A method for identifying etching defects and predicting loss of a thin-film lithium niobate waveguide

Abstract

The application discloses a kind of thin film lithium niobate waveguide etching defect identification and loss prediction method, at least two kinds in scanning electron micrograph, atomic force microscopic height data and scattering micrograph are obtained, and space-view observation matrix is formed;Defect support is applied to direction continuous, limited branch and layout boundary constraint;Through structured defect recovery, separate normal process state response and local defect response, and utilize the geometric detection data with actual spatial scale calibration relationship to recover sidewall normal geometric deviation and sidewall roughness power spectrum;According to the difference of sidewall roughness spectrum, particle load and branch defect, differential propagation loss mapping is established, and defect detection result and propagation loss prediction result are obtained.The application can avoid directly explaining the dimensionless abnormal response of different detection channels as actual sidewall geometry, and reduce the risk of repeatedly counting the reference structure itself scattering loss.

Description

Technical Field

[0001] This invention relates to the manufacturing inspection and optical performance evaluation of thin-film lithium niobate photonic devices, and particularly to a method for identifying etching defects and predicting losses in thin-film lithium niobate waveguides. Background Technology

[0002] Thin-film lithium niobate waveguides are typically formed through processes such as mask pattern transfer, dry etching, residue removal, and cladding. Sidewall roughness, redeposited particles, microgrooves, edge collapse, and localized cracks can alter the guided mode boundary and cause scattering loss. Scanning electron microscopy (SEM) images can provide sidewall contour and particle information, atomic force microscopy (AFM) data can provide nanometer-scale height information, and scattering microscopy images can reflect localized scattering intensity; however, different detection channels have different dimensions, spatial resolution, and field of view, resulting in different response amplitudes for the same actual defect on different detection channels.

[0003] Existing defect identification methods often employ grayscale thresholding, edge detection, or pixel-by-pixel classification, which can easily misidentify normal periodic textures as defects and fragment the same defect extending along the ion incident direction or the reaction product flow direction into multiple regions. While ordinary low-rank sparse decomposition can separate repeating backgrounds from local anomalies, point-by-point sparsity penalty does not utilize the directional continuity, finite branches, and layout boundary relationships of defects. Directly imposing spatial topological constraints on the anomaly matrix, which mixes lateral positions, detection channels, and repeating fields of view, can further confuse channel response amplitudes with actual defect locations.

[0004] On the other hand, the normalized image anomaly response does not have a definite length dimension and cannot be directly used as the sidewall roughness input scattering loss model in the absence of geometric calibration. Existing image detection results usually stop at the defect area or category, without jointly mapping the defect spatial support, actual sidewall geometry, sidewall roughness power spectrum, and waveguide mode field shared by multiple detection channels to the propagation loss; if the measured total loss of the reference waveguide is directly added to all defect scattering terms of the waveguide under test, the sidewall scattering already included in the reference waveguide itself may be double-counted.

[0005] Therefore, there is a need for a method that can clearly distinguish between multi-detection channel response and shared space defect support, use shared space defect support to determine the spatial location of defects, and combine detection data calibrated with actual spatial scale to restore the actual geometry of the sidewall, and establish a physical mapping from etching defects to propagation loss based on the differential form of the reference structure; and, in the case of actual propagation loss measurement of the object under test, the actual propagation loss can also be used to further verify the defect recovery results. Summary of the Invention

[0006] This invention provides a method for identifying etching defects and predicting losses in thin-film lithium niobate waveguides. It organizes multi-mode detection data, etching direction, layout contour, geometric detection data with actual spatial scale calibration relationships, mode field scattering kernels, and reference structure losses into a processing chain consisting of signal formation, shared-space defect recovery, physical geometric recovery based on reference boundaries, and differential loss mapping. This addresses the problems of inconsistencies between multi-channel anomaly responses and actual spatial topology, the inability to directly convert dimensionless defect responses into physical geometric quantities, and redundant calculations of reference losses. In an optional embodiment, when the actual propagation loss of the object under test is measured, the deviation between the predicted propagation loss and the actual propagation loss is used to physically verify the defect recovery results. The method of this invention includes the following steps: S01, acquire at least two of the following after etching of the thin-film lithium niobate waveguide: scanning electron microscopy image, atomic force microscopy height data, and scattering microscopy image, and acquire the waveguide layout outline, etching main direction, detection coordinates, repeating field of view markers, and effective sampling markers; establish a common spatial sampling grid along the waveguide propagation direction and the lateral direction, and register the original image or height data of each detection channel to the common spatial sampling grid; for each common spatial sampling position, perform interpolation or region aggregation based on its corresponding pixel or pixel region in the corresponding detection channel to obtain the spatial sampling observation value of each detection channel; perform dimensionless standardization on the spatial sampling observation value according to the channel statistical parameters of the defect-free calibration region, and form a spatial-view observation matrix according to the combination of lateral position, detection channel, and repeating field of view.

[0007] In the preferred technical solution, a common spatial sampling grid is established within the waveguide coordinate system. ,in, For the first waveguide propagation direction Each sampling location For the horizontal first The sampling location. For the first sampling location. The first detection channel Based on the registration relationship between the detection channel and the waveguide coordinate system, the sampling position in the common space is determined using a repeated field of view. The corresponding pixel set in the original detection data And calculate the spatially sampled observations:

[0008] in, Indicates the first The first detection channel The original pixel value or height sampled value in a repeating field of view. Spatial resampling operators for the corresponding detection channels include one of interpolation, regional averaging, regional median, or spatial weighted aggregation.

[0009] The obtained spatial sampling observations are channel-normalized according to the defect-free calibration area:

[0010] Where and are the median and interquartile range of the i-th detection channel in the defect-free calibration region, respectively; is the background correction or dynamic range transformation function corresponding to the detection channel; and is the numerical stability term. The original pixel values ​​in the scanning electron microscopy channel are the electron microscopy grayscale response, the original sampled values ​​in the atomic force microscopy channel are the surface height, and the original pixel values ​​in the scattering microscopy channel are the scattered light intensity; the standardized results of each channel are dimensionless observations. The original height values ​​of the atomic force microscopy channel, the edge coordinates obtained by pixel size calibration of the scanning electron microscopy image, and other detection data that can obtain the actual boundary position through independent geometric calibration are simultaneously retained and not discarded due to the construction of the dimensionless observation matrix. The data with actual spatial scale calibration relationships and that can be used for sidewall boundary or independent geometric quantity recovery are collectively referred to as the geometric detection data set. Among them, data that can be converted into sidewall normal boundary coordinates is used for sidewall geometric deviation sequence recovery in step S02, while data that can only provide height, sidewall angle, or scattering intensity but cannot be converted into sidewall normal boundary coordinates are used as independent geometric descriptors or defect support confidence. The combined index is denoted as... This allows us to obtain the elements in the space-view observation matrix. Specifically: Indexing the columns of the spatial-view observation matrix With lateral spatial location index Detection Channel Index and repeating field index Establish a one-to-one correspondence, where, , , and in accordance with:

[0011] triplet Mapped to the column indices of the space-view observation matrix, where, , and These represent the number of lateral spatial locations, the number of detection channels, and the number of repeated fields of view, respectively. The total number of columns in the observation matrix is... .

[0012] In the preferred technical solution, step S01 includes: constructing an observation matrix with the sampling positions along the waveguide propagation direction as rows and the combination of lateral positions, detection channels, and repeated fields of view as columns. A predetermined channel transformation function is applied to different detection channels. For the scanning electron microscope detection channel, an identity transformation is used. ,in This represents the grayscale response obtained under fixed or calibrated imaging parameters and then spatially resampled. For the atomic force microscopy detection channel, a height transformation of the background-de-scanning plane is used:

[0013] in, , , Height samples from a defect-free reference region or within the scanning reference plane are obtained through least-squares plane fitting. For the scattering microscopy detection channel, the following method is used:

[0014] in, The dark background intensity is obtained from the median of the dark field image under the same acquisition parameters; when there is no independent dark field image, it is obtained from the low quantile intensity of the non-waveguide background region determined by the layout. The median of the positive scattering intensity after subtracting the dark background in the defect-free calibration region. To prevent numerical stability terms from being divided by zero.

[0015] For the first Each detection channel, in a defect-free calibration sampling set The median of the detected values ​​after the transformation is calculated. and interquartile range and define:

[0016] in, This is a numerically stable term. After index mapping, we obtain... .

[0017] The normal detection signal of the qualified etched area within the same process-related batch is represented as the superposition of the reference sidewall response and the response of a finite number of process state disturbances. Local defect response and acquisition noise are added as additional terms, and the following signal formation model is established:

[0018] in, This is an index of the sampling position along the waveguide propagation direction. This represents the number of sampling positions in this direction; A combined index for lateral position, detection channel, and repeating field of view. This represents the total number of composite indexes. To complete the coordinate registration and channel normalization of the dimensionless detection values; For the defect-free calibration area associated with the same process, in the first The baseline response on each combined channel is obtained from the median of multiple defect-free fields of view; The number of effective process states that can affect normal sidewall signals is determined by the reconstruction residual that leaves a defect-free field of view and the noise of repeated measurements. For the first The sampling position of the first sampling location Each process state coefficient is obtained from cross-sectional measurements, equipment records, or response basis projection of a defect-free region. For the first The process state is in the first The response basis on each combined channel is obtained from the finite difference response or principal component loading of the calibration region; , , for A column vector of all 1s; This represents the additional response of localized etching defects on the corresponding combined channels; To collect noise and registration residuals. Normal response matrix. Generated by finite process states and thus possessing low rank, defect response It occupies only a local space in the sidewall detection zone and has structured sparse support.

