based on the calculated Euclidean spatial distance: ; in Representative assigned to the first The adaptive distance weight coefficients of each spatial benchmark feature are strictly constrained to a range of 0 to 1. This represents the preset distance attenuation factor, which is determined based on the expected warping degree of the sample. This represents the total number of extracted spatial reference features.

[0028] The aforementioned weighting algorithm breaks the inherent logic of equal weighting for all feature points in conventional global rigid registration. By assigning higher fitting weights to feature nodes closer to the target failure point, it can forcibly correct local spatial deformation at the microscale, providing a deformation-resistant mathematical benchmark for coordinate system alignment between heterogeneous devices.

[0029] After obtaining the actual physical measurement coordinates and corresponding weights, the system establishes the target loss function and substitutes it into the affine transformation model for minimization: ; in This represents the weighted objective loss function value that needs to be minimized. Representing the The actual physical measurement coordinate vector of each spatial reference feature in the FIB device coordinate system; Representing the The coordinate vectors of a spatial reference feature in the X-ray coordinate system; Represents the three-dimensional rotation matrix to be solved; This represents the three-dimensional translation vector to be solved.

[0030] The system uses the least squares method to iteratively solve for the optimal three-dimensional rotation matrix and three-dimensional translation vector, which together establish the spatial transformation relationship between the devices. This step fundamentally breaks down the data barrier between the non-destructive testing space and the destructive physical processing space, minimizing the absolute position drift error.

[0031] After establishing the spatial transformation relationships, the system directly applies the 3D rotation matrix and 3D translation vector to the initial voxel density matrix. Since the rotation operation causes an angular offset between the original 3D voxel mesh and the Cartesian coordinate axes of the FIB device coordinate system, the system immediately performs a 3D mesh resampling and alignment operation. The system uses a trilinear interpolation algorithm to reassign values ​​to the rotated coordinate system, generating a mapping density matrix whose mesh orientation is absolutely parallel to the FIB hardware machining axes.

[0032] The system performs a normal vector rotation transformation and an origin translation transformation on the ideal target cross-section matrix. By changing the direction of its normal vector, it aligns it with the preset incident tilt angle of the electron beam or ion beam in the FIB device, thereby generating a mapped cross-section matrix.

[0033] The aforementioned physical space resampling and cross-sectional attitude adjustment transform the X-ray voxel data, which originally only had virtual reference significance, into a processing base map with an absolute coordinate system that can be directly recognized and executed by FIB processing hardware. This provides input parameters with a completely consistent physical reference system for the subsequent construction of a high-precision sputtering prediction model.

[0034] like Figure 3As shown, S3, based on the mapping density matrix and the mapping cross section matrix, a sputtering prediction model is constructed and optimized to generate the optimal residence time matrix under the current control cycle; Furthermore, in S3, the sputtering prediction model constructed based on the mapping density matrix and the mapping cross-section matrix includes: Extract the Gaussian diffusion kernel function parameters characterizing the high-energy ion beam current density distribution and the system incident tilt angle parameters of the ion beam from the FIB device; A nonlinear physical mapping operator is defined to convert the mapping density matrix into an ion sputtering yield matrix that characterizes the material removal rate of each voxel node. By inputting the ion sputtering yield matrix, Gaussian diffusion kernel function parameters, and system incident tilt angle parameters into the discrete-time state transition equation, a sputtering prediction model is established with residence time as the control input and topography depth as the state output.

[0035] In S3, optimization is performed to generate the optimal dwell time matrix for the current control cycle, including: Based on the sputtering prediction model, a rolling optimization cost function containing prediction time domain and control time domain is constructed. In the rolling optimization cost function, a depth error penalty term is configured to characterize the state tracking accuracy, and a dwell time increment penalty term is configured to characterize the smoothness of beam change. Under the boundary constraint condition of setting the maximum beam output physical limit of the FIB device as the boundary condition, the minimum value of the rolling optimization cost function is solved by the quadratic programming algorithm. The control variable of the first time step is extracted from the predictive control sequence corresponding to the minimum value obtained from the solution, and used as the optimal dwell time matrix under the current control cycle.