[0019] In the preferred technical solution, step S01 further includes: expanding the combined column index into Accordingly, the defect response is written as The response amplitude and dimensional normalization scale of the same actual defect may differ in different detection channels, but its wafer spatial location should be consistent. Therefore, a shared spatial defect amplitude is defined across detection channels and repeated fields of view:

[0020] in, Sampling location The dimensionless shared space defect amplitude at the location; For the first The first detection channel The non-negative dimensionless weights of each repeated field of view are calculated, with the sum of the normalized effective weights being 1, and are based on the reciprocal of the variance of repeated measurements, spatial resolution, and signal-to-noise ratio of the corresponding channel; the weights of the invalid channels are... Take 0. Used for subsequent topological constraints and defect connectivity determination of directed river graphs, on each detection channel. The original response characteristics of the corresponding channel are preserved. The shared spatial defect amplitude is then... Defined at the position along the waveguide propagation direction Horizontal position On the constructed two-dimensional common space grid. For any river map node. ,make:

[0021] Its nodal magnitude is defined as:

[0022] For any directed edge ,in , , indicating from spatial location Pointing to the adjacent downstream spatial location A directed connection.

[0023] In the preferred technical solution, step S01 further includes: writing the observation relationship as And construct an effective sampling weight matrix of the same dimension. For effective observation, The element is the normalized value of the reciprocal of the standard deviation of repeated measurements for that channel; for observations that are unqualified in terms of equipment quality, fall outside the detection band after registration, or are missing. The element is 0. Number of process states. The selection criteria are: the weighted reconstruction residual, which leaves a defect-free field of view, is initially no higher than the noise upper limit obtained from the 95th quantile of the repeated acquisition differences, and the singular values ​​corresponding to the response basis are preserved to be higher than the minimum value at the tail of the noise spectrum; if no such conditions are met... If the automatic identification fails, the process batch will be reclassified or a normal calibration sample will be added.

[0024] S02, based on the shared space defect amplitude mapping, etching main direction and waveguide layout outline defined in step S01, establish a directed river map, and define the direction continuity, finite branches and layout boundary constraints of the shared space defect support; determine the spatial location that needs to be geometrically described by the shared space defect support, and define the recovery of the sidewall normal geometric deviation sequence with actual spatial dimensions using the geometric detection data set, reference sidewall boundary and geometric calibration parameters retained in step S01, and form the relationship between the continuous descriptor vector and the discrete topological descriptor vector.

[0025] Based on the aspect ratio, main direction consistency, and region scale of the connected regions corresponding to the shared space defect amplitude, candidate defects are supported. Further classified into directional defect supports Non-directional local defect support Among them, microgrooves, cracks, and redeposition zones with obvious directional extension characteristics are classified as directional defect supports. Isolated particles, local particle clusters, and local roughness anomalies without a stable principal direction are classified as non-directional local defect supports. .

[0026] In the preferred technical solution, step S02 includes: taking the effective spatial sampling positions located within the detection zone on the sidewall of the layout as a set of nodes; forming a set of directed edges from adjacent nodes, with the connection direction pointing from upstream nodes to downstream nodes and the angle between the connection direction and the main etching direction not exceeding a direction threshold; and applying river topology soft constraints to the directional defect support.

[0027] in, and These are the adjacent upstream and downstream nodes, respectively; For directed edge weights, For the edge The direction angle, The principal etching direction angle is obtained from the etching equipment orientation record or the calibrated trench direction. The direction deviation penalty coefficient is determined by the minimum connectivity error criterion of the verified defect set; For candidate branch node groups, This represents the shared defect magnitude vector of the branch node and its candidate downstream branches; and These are the directional continuity weights and branch group weights, respectively, which are jointly determined by the defect support intersection-union ratio and connectivity error on the calibration set.

[0028] In the preferred technical solution, step S02 further includes: defining a feasible set of directional defect supports:

[0029] in, The effective defect path is limited to extend generally along the downstream direction of etching; The number of valid downstream branches of non-leaf nodes is limited to the upper limit obtained from the statistics of the reviewed defect samples; The restricted defect supports are located within the sidewall detection zone after the layout and detection image are registered. The orientation threshold is determined by the angle distribution of the verified defect paths relative to the main etching direction, taking the minimum angle covering a predetermined proportion of verified defect paths, preferably 95%. River topology soft constraints are used to control the continuity of supports, and feasible sets are used to exclude supports that do not meet the orientation, branch, or layout boundary conditions; the two are not interchangeable.

[0030] In the preferred technical solution, step S02 further includes: defining a geometric restoration relationship, which is used to determine the spatial location of the defect that needs to be geometrically described based on the shared space defect amplitude after the structured defect restoration is completed, and to restore the sidewall normal geometric deviation sequence with actual spatial dimensions using the geometric detection data set retained in step S01.

[0031] Taking the first sampling position of the effective sidewall interval as the origin of the arc length coordinate, the... The arc length coordinates of each sampling position are defined as follows:

[0032] in, The actual spatial spacing between adjacent valid sidewall geometric sampling points is determined by the calibrated pixel size or the scanning spacing of the corresponding geometric detection channel. The reference sidewall boundary is positioned at the arc length position. The actual spatial coordinates of the location are as follows Its unit normal vector is denoted as The reference sidewall boundary is preferably the measured average sidewall boundary of a defect-free reference structure that has a predetermined process association with the waveguide under test; when the measured average boundary is unavailable, the nominal sidewall boundary of the waveguide layout registered with wafer coordinates is used.

[0033] For the A detection channel capable of obtaining the sidewall boundary position through independent geometric calibration and the first A repeated field of view, the actual sidewall boundary points obtained after coordinate registration, scale conversion and sidewall edge extraction are denoted as... And define the detection channel in the first... The sidewall normal geometric deviation obtained at each sampling location is:

[0034] in, The units are nm or μm. For scanning electron microscopy detection channels, it is preferable to determine the actual sidewall boundary points within the reference sidewall normal neighborhood based on grayscale gradient peaks or sub-pixel edge fitting; for atomic force microscopy detection channels, they only participate in the detection process if their height data can be converted into sidewall normal boundary coordinates through probe correction, coordinate registration, and independent geometric calibration. The calculation is as follows: For detection channels that only provide sidewall height, local sidewall angle, or scattering intensity but cannot be converted into sidewall normal boundary coordinates, their detection values ​​are not included in the calculation. Numerical fusion, and used as an independent geometric descriptor or defect support confidence level.

[0035] Definition of the first The geometric detection channel number The repeated field of view in the first... Validity identifier of each sampling location When the location is covered by the corresponding field of view, the registration residual meets the requirements, and the edge extraction confidence reaches a predetermined threshold. Otherwise, take 0. The standard deviation is based on the repeated measurements of the corresponding geometric quantity. Determine the normalized fusion weights:

[0036] in, To prevent numerically stable terms with a denominator of zero. When at least one geometric detection channel is active, the first... The actual normal geometric deviation of each sidewall sampling location is defined as:

[0037] When there is no valid geometric detection value at a certain sampling location, the location is marked as an invalid geometric sampling point and excluded from the valid sampling set for subsequent power spectrum calculations, without being replaced by a zero value.

[0038] In a preferred embodiment, step S02 further includes: processing the sidewall geometry sequence after removing the average contour. Windowing and calculation of spatial power spectral density:

[0039] Where is the sidewall roughness power spectral density at the i-th spatial frequency; is the average sidewall deviation within the effective interval; is the i-th window function coefficient; is the window power normalization coefficient; is the spatial angular frequency; and is the imaginary unit. A continuous descriptor vector is formed from the sidewall geometric sequence and its power spectrum, sidewall angle, and particle load. The continuous descriptor includes at least one or more of the following: power spectrum discrete coefficients, root mean square roughness, correlation length, sidewall angle deviation, and normalized particle area loading; the number of effective branches and branch levels are statistically determined by the updated directed river graph, and the number of particle connected regions is statistically determined by the connected regions supported by non-directional local defects, forming a discrete topological descriptor vector. Let the complete defect description vector be . The complete defect description vector is used for defect classification, geometric statistics, and result output. The descriptive quantities directly related to propagation loss and their deterministic derivatives are further combined into a loss-related description vector in step S03.

[0040] S03 calculates the defect scattering nucleus based on the cross section of the waveguide under test, the refractive index of the material, the operating wavelength, and the normalized guided mode field of unit power. The scattering nucleus scale and reference loss are calibrated using a reference structure with a predetermined process association with the waveguide under test. A differential propagation loss mapping is established according to the sidewall roughness spectrum, particle load, and branch defect increment of the waveguide under test relative to the reference structure.

[0041] Preferably, the predetermined process correlation refers to the reference structure and the waveguide under test having at least the same thin film material layer system, nominal etching process formulation, and nominal waveguide cross-section type, and the difference between at least one key cross-sectional parameter of the reference structure (etch depth, top width, and sidewall angle) and the waveguide under test does not exceed the corresponding calibration threshold; the reference structure is preferably located in the same wafer, the same etching batch, or a calibration batch verified by process consistency. Each calibration threshold is determined based on the sensitivity of the scattering nucleus to the corresponding cross-sectional parameter and the loss error of the independent verification structure.

[0042] In the preferred technical solution, step S03 includes: calculating the wavelength of the waveguide under test according to the following relationship. and guide mold Propagation loss below:

[0043] Among them, except for the reference propagation loss The last three terms together represent the propagation loss correction amount of the waveguide under test relative to the reference structure caused by the differences in sidewall roughness spectrum, particle load, and branch defect; this correction amount is used to correct the propagation loss of the reference structure and is not output as an independent prediction result. For the waveguide under test at wavelength and guide mold The predicted propagation loss is given in dB / cm. The propagation loss is measured by the back-cutting method or calculated from the intrinsic quality factor of the reference ring resonator for a reference straight waveguide that has a predetermined process association with the waveguide under test. The unit is dB / cm. and These are the spatial power spectral densities corresponding to the actual sidewall geometric sequences of the waveguide under test and the reference structure, respectively. The scattering sensitive nucleus is calculated based on the cross section of the waveguide under test, the refractive index of the material, and the normalized guided mode field of unit power. Its overall size is calibrated only by an independent reference structure. and These are the lower and upper limits of the spatial frequency integration, respectively, which are jointly determined by the field of view length, sampling interval, and effective sensitive frequency band of the guided mode field.

[0044] In the preferred technical solution, step S03 further includes: detecting the first waveguide within the test band. The actual projected area of ​​each particle's connected region is denoted as . The actual length and width of the detection strip are recorded as follows: and And define the dimensionless normalized particle area loading:

[0045] in, This represents the number of connected regions in the particles. The number of effective branch defects in a directed river graph. The effective number of branch defects per unit inspection length, with the unit being the reciprocal of the length; and These are the normalized particle area load and branch defect density corresponding to the reference structure, respectively; This is the particle loading correction factor, in dB / cm; This is the branch defect correction factor, and its unit is... The value is dB / cm; both are obtained by performing non-negative weighted least squares fitting on an independent calibration structure that includes verified particle defects and branch defects.

[0046] In a preferred embodiment, step S03 further includes: discretizing the differential propagation loss relationship to facilitate unified calculation of multiple target wavelengths and guided modes. The sidewall roughness power spectrum obtained in step S02 is then applied to a predetermined spatial frequency. Discrete values ​​and normalized particle area loading on and branch defect density Composition loss-related descriptive vector:

[0047] Accordingly, the loss-related descriptor vector corresponding to the reference structure is denoted as:

[0048] Assuming the target wavelength-guided mode combination is according to Arrangement, number Each combination corresponds to a wavelength and guide mold ;by The first value is determined by the spatial frequency integral discretization rule used. If there are integral weights, then construct the loss mapping matrix. , its first Behavior:

[0049] in, It can be obtained according to trapezoidal integral, rectangular integral, or other deterministic numerical integration rules adapted to the spatial frequency sampling grid. The reference propagation loss of each target wavelength-guided mode combination is arranged into a vector. Then the scalar differential propagation loss relationship in step S03 can be uniformly expressed as:

[0050] in, This represents the predicted propagation loss vector for each target wavelength-guided mode combination. The loss-related descriptive vector... Only includes descriptive quantities that directly lead to the differential propagation loss relationship in step S03; the complete defect description vector defined in step S02. It is still used for defect classification, geometric statistics, and result output, and it is not required that all its components enter the propagation loss mapping.

[0051] In a preferred embodiment, step S03 further includes: verifying the validity of the loss calibration of the reference structure before performing propagation loss prediction. The reference structure should meet predetermined process association conditions with the waveguide under test and have effective propagation loss measurements corresponding to the target wavelength and guided mode. When the reference structure loss measurement is missing, the measurement uncertainty exceeds the predetermined upper limit, or the reference structure and the waveguide under test do not meet the predetermined process association conditions, the propagation loss numerical prediction is not performed, a "reference calibration needs to be supplemented" flag is output, and the process is transferred to re-inspection or reference structure supplementation measurement.

[0052] S04, based on process state coefficient and the response of etching defects in each detection channel As the active variable, a structured defect recovery problem is constructed based on the effective sampling weights, the smoothness of the normal process state, and the structural constraints of the shared space defect structure, and solved using an alternating update method.

[0053] In the preferred technical solution, step S04 includes: solving the following structured defect recovery problem based on the signal formation model of step S01 and the shared space defect structure constraints of step S02:

[0054] The first item is the consistency item of valid observation data; Let be the first-order difference matrix along the waveguide propagation direction. Smoothing weights for normal process conditions; The cross-detection channel and repeated field-of-view shared spatial defect amplitude mapping defined in step S01 is denoted as ; This is a structured defect regularization term that acts on the shared space defect support; The weights are for structural defect constraints.

[0055] Preferably, the structured defect regularization term is defined as:

[0056] in, and These are the directional defect supports and non-directional local defect supports determined in step S02 based on the aspect ratio, principal direction consistency, and regional scale of the current shared space defect amplitude. Determined rather than treated as an independent activity variable; The directed river topology soft constraints are defined for step S02. For directional defect supports, further directional continuity, finite branching, and map boundary feasibility repairs are performed; for non-directional local defect supports, no downstream directional constraints are applied, only spatial sparsity and map boundary constraints are applied.

[0057] In the preferred embodiment, step S04 further includes: fixing the current etching defect response. At that time, the process state coefficients are updated based on the consistency term of valid observation data and the process state smoothing term:

[0058] Fixed updated process state coefficients At that time, the etching defect response is updated based on the consistency term of the valid observation data and the shared space defect structure constraints:

[0059] The The subproblems can be solved using weighted least squares or conjugate gradient methods; The subproblems can be solved using proximal gradients, primal-dual algorithms, or alternating direction multiplier methods. Each update... Then, according to Recalculate the shared space defect amplitude and update the directional defect supports and non-directional local defect supports according to step S02; perform directional weighted map updates and directional river feasible support repairs on the directional defect supports.

[0060] When the objective function changes relatively within a predetermined number of consecutive rounds and and When the relative changes are all below the corresponding stopping threshold, the alternating iteration stops; if the stopping condition is not met by the processing time limit, the defect recovery result that most recently met the layout boundary constraints is returned and marked as "needs re-inspection".

[0061] After the structured defect recovery is completed, the final etch defect response is used as a basis. The shared space defect amplitude, actual sidewall normal geometric deviation, complete defect description vector, and loss-related description vector defined in step S03 are calculated sequentially:

[0062]

[0063]

[0064]

[0065] in, The calculation is performed according to step S02 using the final sidewall normal geometric deviation sequence, independent geometric descriptions, and shared space defect support. The final directed river map and non-directional local defects support direct statistics, which together constitute a complete defect description vector for defect classification and result output. ; Following step S03, the discrete values ​​of the sidewall roughness power spectrum, normalized particle area load, and branch defect density are extracted from the final recovery result, and used only for propagation loss calculation. Forming a sequence of sidewall normal geometric deviations:

[0066] Then, the propagation loss prediction vector is calculated according to the discrete differential propagation loss mapping in step S03:

[0067] in, The loss mapping matrix is ​​constructed in step S03 based on the discrete integral weight of the scattering sensitive nucleus, the particle load correction coefficient, and the branch defect correction coefficient. and These are the loss-related description vector of the reference structure and the propagation loss vector, respectively.

[0068] In one alternative implementation, when the waveguide under test has actual propagation loss measurements at some target wavelength-mode positions, the actual propagation loss measurements are used to perform physical consistency verification on the propagation loss prediction results obtained from the etching defect response.

[0069] Let the objective function of the structured defect recovery problem mentioned in step S04 be:

[0070] Response to current etching defects First, the shared space defect amplitude, actual sidewall geometry, and loss-related descriptive vector are calculated according to steps S01 and S02, and the loss-related descriptive vector is denoted as... The current etching defect response is calculated using the reference structure differential propagation loss mapping established in step S03. Corresponding propagation loss prediction vector Let the actual propagation loss measurements of the waveguide under test at certain wavelength-mode positions form a vector. To select the matrix Extracting the predicted value corresponding to the actual measurement location from the complete propagation loss prediction vector, the propagation loss physical verification residual is defined as:

[0071] The physical verification residual characterizes the degree of inconsistency between the predicted propagation loss value corresponding to the current etch defect recovery result and the actual measured propagation loss value. To ensure that the recovered etch defect can both explain the multi-detection channel observation data and is consistent with the actual propagation loss measurement, a propagation loss physical verification term is added to the aforementioned structured defect recovery objective function, resulting in:

[0072] in, The covariance matrix of the actual propagation loss measurement is defined as follows: , This is a physical verification weight for propagation loss. The additional item only changes the process state coefficient. and Etching Defect Response The preferred solution does not treat propagation loss, shared space defect amplitude, or loss-related descriptor vector as new independent active variables.

[0073] S05, based on the final etching defect response and shared space defect support obtained in step S04, generate defect detection results; based on the actual sidewall geometry and defect description quantity obtained in step S02 and the reference structure differential propagation loss mapping established in step S03, generate propagation loss prediction results; based on the defect detection results, propagation loss prediction results and product judgment rules, form automatic judgment results, and generate re-inspection information and process traceability information based on the automatic judgment results.

[0074] In the preferred technical solution, step S05 includes: based on the final shared space defect amplitude obtained in step S04. The effective defect region is determined by supporting directional and non-directional defects. For each effective defect region, its position in the common space sampling grid is reverse-mapped to wafer coordinates and original detection image coordinates to form a defect mask. The defect location, length, lateral width, direction, number of branches, branch level, and sidewall geometric statistics are calculated based on the spatial range, main direction, river topology, and actual sidewall geometry of the corresponding region.