[0036] Specifically, step S3 constitutes the core algorithm planning hub of the entire scheme. The input end receives the pre-processed mapping density matrix and mapping cross-section matrix, as well as the inherent electro-optical parameters of the underlying hardware. The system relies on the control layer algorithm to perform modeling and numerical calculations, and the output end sends the optimal residence time matrix of the current control cycle to the physical electromechanical interface to directly drive the ion beam scanning coil.

[0037] The scheme extracts Gaussian diffusion kernel function parameters characterizing the high-energy ion beam density distribution and incident tilt angle parameters of the equipment system. Based on the physical law that different material compositions have different absorption rates of high-energy ions, a nonlinear physical mapping operator is set within the system. The system, based on an empirical ion penetration model from materials science, transforms the mapping density matrix into an ion sputtering yield matrix characterizing the material removal rate of each voxel node. The formula for the forward mapping physical operator is as follows: ; in Representing coordinates Ion sputtering yield at the location; This represents the voxel density at the corresponding coordinate in the mapping density matrix; This represents an empirical constant characterizing the energy of an ion beam. The nonlinear influence index representing the material density ranges from 1.2 to 2.0; To prevent the denominator from being zero, a smoothing compensation coefficient is used; The limiting background sputtering rate represents the underlying substrate. The extracted parameters together constitute the discrete-time state transition equation. To accurately match the spatial dimension and the physical diffusion process, the system prioritizes calculating the single-point sputtering depth in its computational logic, subsequently superimposing the convolution effect of the beam distribution. The updated state transition equation is as follows: ; in The predicted topographic depth matrix for the next time step obtained from the deduction; The topographic depth matrix represents the current time step; The residence time matrix represents the control input quantity; The incident tilt angle of the system representing the ion beam; The Hadamard product operation represents the matrix operation, which is the element-wise multiplication of matrix elements. Represents the two-dimensional convolution operator; The parameters represent the Gaussian diffusion kernel function. This evolution equation establishes a quantitative relationship between residence time and the amount of material removed in three-dimensional space. By binding static prior three-dimensional data with material sputtering yield in the model, it fills the technical gap in traditional physical processing that relies solely on two-dimensional surface images to estimate depth.

[0038] Based on the established sputtering prediction model, the system compiles a rolling optimization cost function that integrates the prediction time domain and the control time domain: ; in The total cost value of the solution representing the cost function; The total time step that the representative model predicts for the future is the prediction time domain; The total time step representing the system's generation of intervention commands is the control time domain, and the set conditions must be met. Greater than or equal to . The weight of the depth error penalty term represents the configuration. The future number derived from the deduction Gait morphology; This represents the target machining reference surface defined by the mapped section matrix. The weight of the dwell time increment penalty term representing the smooth change of the control beam; This represents the step change in the dwell time between adjacent control cycles.

[0039] The system retrieves the highest beam emission threshold from the physical limits of the equipment hardware as a boundary constraint and uses a quadratic programming algorithm to retrieve a control sequence that minimizes the total solution cost. The system extracts the first time-step variable from the control sequence and assigns it the optimal dwell time matrix for the current control cycle. This step utilizes a look-ahead prediction algorithm to replace the passive, lagging single-step error feedback. Based on the three-dimensional depth structure, the control system anticipates abrupt changes in material hardness and pre-emptively smooths out or increases the ion beam output power, avoiding the curtain effect artifacts caused by cutting rate mismatches at heterogeneous material interfaces.