[0075] For the Let there be a defect region, and its effective spatial node set be denoted as . The wafer coordinate position is determined by the set of wafer coordinates corresponding to the node; the defect length is calculated along the main direction of the region, and the lateral width is calculated along the normal of the main direction. The number of branches and the branch level of directional defects are statistically determined by the corresponding directed river subgraph, and the number of particles and the area of ​​non-directional local defects are statistically determined by the corresponding connected regions.

[0076] Based on the aforementioned geometric and topological features, the defect type is determined according to the predetermined defect category criteria, and abnormal areas that do not meet the defined category criteria are marked as unclassified defects.

[0077] In the preferred embodiment, step S05 further includes: forming a loss-related description vector based on the final recovery result.

[0078] And calculate the propagation loss prediction vector for each target wavelength-guided mode combination according to the reference structure differential propagation loss mapping in step S03:

[0079] It also outputs the reference structure batch, scattering kernel version, and reference calibration validity status used, so that each propagation loss prediction result can be traced back to the corresponding geometric descriptor and reference calibration data.

[0080] In the preferred technical solution, step S05 includes: determining the defect type based on the spatial location of the defect, the sign of the actual geometric deviation, the aspect ratio, the change in sidewall height, and the river topology. Defects located outside the designed sidewall and exhibiting localized positive material residue or particle accumulation are marked as redeposition defects; narrow strip-shaped defects extending continuously along the main etching direction and exhibiting localized inward depressions are marked as microgrooves; defects with continuous lateral recession of the sidewall boundary and a local width exceeding the collapse threshold are marked as collapse defects; narrow linear defects with high aspect ratio, obvious directional continuity, and spanning multiple adjacent sampling positions are marked as cracks; abnormal areas that do not meet the defined category criteria are marked as unclassified defects and enter the re-inspection. The collapse threshold, aspect ratio threshold, and threshold for the number of sampling positions spanned are all determined by the inter-category separation criterion of the corresponding geometric statistics of the reviewed defect samples or the minimum classification error criterion of the validation set, and are recorded together with the threshold version.

[0081] In the preferred technical solution, step S05 further includes: calculating the standard uncertainty of loss based on the uncertainty propagation of continuous descriptors, scattering kernel calibration, scattering model, multi-detection channel registration, and geometric recovery.

[0082] in, The standard uncertainty of each element of the propagation loss vector is expressed in dB / cm. The covariance is a descriptive measure of loss obtained through repeated testing or resampling of calibration samples. The calibration covariance is generated for reference loss measurement and scattering kernel scale fitting; The predicted residual covariance of the differential scattering loss model on an independent complex kernel structure; The covariance formed by coordinate registration and geometric recovery error propagation for multiple detection channels; This indicates extracting the diagonal elements of the matrix and taking the square root of each element. When using the optional loss physical verification method described in step S04, the covariance generated by repeated loss measurements of the object under test can also be considered. The corresponding uncertainty propagation should be taken into account. The prediction interval is... Coverage factor The output is determined based on the number of independently verified samples and the target coverage probability. Output records include wafer coordinates, defect category criterion version, detection channel version, geometric calibration version, scattering nucleus version, reference structure batch, stop reason, and feasibility marker. When using optional loss physical verification, the actual loss measurement location and measurement version are also recorded.

[0083] For waveguide segments marked as to be re-inspected, the wafer coordinates, chip coordinates, and original detection field coordinates are obtained by reverse transformation based on the common space coordinates corresponding to the defect mask. Microscopic re-inspection coordinates and the corresponding defect area range are generated, and the defect type to be re-inspected, the predicted propagation loss value, and the prediction interval are sent to the re-inspection interface.

[0084] Simultaneously, the test results are associated with the wafer number, chip number, waveguide segment identifier, etching equipment, etching batch, test channel version, geometric calibration version, scattering core version, and reference structure batch to form a process traceability record. For waveguide segments with excessive loss or abnormal defects, a corresponding process traceability identifier is generated based on the defect type, defect direction, and spatial location. This identifier is used for subsequent queries of the etching equipment location, etching batch, mask pattern, and cleaning process records related to the defect. The process traceability identifier is used to assist process engineers in locating the source of the anomaly without directly modifying the manufacturing equipment process parameters.

[0085] This invention also provides a system for identifying etching defects and predicting losses in thin-film lithium niobate waveguides, including a multimodal detection and registration module, a defect spatial support and river map construction module, a structured defect recovery module, a geometric recovery and descriptor generation module, a scattering kernel calibration and loss prediction module, and a re-inspection and process interface module. The multimodal detection and registration module forms a spatial-view observation matrix with effective sampling weights and retains the combined index of lateral position, detection channels, and repeated fields of view. The defect spatial support and river map construction module defines a mapping for calculating the shared spatial defect amplitude from the defect responses of each detection channel and generates directed edges, branch node groups, and shared support constraints based on the main etching direction and layout boundary. The structured defect recovery module uses process state coefficients and etching defect responses of each detection channel as active variables, performing alternating recovery based on effective observation consistency, process state smoothing, and shared spatial defect structure constraints. The geometric recovery and descriptor generation module determines the geometric detection area based on the shared spatial defect support and calls the data calibrated at the actual spatial scale. The geometric inspection data and reference sidewall boundary are fused together using the sidewall boundary normal projection and weighted variance of repeated measurements to form an actual sidewall normal geometric deviation sequence. This sequence is then combined with geometric quantities such as independent sidewall angles and heights to form a complete defect description vector. From this vector, a loss-related description vector is formed using descriptive quantities directly related to propagation loss and their deterministic derivatives. The scattering kernel calibration and loss prediction module establishes a differential propagation loss mapping based on the unit power normalized guided mode field, reference structure propagation loss, and reference loss-related description vector. It also generates a propagation loss prediction value based on the loss-related description vector of the waveguide under test. The re-inspection and process interface module outputs the defect location and type, actual sidewall geometry, loss prediction interval, reference calibration validity status, and traceability identifier. When the actual propagation loss measurement data of the object under test is configured, the structured defect recovery module can also call the loss physics verification subunit to further verify the etching defect response based on the deviation between the predicted and actual losses.

[0086] This invention has at least the following beneficial effects: by expanding the combined index into lateral position, detection channels, and repeated fields of view, and forming a shared spatial defect amplitude from multi-channel abnormal responses, the river topological constraints act on the actual spatial support rather than channel values ​​of different dimensions; by determining the spatial location of the defect through the shared spatial defect amplitude, and by using geometric detection data calibrated to the actual spatial scale to perform normal projection and multi-field fusion relative to the reference sidewall boundary, the dimensionless defect response is avoided from being directly converted into the actual length, thus providing a clear physical dimension interface between the sidewall roughness power spectrum and the scattering kernel; by using a structured defect recovery model with only process state coefficients and etching defect responses as active variables, normal process state changes are separated from the defect spatial structure, avoiding a decrease in model interpretability due to too many active variables; by using a reference structure differential loss model, the sidewall scattering of the reference waveguide itself is avoided from being repeatedly included, thus providing a clear geometric and calibration source for propagation loss prediction; and when the actual propagation loss of the object under test is measured, the deviation between the predicted loss and the measured loss can be used to further physically verify the defect recovery results. Attached Figure Description

[0087] Figure 1 This is the overall flow chart and optional loss physical verification relationship diagram of the method for identifying etching defects and predicting losses in thin-film lithium niobate waveguides according to the present invention. Figure 2 A graph showing the correspondence between combined indexes, multi-detection channel defect responses, and shared space defect amplitudes; Figure 3 A diagram showing the physical mapping relationship between shared space defect support, actual sidewall geometry, complete defect description, loss-related description vector, and differential propagation loss; Figure 4 A flowchart for alternating structured recovery of process state coefficients and etching defect responses, and optional loss physical verification. Figure 5 A system structure diagram for implementing the method of this invention; Figure 6 This is a numerical simulation example showing the distribution of multiple channel observations, effective observations, setting defect support, restoring defect support, and false alarm / missed detection for the same object. Figure 7 This is a comparison chart of normal process response reconstruction, channel defect response, and shared space defect amplitude in the numerical simulation embodiment; Figure 8 The original grayscale of the sidewall of the same bridging simulation object, the extracted boundary coordinates, and the boundary measurement error map are used. Figure 9 The total electric field and sidewall perturbation scattering field diagrams are obtained by solving the independent electromagnetic boundary values ​​for the bridging simulation object C004. Detailed Implementation

[0088] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0089] The following description, in conjunction with the accompanying drawings, illustrates a fusion embodiment of the present invention. This description is intended to enable those skilled in the art to implement the invention and is not intended to limit the scope of protection to a single device model, wavelength, or waveguide size. Preferred features, optional features, and alternative implementations in this embodiment may be used in combination without conflict.

[0090] like Figure 1 As shown, after etching and cleaning the thin-film lithium niobate waveguide, the wafer number, chip number, layout layer, etching equipment location, and process batch are obtained from the manufacturing execution system. Top-view or tilted field-of-view images are obtained using a scanning electron microscope, height data near the sidewalls is obtained using an atomic force microscope, and scattering intensity of the same waveguide segment is obtained using scattering microscopy; at least two of these detection channels are selected. The affine or non-rigid registration relationship between the channel coordinates and the wafer coordinates is determined using layout alignment marks or wafer alignment marks. The upper limit of the registration residual is determined by the repeatability error distribution of the same calibration mark; fields of view with registration residuals exceeding the upper limit are not included in automatic loss prediction but are transferred to re-inspection.

[0091] The registered field of view is divided into detection zones that are continuous along the propagation direction and laterally cover both sides of the waveguide. The pixel spacing of the detection zones is read from the equipment calibration file. Each detection channel performs background correction, spatial resampling, and dimensionless normalization according to step S01 to form a space-view observation matrix. and effective sampling weight matrix Simultaneously, the original detection data, along with their registration and scale calibration parameters, which can be obtained through actual spatial scale calibration to obtain the sidewall boundary coordinates or independent geometric quantities, are retained to form a geometric detection data set. The original grayscale values ​​of the scanning electron microscope images, the pixel-sized calibrated edge coordinates, and the original height data of the atomic force microscopy channels are not discarded during the construction of the dimensionless observation matrix. These are retained. The index mapping is performed. A calibration snapshot matrix is ​​constructed using the defect-free calibration field of view. The singular value spectrum is compared with the repeated measurement noise spectrum, and a portion of the defect-free field of view is reserved. The number of candidate process states is incremented from 1. When the weighted reconstruction residual of the baseline response and process state response basis of the reserved field of view obtained from the other fields of view is not higher than the noise upper limit for the first time, the corresponding minimum candidate value is taken as the number of process states. If there is a process formula change or a large-scale abrupt change in etching depth in the normal region, the model is divided into blocks according to the process segment to avoid forcibly interpreting non-stationary normal changes as local defects.

[0092] Solve for the initial defect response of each detection channel. Then, based on the repeated measurement variance, spatial resolution, and signal-to-noise ratio of the corresponding channels, a [formulation / determination] is generated. Calculate the amplitude of shared space defects Combining Figure 2 River map nodes, directional continuity, and branching relationships all affect... The abnormal responses of each detection channel are coupled to each other only through the shared space support; thus, the scattering microscopy image can enhance the confidence of the defect location, and will not mistake the scattering intensity for the sidewall length deviation when there is no geometric calibration.

[0093] like Figure 2 and Figure 3 As shown, the location record was obtained from the etching equipment. When equipment recording is unavailable, alternative directions are obtained from the main direction of the confirmed etching stripes using structural tensor statistics, and the direction source is recorded as "image estimation". Within a neighborhood adapted to the actual pixel scale, downstream edges are established only for nodes whose included angles satisfy the direction threshold. A candidate branch node group consists of one upstream node and two or more candidate downstream nodes. After the total variational update of the direction-weighted graph, isolated nodes that are in the opposite direction and lack neighborhood support are first deleted. Then, edge costs are constructed using defect amplitude changes, direction deviations, and the number of newly added branches. Minimum-cost directed flow or deterministic path repair is performed, and finally, intersection with the layout sidewall detection strip is calculated.

[0094] For the shared space defect support obtained from the structured defect recovery, the sidewall locations requiring geometric description are first determined. The measured average sidewall boundary of a defect-free reference structure with a predetermined process association with the waveguide under test is used as the reference boundary; if the measured average boundary is missing, the nominal sidewall boundary of the waveguide layout registered with wafer coordinates is used. For scanning electron microscopy detection channels, the actual sidewall edge coordinates are extracted in the reference sidewall normal neighborhood using grayscale gradient peaks or sub-pixel edge fitting, and converted to actual spatial coordinates based on the device pixel size; for atomic force microscopy data, after probe correction and spatial registration, it participates in sidewall normal geometric deviation fusion only if it can be converted to sidewall normal boundary coordinates through independent geometric calibration; otherwise, its height or local sidewall angle is used as an independent geometric descriptor. Following step S02, the actual boundary points obtained from each effective geometric detection channel are projected relative to the reference sidewall boundary along the unit normal, and weighted and fused according to the variance of repeated measurements to obtain the actual sidewall normal geometric deviation sequence. The root mean square roughness, autocorrelation function, correlation length, and power spectrum are all derived from the above. The calculation is performed, rather than by normalizing the image anomaly amplitude; the number of branches, branch levels, and the number of particle connected regions are directly statistically supported by the final defect.

[0095] Scattering nuclei The normalized guided mode field per unit power is calculated by determining the waveguide cross-section and material refractive index. The cross-sectional geometry is derived from layout and cross-sectional measurements, while the material refractive index is obtained from a verified material model or ellipsometric measurements from the same batch. Reference loss is obtained through multi-length cut-back measurements of a straight waveguide with a predetermined process association with the waveguide under test. When using a ring resonator, propagation loss is calculated based on the intrinsic quality factor, group refractive index, and operating wavelength, and the conversion model is recorded. Simultaneous acquisition is performed for each reference structure. and During calibration, the roughness spectrum increment, particle load increment, and branch defect increment of the test structure relative to the reference structure are calculated. The measured total loss of the reference waveguide is not directly added to all defect scattering terms of the test waveguide, thus avoiding the duplication of sidewall scattering already included in the reference waveguide. The calibration set and the final verification set are separated; new process batches only use the old scattering kernel scale after the reference structure has passed retesting.

[0096] like Figure 4 As shown, the solver uses process state coefficients and Etching Defect Response Perform alternating structured recovery for active variables. (Fixed) At that time, updates are made based on the consistency term of valid observation data and the process state smoothing term along the propagation direction. Fixed update At that time, updates are made based on the consistency term of valid observation data and the regularization term of shared space defect structure. Each update Afterwards, according to The amplitude of shared spatial defects is recalculated, and the directional defect supports and non-directional local defect supports are updated according to the aspect ratio, main direction consistency and regional scale of the current connected region. The directional defect supports are updated with directional weighted maps and directional river feasible supports are repaired, and the non-directional local defect supports are repaired with spatial sparsity and map boundary repair.

[0097] Once the objective function and active variables have met the stopping condition for a predetermined number of consecutive cycles, the final etching defect response is fixed. Calculate the amplitude of the shared space defect sequentially. And call according to step S02 Recover the sidewall normal geometric deviation sequence; form a complete defect description vector based on the sidewall normal geometric deviation sequence, independent geometric descriptors, and the final defect support. And according to step S03, form from the descriptive quantities directly related to propagation loss And then according to Calculate the predicted propagation loss. The overall scale of the scattering kernel is only allowed to be updated based on the loss measurement of an independent reference structure, and not based on the prediction results of the device under test itself. If the feasible conditions for directional support cannot be met temporarily, the layout boundary constraints remain unchanged and the soft weights of the branches obtained from the sample statistics are relaxed in a predetermined order; if it is still not feasible or the processing time limit is reached, "manual review required" is output, the uncertainty is increased and no automatic pass / fail judgment is output.

[0098] In an optional implementation with actual propagation loss measurement of the object under test, the weighted residual between the currently predicted propagation loss and the measured propagation loss can be added as an additional physical verification term to the structural defect recovery objective function, and the result can be obtained using the aforementioned main scheme. This initial value is used to perform a limited number of secondary verification updates; this step is not performed if there is no actual propagation loss measurement.

[0099] Specifically, for any lithium niobate straight waveguide under test, the operation record sequentially reads and solidifies the film thickness, waveguide top width, etching depth, sidewall angle, detection length, scanning electron microscope pixel size, atomic force microscope sampling interval, target wavelength, target mode, observation matrix dimension, number of process states, noise upper limit, river direction threshold, branch upper limit, and reference waveguide loss. After solving, the recovered root mean square roughness, correlation length, defect categories, propagation loss prediction value, and prediction interval are recorded. When using optional loss physical verification, the corresponding measured loss, verification residual, and defect recovery results before and after verification are further recorded. The above input values ​​are directly derived from the sample layout, cross-sectional measurement, testing equipment calibration file, and reference structure associated with the same process. The output values ​​are calculated by steps S01 to S05 of this invention. Background loss, geometric calibration parameters, or calibration covariance are not automatically reused between different batches; in actual applications and verifications, simulation or experimental records of the same waveguide section retained by the enterprise are used to fill in the data accurately, and estimated values ​​are not used to replace measured facts.

[0100] like Figure 5 As shown, the system generates defect types according to the category criteria in step S05, overlays the final defect mask onto the original detection image, and provides the defect propagation direction length, lateral width, number of branches, actual sidewall geometry, roughness, and correlation length. It also outputs predicted propagation loss values ​​for the wavelength and mode specified in the product specifications. The system includes prediction intervals and reference calibration validity markers. When the propagation loss measurement of the corresponding reference structure is missing or the calibration validity verification fails, the waveguide under test will not undergo automatic propagation loss prediction, and the system will generate a reference structure supplementary measurement or manual verification marker. When the upper limit of the prediction interval exceeds the loss specification, the re-inspection interface generates microscopic re-inspection coordinates and associates the corresponding waveguide segment, etching batch, geometric calibration version, and reference structure batch. Process engineers can trace the ion beam angle, gas ratio, mask integrity, or cleaning steps based on the defect direction and type, but the system will not automatically modify the equipment formula when enterprise process authorization is lacking.

[0101] In an alternative approach, the process state coefficients can be obtained using low-rank factorization with smoothing constraints, and structured defect recovery can be achieved using proximal gradient, primal-dual algorithms, or alternating direction multiplier methods. Regardless of the numerical solution method used, the shared spatial defect amplitude of multiple detection channels, the topological constraints of directional defect rivers, the actual sidewall geometric recovery, and the differential propagation loss mapping of the reference structure are all preserved. Physical verification of the actual propagation loss of the object under test is an optional enhancement step and is not a necessary condition for performing the basic defect identification and loss prediction process of this invention.