[0040] like Figure 3 As shown, S4 controls the FIB device to perform physical ion milling operation according to the optimal residence time matrix, obtains the real-time cross-sectional image of the sample after milling, and extracts the real current physical morphology matrix. Furthermore, in S4, the FIB device is controlled to perform physical ion milling operations based on the optimal residence time matrix, acquiring real-time cross-sectional images of the sample after milling and extracting the true current physical morphology matrix, including: The optimal dwell time matrix is ​​compiled into drive control instructions for the hardware scanning coil, which control the FIB device to perform grating scanning milling in the target area in a single control cycle. The electron microscope integrated into the FIB device is used to perform in-situ cross-sectional scanning of the milled target area to obtain real-time cross-sectional images; Subpixel-level edge detection and physical scale mapping are performed on real-time cross-sectional images to locate the real material removal boundary contours, and the real material removal boundary contours are converted into the current physical morphology matrix.

[0041] Specifically, step S4 undertakes the dual tasks of realizing the physical machining actions and extracting the actual cutting state. The data flow process in this step is manifested as the input end receiving the optimal dwell time matrix generated by the algorithm planning, and the output end feeding back the current physical morphology matrix representing the actual machining depth to the downstream error comparison module.

[0042] The system first resolves the digitized optimal residence time matrix into a sequence of control voltage pulses, directly driving the scanning deflection coils within the focused ion beam apparatus. The high-energy ion beam is then controlled to perform point-by-point grating scanning within the target region of the sample. Within a set control cycle, the material in the target region undergoes physical sputtering and ablation strictly according to the residence time distribution allocated by the matrix. This process transforms the predictive control commands from the software layer into microscale, localized material removal actions.

[0043] After a single milling cycle, the system interrupts ion beam emission and activates the electron microscope module integrated into the dual-beam processing equipment. The electron beam probe performs in-situ scanning of the freshly exposed cut surface, acquiring information on the cross-sectional morphology and secondary electron or backscattered electron contrast of the internal material, thereby generating a real-time cross-sectional image. This in-situ acquisition method within the equipment cavity eliminates the risk of oxidation contamination caused by sample transfer during the process, ensuring spatial consistency of the visual measurement data.

[0044] For the acquired cross-sectional data, the system runs a sub-pixel level edge detection operator to extract the grayscale boundary contour between the stripped material area and the unprocessed underlying layer in the image. Because there is a certain geometric projection angle between the electron microscope's observation angle and the actual milled cross-section, the system must perform physical scale mapping on the pixel-level contour data. The specific spatial depth conversion formula is as follows: ; in Represents the first element in the generated current physical topography matrix. Line 1 The actual physical machining depth corresponding to the discrete coordinate points. This represents the total vertical pixel offset of the corresponding boundary point extracted by the edge detection operator from the initial zero-position reference line on the real-time cross-sectional image. The scale represents the actual physical length of a single pixel in the current working field of view and magnification of the device. This represents the inherent systematic geometric tilt angle between the optical axis observed by the electron microscope and the actual milled cross section of the sample.

[0045] After geometric projection attenuation compensation and physical size conversion, the pixel contour lines in the two-dimensional cross-sectional image are restored to the current physical morphology matrix describing the three-dimensional cutting depth. This measured matrix objectively records the actual sputtering hysteresis or lead generated when the heterogeneous packaging material encounters ion bombardment, establishing an indispensable underlying error reference scale for triggering the reverse update of the Kalman state in the next cycle.

[0046] like Figure 3 As shown, S5, calculate the spatial residual between the current physical morphology matrix and the theoretical predicted morphology calculated based on the sputtering prediction model, use the spatial residual to inversely correct the mapping density matrix, and return to execute the step of building the sputtering prediction model until the current physical morphology matrix approximates the mapping section matrix. Furthermore, in S5, the spatial residual between the current physical topography matrix and the theoretically predicted topography calculated based on the sputtering prediction model is calculated, and the mapping density matrix is ​​inversely corrected using the spatial residual, including: Retrieve the theoretical predicted morphology of the sputtering prediction model in the previous control cycle. Align the current physical topography matrix with the theoretically predicted topography in spatial coordinates, and calculate the depth difference sequence between the two at the corresponding pixel nodes to generate spatial residuals; The state update gain matrix is ​​calculated based on the system prediction covariance and the visual extraction measurement noise variance. The physical topography drift is then calculated by multiplying the state update gain matrix with the spatial residual. The physical topography drift is converted into a local density correction compensation by using the sputtering yield inverse mapping operator, and the local density correction compensation is then superimposed onto the mapping density matrix to complete the update.