[0102] Numerical simulation examples

[0103] The following combination Figures 6 to 9 Numerical simulation examples of this invention are provided to verify the correspondence between multi-channel observation of the same object, alternating recovery of normal process conditions and local defect responses, shared space support and river topological constraints, as well as sidewall geometry, mode field scattering kernels, and reference differential loss. The images, boundaries, and electromagnetic results in this embodiment are all numerical simulation data; the grayscale and height channels use imaging approximations; the physical evaluation uses a two-dimensional effective refractive index electromagnetic model; and the numerical reference structure is used only for simulation reference calibration and is not considered as measurement results from physical scanning electron microscopy, atomic force microscopy, or reference waveguide loss.

[0104] I. Multi-channel input for the same object and normal process calibration

[0105] The common spatial grid is set to 128×40 points, with a sampling interval of 0.1 μm along the propagation direction and a lateral sampling interval of 0.025 μm, resulting in a calculated area of ​​12.8×1.0 square micrometers. Lateral column indices 3 to 36, starting from 0, are used as the effective detection band. Each simulated object contains two grayscale responses and two height responses, resulting in four views and forming a 128×160 spatial-view observation matrix. Each view is generated from the same height field and the same directional defect and particle region.

[0106] The height field is obtained by superimposing normal process fluctuations and local defects. The grayscale channel adopts a linearized response of height and lateral gradient, while the height channel uses a small-scale Gaussian smoothed probe approximation, with channel noise added separately. Translation per axis for each view is within ±0.65 pixels, and the standard deviation of the repeatability error for the four common markers is 0.025 pixels; translation is estimated from the common markers and interpolated to the common grid. Locations with missing measurements and locations contaminated by the interpolation neighborhood of missing measurements are not included in the data consistency calculation. This imaging approximation is used to verify the reconstruction relationship of common spaces.

[0107] Normal calibration uses 20 defect-free objects, 14 of which are used to construct the median baseline and for view-by-view calibration. Figure 4 The quantile interval and principal component response basis are used, with an additional 6 used for residual verification. The number of process states selected is the first to simultaneously satisfy the condition that the retained residuals do not exceed the upper limit of the repeatability difference noise and that the retained singular values ​​exceed twice the tail of the noise spectrum. When the number of states increases from 2 to 3, the retained mean squared residual decreases from 0.16254 to 0.02486, which is lower than the noise upper limit of 0.03531; therefore, 3 process states are selected. This selection process uses only defect-free calibration data.

[0108] like Figure 6 As shown, Figure 6 A and Figure 6 B represents the grayscale observation and height observation of the same object, respectively. Figure 6 C represents the number of valid observations after registration. Figure 6 D represents independently stored configuration defect support. Figure 6 E represents the defect support for joint recovery. Figure 6 F represents point-by-point false alarms and missed detections. The recovery results retain the directional main trunk, branches, and local particles, with errors mainly distributed in weaker edges and local areas. Different channels coordinate through common location and validity information; grayscale response amplitudes are not directly converted into height or sidewall displacement.

[0109] II. Alternating Recovery of Process Conditions and Defect Responses

[0110] In this numerical implementation, the observation matrix, baseline response, process response basis, and effective sampling weights are fixed; only the process state coefficient matrix A and the etching defect response matrix S are optimized. A has a dimension of 128×3, and S has a dimension of 128×160. S is also stored as a 128×40×4 array to preserve spatial location and view index. Shared spatial defect amplitudes u are aggregated with equal weights based on the effective views of the same node; the data consistency term is weighted according to the repeated observation variance. Nodes with invalid views are not recovered, and S corresponding to out-of-band or invalid observations is set to zero.

[0111] The effective coefficients of the shared sparse term, the total graph variation term, and the branch group term in the structured constraints are set to 0.8, 0.12, and 0.05, respectively. The shared sparse term acts on both directional and non-directional supports, while the total graph variation and branch group terms act only on directional candidate regions. To facilitate numerical gradient calculation, a smooth approximation is used for the norm zeros. With S fixed, a linear system is constructed row-wise, and A is updated by combining the propagation direction process smoothing term. A 10 is added to the linear system. -7 Diagonal stabilizing term; when A is fixed, the gradient of S is updated backtrackingly based on the chain derivative of the shared magnitude, so that the structural constraints acting on u are transmitted to the defect responses of each view.

[0112] The vertical span of the directional candidate region shall be no less than 12 rows, and the ratio of the vertical to horizontal grid span shall be no less than 2. The downstream edge connects to the adjacent horizontal position of the next propagation row, with a maximum horizontal offset of one column; under the above sampling interval, the local discrete adjacency angle shall not exceed 14.04°. Additionally, the overall principal axis of the defect is verified for direction; a re-inspection mark is generated when the overall principal axis direction deviates by more than 5°. The overall direction verification and local discrete adjacency are applied at different spatial scales.

[0113] Feasible support repair is only performed when there is observational support both upstream and downstream and the current amplitude is greater than 35% of the detection threshold. This involves filling in a gap in the propagation line and deleting directional segments with fewer than 7 pixels or a vertical span of less than 5 lines. Continuous horizontal pixels in the same line are first compressed into path sections, and then downstream connections between adjacent sections are established. Each node retains at most two branches with observational support. Local particles are only treated for spatial sparsity and map boundary adjustments. When high-amplitude infeasible nodes are deleted, the corresponding S is simultaneously reset to zero to allow the repair results to be included in subsequent calculations.

[0114] After each updated proposal for S is generated, the graph is reconstructed and the objective function is calculated. If the objective function increases, the proposal is rejected, and the previous S is retained. The iteration stops when the relative changes of A, S, and the objective function are all below 0.003 for three consecutive rounds, and the defect support no longer changes. The upper limit of iteration is 70 rounds. This stopping condition is used in this finite-precision implementation and does not interpret the smooth approximation and dynamic graph repair as an exact global solution to the original non-smooth problem.

[0115] like Figure 7 As shown, Figure 7 A compares the normal response setpoint at a fixed lateral position with the reconstructed value under process conditions. The normal low-frequency changes are preserved, but local amplitude and offset residuals still exist. Figure 7 B represents the defect response S for high-level channel recovery. Figure 7 C represents the shared space defect amplitude u obtained by aggregating all views. Normal process response, channel anomaly, and shared space support sequentially form a traceable calculation relationship. Subsequent sidewall geometry is still extracted from the retained original geometric channels, with u serving only as a dimensionless spatial criterion.

[0116] III. Freeze Test and Ablation Results

[0117] Six additional tagged calibration objects were used solely for selecting the detection threshold for each method from three candidate thresholds (0.35, 0.55, and 0.80) based on the average cross-union ratio. After parameter freezing, 24 new test objects were used, 18 of which used conventional noise, and the noise amplitude of the remaining 6 was amplified to 1.8 times. Thresholds were not reselected during the testing phase. All items in Table 1 are arithmetic means of the indicators for each object.

[0118] The control group that removes topological constraints retains alternating updates of A and S and shared sparse terms, while removing the total graph variation, branch groups, and path repair. The control group that removes process separation cancels the restoration of normal process states but retains topological restoration. The basic detector performs a normal projection, followed by 19 rows of median detrending, thresholding, closing operations, and small connected component removal. Support F1 and directional adjacency F1 are used to evaluate support and adjacency relationship restoration, IoU represents the intersection-union ratio, and MAE represents the mean absolute error.

[0119] Table 1 Recovery results of 24 frozen test subjects

[0120] The support F1 for the complete algorithm implementation is 0.9070, and for the basic detector it is 0.4296. After removing the process separation, the support F1 is 0.3506, indicating that under the set low-dimensional process variation conditions, the joint separation of normal process and local defects plays a role in the recovery result. Compared with the control without topological constraints, the support F1 increases by 0.0180, and the 95th percentile interval obtained by resampling 10,000 times by object pairing is [0.0080, 0.0296]. This interval reflects the fluctuation of the small sample simulation in this group.

[0121] Topology processing reduced the branch count (MAE) from 0.5000 to 0.0833 and increased the particle IoU from 0.5445 to 0.6324; the particle mean absolute area error remained at 0.02375 square micrometers. The directional adjacency F1 of the complete algorithm and the control group without topology constraints were 0.9013 and 0.9014, respectively, which are basically the same, indicating that the improvement under this set of conditions is mainly reflected in region support and branch statistics. The objective function of all 24 test objects did not increase after the graph reconstruction and all reached the preset stopping condition.

[0122] IV. Sidewall Geometry and Reference Differential Interface of the Same Object

[0123] To verify the continuous correspondence between multi-channel recovery, geometric measurement, mode field core prediction, and independent electromagnetic evaluation, six additional bridging simulation samples, C001 to C006, were set up, excluding the 24 test objects in Table 1. The multi-channel observations, sidewall grayscale views, known boundary coordinates, and electromagnetic structures under each number correspond to the same simulated waveguide object. C001 serves as a numerical reference of the same length, with its entire insertion loss obtained from independent electromagnetic solutions used as a reference benchmark; C002 to C006 are five target samples. C004 and C006 retain the re-inspection markers generated by the algorithm; their physical calculation results are only used for diagnosis and not for automatic pass / fail determination.

[0124] Each bridging object retains two 512×320-point grayscale views of the sidewalls, with a lateral sampling interval of 4 nm and a propagation direction sampling interval of 25 nm, resulting in a nominal top view width of 900 nm. The measuring instrument only reads noisy grayscale values, extracts the left and right boundaries using signed gradient peaks and three-point subpixel fitting, and then fuses the results twice. Shared supports are used for defect location and re-inspection; when calculating the sidewall spectrum, valid normal roughness positions within the detection band are retained, and the roughness at non-defect positions is not forcibly cleared to zero.

[0125] Figure 8 Provide the boundary measurement results for the bridged object. Among them, Figure 8 A represents the original grayscale values ​​of the extracted left and right boundaries from the overlay. Figure 8 B represents the nanometer deviation comparison between the coordinates set for the left boundary and the coordinates extracted from the image. Figure 8 C is the difference between the two. The root mean square error of the boundaries of the six objects ranges from 0.3552 to 0.3731 nanometers, corresponding to the set grayscale transition and noise conditions. The image measurement geometry is sent to the scattering kernel prediction end, and the set geometry is sent to the independent electromagnetic boundary value solver end to distinguish the propagation of physical approximation error and image measurement error.

[0126] The original sample length of the bridging object is 12.775 μm. A 1 μm cosine gradient segment is added before and after each segment, connecting to the nominal waveguide port, bringing the total length to 14.775 μm. The same gradient rule is used for setting geometry, measurement geometry, and prediction calculations, without pruning or smoothing the original sample. For C002 to C006, the numerical reference insertion loss of C001 is used as the baseline, and only the scattering prediction difference relative to the reference structure is added. The root mean square error of the differential prediction insertion loss between the known geometric input and the image measurement geometric input is 1.90158 × 10⁻⁶. -5 decibels and 9.85599×10 -6 Decibels. The lower error in the image input in these five cases is due to the partial cancellation of measurement bias and model bias, and does not indicate that the measurement geometry is superior to the known geometry.

[0127] The particle area load and branch defect density were directly statistically derived from the structured reconstruction results of the same object, without being replaced by a set true value. This group of independent electromagnetic evaluations did not construct particles and branches as independent three-dimensional dielectric structures; therefore, the aforementioned errors only evaluate the sidewall geometric path and are not used as the overall loss prediction accuracy for all defect descriptors, nor are they used to quantitatively calibrate the particle load and branch defect correction coefficients. The aforementioned correction coefficients were obtained using the aforementioned method, employing an independent calibration structure containing the verified corresponding defects.

[0128] V. Mode Field Scattering Nuclei and Independent Electromagnetic Evaluation

[0129] The electromagnetic calculations used a thin film thickness of 600 nm, a residual thin film thickness of 300 nm, a nominal waveguide width of 900 nm, and an operating wavelength of 1.55 μm. The material refractive index was determined using the dispersion relation of Zelmon et al. and Malitson. First, the vertical anisotropic TM layer system was solved, and then a two-dimensional effective refractive index model was established. The effective refractive indices of the thick film and the residual thin film were 1.8633204 and 1.5126130, respectively. The effective refractive index of the lateral reference mode was 1.7761750, and the reference mode was normalized to 1 watt per meter in a constant direction. This calculation is a two-dimensional effective refractive index approximation.

[0130] The prediction end constructs a scattering sensitive nucleus based on the overlap of the interface fields between the reference guided mode and the open radiation mode, and performs a first-order interface perturbation integral through geometric perturbation and phase matching relationships. The evaluation end directly uses the deformed dielectric constant distribution to solve the two-dimensional Maxwell single-polarization boundary value problem, preserving the influence of dielectric perturbation on the operator and repeated scattering. Transmission, reflection, and radiation results are then obtained from the port guided mode decomposition and the outer flux surface. The evaluation end does not use the reference differential prediction formula to generate transmittance.

[0131] like Figure 9 As shown, Figure 9 A represents the total electric field obtained by directly solving the C004 object. Figure 9 B is the normalized amplitude of the scattered field obtained by subtracting the nominal incident guided mode from the total field. There are outwardly propagating field components outside the sidewalls; the port guided mode decomposition and the outer flux surface are used together to calculate the scattered energy. This result corresponds to independently stored numerical arrays of complex electric field, magnetic field, dielectric constant, monitoring surface index, and geometric coordinates. The field diagram is obtained from the boundary value solution.

[0132] Six random phases were set for each of the low, medium, and high spatial spectra, resulting in 18 independent test objects. A reference structure was generated using another random seed. Compared to the independent electromagnetic results, the root mean square error of the equivalent attenuation predicted by the reference differential was 0.00463643 dB / cm, the mean absolute error was 0.00259393 dB / cm, and the maximum absolute error was 0.01109 dB / cm. Three profiles with the same root mean square displacement of 3 nm but different spatial spectra had independent electromagnetic equivalent attenuations of 0.197818, 0.365824, and 0.428076 dB / cm, respectively. The comparison showed an unfitted loss scaling factor, indicating that under the given conditions, the overall fluctuation alone is insufficient to describe the scattering coupling between different spatial frequencies and guided modes. The above equivalent attenuation is used for numerical comparison of finite sample segments and is not considered as the accuracy of propagation loss measurement for physical devices.

[0133] The embodiments described herein are preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made to the structure, shape, and principle of the present invention should be covered within the scope of protection of the present invention. Although preferred embodiments of the present invention have been described, those skilled in the art, once they understand the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the present invention. Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention also intends to include these modifications and variations.

Claims

1. A method for identifying etching defects and predicting losses in thin-film lithium niobate waveguides, characterized in that, Includes the following steps: S01, acquire at least two of the following: scanning electron microscopy image, atomic force microscopy height data, and scattering microscopy image after etching of the lithium niobate waveguide of the thin film under test; acquire the waveguide layout outline, etching main direction, detection coordinates, repeating field of view markers, and valid sampling markers; establish a common spatial sampling grid along the waveguide propagation direction and the transverse direction; register the detection data of different detection channels to the common spatial sampling grid; perform dimensionless standardization on the spatial sampling observation values ​​of each detection channel based on the defect-free calibration region; form a spatial-view observation matrix with the sampling position along the waveguide propagation direction as the row and the combination of transverse position, detection channel, and repeating field of view as the column; and retain the geometric detection data with actual spatial scale calibration relationship. S02, establish the signal formation model of the space-view observation matrix, represent the normal detection response under the same process association conditions as a combination of the reference response and a finite number of process state disturbance responses, and take the local etching defect response as an additional response; define the shared space defect amplitude mapping across the detection channel and the repeated field of view based on the etching defect response in each detection channel and the repeated field of view, establish a directed river map based on the shared space defect amplitude, the main etching direction and the waveguide layout outline, and define directional continuity constraints, finite branch constraints and layout boundary constraints for the shared space defect support; S03, determine the spatial location requiring geometric description based on the shared space defect support, recover the sidewall normal geometric deviation sequence with actual spatial dimensions using the geometric detection data, reference sidewall boundary and geometric calibration parameters, and obtain the sidewall roughness power spectrum based on the sidewall normal geometric deviation sequence; calculate the defect scattering sensitive nucleus based on the cross section of the waveguide under test, material refractive index, operating wavelength and unit power normalized guided mode field, and establish the differential propagation loss mapping of the waveguide under test relative to the reference structure using the propagation loss of the reference structure with a predetermined process association with the waveguide under test, as well as the sidewall roughness power spectrum, particle load and branch defect information of the reference structure; S04: Using the process state coefficient and the etching defect response of each detection channel as active variables, a structured defect recovery problem is constructed based on the consistency of effective observation data, the smoothness of normal process state, and the structured defect constraints acting on the shared space defect support. The process state coefficient and etching defect response are solved using an alternating update method. During the etching defect response update process, the shared space defect amplitude is recalculated, and the directional defect support, non-directional local defect support, and the directed river map are updated. After the predetermined stopping condition is met, the final shared space defect support, the actual sidewall normal geometric deviation sequence, and the loss-related descriptive vector are obtained based on the final etching defect response. The propagation loss prediction result is obtained through the differential propagation loss mapping. S05, based on the final shared space defect support, generate the defect location, defect range and defect type, based on the propagation loss prediction result and the preset product judgment rule, form an automatic judgment result, and generate re-inspection information and process traceability information based on the automatic judgment result.

2. The method for identifying etching defects and predicting losses in thin-film lithium niobate waveguides according to claim 1, characterized in that, In step S01, for the first The first detection channel A repeated field of view is used. Based on the registration relationship between the detection channel and the waveguide coordinate system, the original pixel or height sampling values ​​corresponding to the sampling position in the common space are interpolated, averaged in the region, averaged in the region, or spatially weighted and aggregated to obtain spatial sampling observation values. The spatial sampling observation values ​​are then standardized based on the median and interquartile range in the defect-free calibration region. index the horizontal spatial location Detection Channel Index and repeating field index Combined column indexes mapped to the spatial-view observation matrix And establish the following signal formation model: ， in, For the first The sampling position in the propagation direction is at the _th ... Dimensionless observations on each combined channel For the defect-free calibration area in the first Reference response on each combined channel The number of effective process states, For the first The sampling position corresponding to the first Each process state coefficient For the first The process state is in the first Response bases on a combination of channels This is a response to localized etching defects. To collect noise and registration residuals; And construct an effective sampling weight matrix with the same dimension as the space-view observation matrix. For valid observations, the weight is determined based on the standard deviation of repeated measurements of the corresponding detection channel. For invalid observations, observations that fall outside the detection band after registration, or observations that are missing, the corresponding weight is set to zero.