[0047] In S5, the current physical topography matrix approximating the mapped section matrix includes: Calculate the absolute distance norm between the current physical topography matrix and the mapped section matrix at global pixel nodes; The absolute distance norm is compared with the system's preset sample preparation tolerance threshold. When the absolute distance norm is greater than the sample preparation tolerance threshold, the time step index of the control cycle is shifted forward, and the subsequent operation of building the sputtering prediction model is continued with the corrected mapping density matrix. When the absolute distance norm is less than or equal to the sample preparation tolerance threshold, it is determined that the cutting depth has reached the target failure point, triggering an equipment interruption command to end the physical ion milling operation.

[0048] Specifically, step S5 executes the closed-loop error correction and termination judgment for the entire adaptive machining system. The input end receives the current physical topography matrix extracted in step S4, the previously reserved mapping section matrix, and the theoretical predicted topography derived by the prediction model in the previous cycle. After residual extraction, Kalman gain calculation, and distance norm operation, the output end generates two paths based on the judgment logic: one is to generate the corrected mapping density matrix and send it back to the prediction modeling module to start the loop of the next time step; the other is to directly issue a device interrupt command to the hardware electromechanical interface to terminate machining.

[0049] The system retrieves the theoretically predicted topography generated in the previous control cycle, aligns it with the currently acquired physical topography matrix using spatial coordinates, and then performs depth subtraction on the corresponding pixel nodes. ; in This represents the spatial residual matrix generated by the calculation; Represents the current physical topography matrix; The representative theory predicts the morphology.

[0050] Considering that electron microscopes inevitably introduce random white noise caused by fluctuations in secondary electron yield when acquiring real-time images, the system introduces the Kalman filter concept to calculate the physical morphology drift: ; ; in This represents the calculated state update gain matrix; The prediction covariance matrix represents the system's settings; Represents the variance matrix of visual extraction measurement noise; This represents the actual physical shape shift calculated after noise filtering.

[0051] The above calculation process eliminates the observation error interference caused by in-situ imaging, ensuring that the morphology drift extracted by the system truly reflects the nonlinear abrupt change in the material's ion sputtering rate.

[0052] After obtaining the actual physical topography drift, the system does not issue it as a mechanical axis compensation parameter. Instead, it uses the sputtering yield inverse mapping operator to perform cross-domain data transformation. Specifically, based on the inverse function principle of the forward mapping physical operator, the system constructs an inverse mapping operator formula to convert the physical topography drift into a local density correction compensation amount. ; in This represents the amount of local density correction compensation. This represents the calculated physical topography drift. This represents the historical voxel density corresponding to the previous control cycle. , , , These represent the empirical constant, influence exponent, compensation coefficient, and background sputtering rate, which are consistent with the definition of the forward mapping physical operator.

[0053] Subsequently, the system inversely superimposes the local density correction compensation amount onto the mapped density matrix to complete the density field update for this period: ; in, This represents the updated mapping density matrix. By introducing an inverse mapping operator, the limitation of traditional closed-loop schemes, which can only perform one-dimensional compensation of mechanical axes, is improved, thus avoiding the error divergence problem caused by the lack of updating of underlying data in the heterogeneous material cutting prediction model.

[0054] Conventional techniques typically use measurement errors directly to correct the cutting depth of the next cut. Our proposed inverse correction mechanism transforms physical topography drift across domains into local density correction compensation, and directly superimposes it onto the prior mapped density matrix source. This step fundamentally corrects the beam hardening artifact bias inherent in the original X-ray 3D reconstruction data, reshaping the evolution prediction benchmark for all subsequent control cycles.

[0055] At the end of each iteration, the system calculates the absolute distance norm between the current physical topography matrix and the target location, i.e., the mapped section matrix: ; in Represents the absolute distance norm of the global pixel nodes obtained through calculation; This represents the total number of global pixel nodes contained within the cross-sectional field of view; Represents the current physical topography matrix at the th The cutting depth value at each pixel node;

[0056] The system will calculate the obtained absolute distance norm. With respect to the set sample preparation tolerance threshold Perform a size comparison. If... If the system determines that the target layer has not been reached, it advances the time step index of the control cycle and returns to step S3 with the updated mapping density matrix to reconstruct the evolutionary model. The system determines that the actual cutting boundary has conformed to the contour around the target failure point, and the main control board sends a hard interrupt command to the focused ion beam equipment to cut off the ion gun beam emission.

[0057] The algorithm uses the absolute distance norm covering all pixel nodes as the decision criterion, replacing the conventional method of relying solely on single-point ranging at the center of the cross-section. This algorithm eliminates the interference of ranging blind spots caused by local abnormal particle residues, establishes rigorous and objective processing termination conditions, and eliminates the risk of over-cutting damage to the failure points of deeply buried targets caused by long-term ion beam residence.

[0058] Example 2: Physical failure analysis of advanced semiconductor 3D high-density packaging. In this scenario, the failed chip sample contains overlapping high-hardness metal interconnect layers and low-hardness insulating dielectric layers. Engineers need to precisely locate and use FIB (fiber-insulating barrier) to cut downwards to non-destructively expose nanoscale defects buried deep at the interface of heterogeneous materials for subsequent electron microscopy evidence.

[0059] In this application scenario, the main challenges are irreversible cutting damage and uncontrolled target depth caused by nonlinear sputtering of heterogeneous packaging materials. Specifically, due to the significant difference in physical sputtering yield between high-hardness metals and low-hardness media under ion beam bombardment, FIB equipment is highly susceptible to morphological artifacts such as the curtain effect when cutting downwards and crossing the interface of heterogeneous materials, directly damaging the actual cross-sectional structure due to the mismatch in local material removal rates. Furthermore, conventional FIB sample preparation heavily relies on open-loop, hysteresis-based single-step trial-and-error compensation using two-dimensional surface images, lacking the ability to predict the 3D morphology of the deeply buried bottom. Even with the introduction of non-destructive X-ray 3D reconstruction data for positioning, the isolated spatial coordinate systems between the two detection devices and the presence of reconstruction artifacts such as beam hardening in X-rays cause a cumulative drift in the physical depth between the statically calculated mapping coordinates and the actual processed cut surface. This spatial mapping discontinuity combined with hysteresis compensation easily leads to overcutting or blind cutting damage to micro- and nano-scale target defects, resulting in high trial-and-error costs and a complete breakdown of the physical failure analysis evidence chain. To solve the above problems, this invention provides a method for pre-locating sample failure points and mapping FIB coordinates, the structure of which is as follows: Figure 1 As shown. The specific implementation process of this method is as follows: By extracting internal spatial reference features from X-ray reconstruction data, the initial voxel density matrix and ideal target cross-section matrix of the sample are precisely transformed into the working coordinate system of the focused ion beam equipment, establishing a processing reference across physical space. The system builds a sputtering prediction model based on the transformed mapped density matrix and issues residence time commands, replacing the traditional open-loop trial-and-error operation relying on two-dimensional surface images. After the milling operation is executed, the system extracts the spatial residual between the actual physical morphology and the theoretically predicted morphology, and inversely compensates this residual into the underlying mapped density matrix, driving the prediction model to perform the next cycle of rolling deduction based on the updated source data. These steps deeply integrate static prior detection with dynamic physical correction, overcoming the depth runaway defects caused by nonlinear sputtering of heterogeneous packaging materials, preventing irreversible damage to target failure points during deep-buried blind cutting, and ensuring a high success rate in sample preparation for accurately exposing the targeted cross-section of deep-buried defects.