3. The method for identifying etching defects and predicting losses in thin-film lithium niobate waveguides according to claim 1, characterized in that, In step S02, the combined column index of the etching defect response is expanded into three indices: lateral spatial location, detection channel, and repeated field of view, and the first index is determined according to the following formula. The sampling location in the propagation direction and the first Shared spatial defect amplitude at each lateral location: ， in, Indicates the corresponding spatial position in the th order. The first detection channel, the first Etching defect response in a repeating field of view The weights are non-negative, and the sum of the normalized effective weights is 1. The non-negative weights are determined based on at least one of the reciprocal of the repeated measurement variance, spatial resolution, and signal-to-noise ratio of the corresponding detection channel, and the weights corresponding to invalid detection channels are set to zero; the etching defect responses of different detection channels retain their respective response amplitude characteristics, and the shared spatial defect amplitude is used for defect spatial location determination, directed river graph topological constraints, and defect connectivity determination.

4. The method for identifying etching defects and predicting losses in thin-film lithium niobate waveguides according to claim 3, characterized in that, In step S02, candidate defect supports are divided into directional defect supports and non-directional local defect supports based on the aspect ratio, main direction consistency and region scale of the connected region corresponding to the amplitude of the shared space defect. For the directional defect support, the effective spatial sampling position located within the detection zone on the sidewall of the waveguide layout is taken as a directed river graph node. Spatially adjacent node pairs that point from the upstream node to the downstream node and whose connection direction and the angle between them and the main etching direction do not exceed a preset direction threshold are taken as directed edges. A soft river topology constraint including a total variational term of the direction-weighted graph and a branch group constraint term is set for the directional defect support. Among them, the weight of the directed edge increases as the angular deviation between the direction of the directed edge and the main etching direction increases; and the feasible set restricts the overall effective defect path to extend along the downstream etching direction, the number of effective downstream branches of non-leaf nodes to not exceed the preset branch limit, and the defect support to be located within the sidewall detection zone after the layout and the detection image are registered. For the non-directional local defect support, no directional constraint is applied along the downstream etching direction, but spatial sparsity constraint and layout boundary constraint are applied.

5. The method for identifying etching defects and predicting losses in thin-film lithium niobate waveguides according to claim 1, characterized in that, In step S03, the reference sidewall boundary is placed in the arc length coordinate system. The actual spatial coordinates of the location are as follows Its unit normal vector is denoted as For the first... The first detection channel and the first A repeated field of view, the actual sidewall boundary points obtained after coordinate registration, spatial scale conversion and sidewall edge extraction are denoted as... and in accordance with: Determine the sidewall normal geometric deviation obtained from the corresponding detection channel; The normalized fusion weights are determined based on the validity identifiers and repeatability standard deviations of the corresponding geometric detection data, and then categorized as follows: Obtain the The actual sidewall normal geometric deviation at each sidewall sampling location, wherein the normalized fusion weight is negatively correlated with the repeatability variance of the corresponding geometric detection data; When there is no valid geometric detection data at a certain sampling location, the sampling location is marked as an invalid geometric sampling point and excluded from the valid sampling set for subsequent sidewall roughness power spectrum calculation, instead of using zero value for replacement.

6. The method for identifying etching defects and predicting losses in thin-film lithium niobate waveguides according to claim 1, characterized in that, In step S03, the sidewall method further includes windowing the sidewall normal geometric deviation sequence after removing the average contour, and according to: Calculate the spatial power spectral density of the sidewall roughness, where, This represents the actual spatial spacing between adjacent valid geometric sampling points. The number of effective sampling points, The window power normalization coefficient, For the window function coefficients, Spatial frequency; The discrete values ​​of the spatial power spectrum of the sidewall roughness at a preset spatial frequency and the normalized particle area load are used to determine the sidewall roughness spatial power spectrum at a preset spatial frequency. and branch defect density The loss-related descriptive vector consists of: ， ， To detect the first in the band The actual projected area of ​​each particle's connected region. and These are the actual length and width of the detection strip, respectively. This represents the number of valid branch defects in a directed river graph.

7. The method for identifying etching defects and predicting losses in thin-film lithium niobate waveguides according to claim 1, characterized in that, In step S03, the reference structure and the waveguide under test have at least the same thin film material layer system, nominal etching process formulation and nominal waveguide cross-section type, and the difference between at least one key cross-sectional parameter of the reference structure, such as etching depth, top width and sidewall angle, and the waveguide under test does not exceed the corresponding calibration threshold. For the target wavelength and guide mold The predicted propagation loss of the waveguide under test is determined according to the following formula: in, For the reference structure, the measured propagation loss at the corresponding wavelength and guided mode, and These are the spatial power spectral densities of the sidewall roughness of the waveguide under test and the reference structure, respectively. The scattering sensitive nucleus is calculated based on the cross-section of the waveguide under test, the refractive index of the material, and the normalized guided mode field per unit power. and These are the normalized particle area loads of the waveguide under test and the reference structure, respectively. and The branch defect densities of the waveguide under test and the reference structure are respectively. and These are the particle load correction factor and the branch defect correction factor, respectively. The propagation loss of the reference structure is corrected only by the difference in sidewall roughness spectrum, particle load, and branch defect between the waveguide under test and the reference structure.

8. The method for identifying etching defects and predicting losses in thin-film lithium niobate waveguides according to claim 1, characterized in that, In step S04, the following structured defect recovery problem is solved: in, This is the process state coefficient matrix. The etching defect response matrix, For an effective sampling weight matrix, Let be the first-order difference matrix along the waveguide propagation direction. Smoothing weights for normal process conditions To obtain the mapping of shared space defect amplitudes based on the etching defect response matrix, This is a structured defect regularization term that acts on the shared space defect support. Weights for structured defect constraints; Fixed current etching defect response matrix Update process state coefficient matrix Fixed updated process state coefficient matrix Update the etching defect response matrix Each update of the etching defect response matrix The amplitude of the shared space defect is then recalculated, and the directional defect support and non-directional local defect support are re-determined based on the current amplitude of the shared space defect. The directional river map is then updated for the directional defect support, and the feasibility repair of direction, branch, and map boundary is performed.

9. The method for identifying etching defects and predicting losses in thin-film lithium niobate waveguides according to claim 1, characterized in that, In step S04, when the waveguide under test has an actual propagation loss measurement at at least one target wavelength-guided mode position, the corresponding propagation loss prediction vector is obtained based on the current etching defect response. Furthermore, a propagation loss physical verification term is added to the objective function of the structured defect recovery problem to obtain: in, The objective function for recovering structured defects without including the physical check term for propagation loss. This is the propagation loss prediction vector obtained based on the current etching defect response. This is a vector composed of the actual propagation loss measurements of the waveguide under test. To extract the selection matrix corresponding to the predicted values ​​at the actual measurement locations from the complete propagation loss prediction vector, The covariance matrix is ​​the actual propagation loss measurement. Physical verification weights for propagation loss; The propagation loss physical verification term only changes the process state coefficient matrix. and etching defect response matrix The optimization results are obtained without setting propagation loss, shared space defect amplitude, or loss-related descriptor vectors as independent active variables.

10. A system for identifying etching defects and predicting losses in thin-film lithium niobate waveguides, employing the method for identifying etching defects and predicting losses in thin-film lithium niobate waveguides as described in any one of claims 1-9, characterized in that, include: The multimodal detection and registration module is used to acquire at least two of the following: scanning electron microscopy images, atomic force microscopy height data, and scattering microscopy images. It registers the detection data from different detection channels to a common spatial sampling grid, forming a spatial-view observation matrix with effective sampling weights, and retains geometric detection data with actual spatial scale calibration relationships. The defect space support and river map construction module is used to calculate the shared space defect amplitude based on the etching defect response in each detection channel and repeated field of view, and to establish a directed river map based on the shared space defect amplitude, the main etching direction and the waveguide layout boundary, forming a directionally continuous, finite branch and layout boundary constraint; The structured defect recovery module is used to perform alternating structured recovery based on the consistency of effective observation data, the smoothness of normal process conditions, and the structural constraints of shared space defects, using process state coefficients and etching defect responses of each detection channel as active variables. During the etching defect response update process, the shared space defect amplitude and the defect support are recalculated. The geometric restoration and descriptive quantity generation module is used to determine the geometric detection area based on the final shared space defect support, call the geometric detection data with actual spatial scale calibration relationship and the reference sidewall boundary, obtain the actual sidewall normal geometric deviation sequence through sidewall boundary normal projection and repeated measurement variance weighted fusion, and generate the sidewall roughness power spectrum and loss-related descriptive vector based on the actual sidewall normal geometric deviation sequence. The scattering nucleus calibration and loss prediction module is used to calculate the scattering sensitive nucleus based on the cross section of the waveguide under test, the refractive index of the material, the operating wavelength, and the normalized guided mode field of unit power. It establishes a differential propagation loss mapping of the reference structure based on the propagation loss and loss-related descriptors of the reference structure that has a predetermined process association with the waveguide under test, and generates the propagation loss prediction result based on the loss-related descriptor vector of the waveguide under test. It also includes a re-inspection and process interface module, which outputs defect location, defect type, actual sidewall geometry, propagation loss prediction results and reference calibration validity status, and generates re-inspection information and process traceability information. When the actual propagation loss measurement data of the waveguide under test is available, the structured defect recovery module is also used to perform physical consistency verification on the etching defect response based on the deviation between the propagation loss prediction result and the actual propagation loss measurement value.

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