[0060] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A sample failure point pre-positioning and FIB coordinate mapping method, characterized in that, Includes the following steps: S1. Obtain the X-ray projection data of the sample to be tested and perform three-dimensional reconstruction processing, pre-locate the target failure point, and extract the initial voxel density matrix, ideal target cross-section matrix and spatial reference features. S2. Based on the spatial reference features, establish the spatial transformation relationship between the X-ray coordinate system and the FIB equipment coordinate system, and transform the initial voxel density matrix and the ideal target cross section matrix to generate the mapping density matrix and the mapping cross section matrix. S3. Construct a sputtering prediction model based on the mapping density matrix and the mapping cross section matrix, and perform optimization to generate the optimal residence time matrix under the current control cycle; S4. Control the FIB device to perform physical ion milling operation according to the optimal residence time matrix, obtain the real-time cross-sectional image of the sample to be tested after milling and extract the real current physical morphology matrix. S5. Calculate the spatial residual between the current physical topography matrix and the theoretical predicted topography calculated based on the sputtering prediction model, use the spatial residual to inversely correct the mapping density matrix, and return to execute the step of constructing the sputtering prediction model until the current physical topography matrix approximates the mapping section matrix.

2. The sample failure point pre-location and FIB coordinate mapping method according to claim 1, characterized in that, In S1, the extraction of the initial voxel density matrix and spatial reference features includes: The X-ray projection data is filtered and back-projected to reconstruct a three-dimensional structural model that reflects the material distribution inside the sample under test. Extract the three-dimensional boundary contour of the heterogeneous encapsulation material from the three-dimensional structural model, and mark the feature inflection points within the three-dimensional boundary contour as the spatial reference feature; Extract the three-dimensional voxel grayscale sequence located within the target processing area in the three-dimensional structural model, perform grayscale normalization mapping on the three-dimensional voxel grayscale sequence, and generate the initial voxel density matrix.

3. The sample failure point pre-location and FIB coordinate mapping method according to claim 1, characterized in that, In S1, the extraction of the ideal target cross-section matrix from the pre-positioned target failure point includes: In the constructed three-dimensional structural model, spatial density anomaly detection is performed, the set of anomalous voxels that have undergone density abrupt changes is extracted, and the three-dimensional spatial centroid of the set of anomalous voxels is calculated as the target failure point. Construct a virtual plane that passes through the target failure point and whose normal vector is parallel to the preset electron beam observation angle of the FIB device; Extract the three-dimensional coordinate set of the three-dimensional structural model on the virtual plane, strip the material density properties of each node on the spatial plane, and extract only the Z-axis physical depth coordinates of each node corresponding to the processing downward direction. Define the two-dimensional depth array composed of the Z-axis physical depth coordinates as the ideal target section matrix characterizing the processing termination boundary.

4. The sample failure point pre-location and FIB coordinate mapping method according to claim 1, characterized in that, In S2, establishing the spatial transformation relationship between the X-ray coordinate system and the focused ion beam (FIB) equipment coordinate system based on the spatial reference features includes: Obtain the actual physical measurement coordinates of the spatial reference feature in the FIB device coordinate system; Calculate the Euclidean spatial distance between each of the spatial reference features and the target failure point, and generate an adaptive distance weight coefficient corresponding to each of the spatial reference features based on the Euclidean spatial distance; The actual physical measurement coordinates and the adaptive distance weighting coefficients are substituted into the affine transformation model for weighted matrix fitting to calculate the spatial transformation relationship, which includes the three-dimensional rotation matrix and the three-dimensional translation vector.

5. The sample failure point pre-location and FIB coordinate mapping method according to claim 1, characterized in that, In S2, the process of converting the initial voxel density matrix and the ideal target cross-section matrix to generate the mapped density matrix and the mapped cross-section matrix includes: The initial voxel density matrix is ​​resampled and aligned in three-dimensional space coordinates using the spatial transformation relationship to generate the mapped density matrix aligned with the coordinate axes of the FIB device coordinate system. By applying the spatial transformation relationship to the ideal target cross-section matrix, a normal vector rotation transformation and an origin translation transformation are performed to generate the mapped cross-section matrix that is aligned with the observation viewpoint of the FIB device.

6. The sample failure point pre-location and FIB coordinate mapping method according to claim 1, characterized in that, In S3, constructing the sputtering prediction model based on the mapping density matrix and the mapping cross-section matrix includes: Extract the Gaussian diffusion kernel function parameters characterizing the high-energy ion beam current density distribution and the system incident tilt angle parameters of the ion beam from the FIB device; A nonlinear physical mapping operator is set up, and the mapping density matrix is ​​converted into an ion sputtering yield matrix characterizing the material removal rate of each voxel node through the nonlinear physical mapping operator; The ion sputtering yield matrix, the Gaussian diffusion kernel function parameters, and the system incident tilt angle parameters are input into the discrete-time state transition equation to establish the sputtering prediction model with residence time as the control input and topography depth as the state output.

7. The sample failure point pre-location and FIB coordinate mapping method according to claim 6, characterized in that, In S3, the optimization solution to generate the optimal dwell time matrix under the current control cycle includes: Based on the sputtering prediction model, a rolling optimization cost function containing prediction time domain and control time domain is constructed. In the rolling optimization cost function, a depth error penalty term for characterizing state tracking accuracy and a dwell time increment penalty term for characterizing beam change smoothness are configured. Under the boundary constraint condition of setting the maximum beam output physical limit of the FIB device as the boundary condition, the minimum value of the rolling optimization cost function is solved by a quadratic programming algorithm. The control variable of the first time step is extracted from the predictive control sequence corresponding to the minimum value obtained from the solution, and used as the optimal dwell time matrix under the current control cycle.

8. The sample failure point pre-location and FIB coordinate mapping method according to claim 1, characterized in that, In S4, controlling the FIB device to perform physical ion milling operation according to the optimal residence time matrix, acquiring a real-time cross-sectional image of the sample after milling, and extracting the true current physical morphology matrix includes: The optimal dwell time matrix is ​​compiled into drive control instructions for the hardware scanning coil, which control the FIB device to perform grating scanning milling in the target area for a single control cycle. The electron microscope integrated into the FIB device is used to perform in-situ cross-sectional scanning of the milled target area to obtain the real-time cross-sectional image; Subpixel-level edge detection and physical scale mapping are performed on the real-time cross-sectional image to locate the real material removal boundary contour, and the real material removal boundary contour is converted into the current physical shape matrix.

9. The sample failure point pre-location and FIB coordinate mapping method according to claim 1, characterized in that, In S5, calculating the spatial residual between the current physical topography matrix and the theoretically predicted topography calculated based on the sputtering prediction model, and using the spatial residual to inversely correct the mapping density matrix includes: Retrieve the theoretical predicted morphology output by the sputtering prediction model in the previous control cycle; Align the current physical topography matrix with the theoretical predicted topography in spatial coordinates, and calculate the depth difference sequence between the two at corresponding pixel nodes to generate the spatial residual; The state update gain matrix is ​​calculated based on the system prediction covariance and the visual extraction measurement noise variance. The physical topography drift is then calculated by multiplying the state update gain matrix with the spatial residual. The physical topography drift is converted into a local density correction compensation amount using the sputtering yield inverse mapping operator, and the local density correction compensation amount is then superimposed onto the mapping density matrix to complete the update.

10. The sample failure point pre-location and FIB coordinate mapping method according to claim 1, characterized in that, In S5, the step of "until the current physical topography matrix approximates the mapping section matrix" includes: Calculate the absolute distance norm between the current physical shape matrix and the mapped section matrix at global pixel nodes; The absolute distance norm is compared with the sample preparation tolerance threshold preset by the system. When the absolute distance norm is greater than the sample preparation tolerance threshold, the time step index of the control cycle is shifted forward, and the subsequent operation of constructing the sputtering prediction model is continued with the corrected mapping density matrix. When the absolute distance norm is less than or equal to the sample preparation tolerance threshold, it is determined that the cutting depth has reached the target failure point, and a device interruption command is triggered to end the physical ion milling operation.

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