Method for detecting and analyzing impurities in gallium oxide single crystal growth based on raman spectrum detection

Abstract

The application discloses a gallium oxide single crystal growth impurity detection and analysis method based on Raman spectrum detection, relates to the technical field of semiconductor crystal detection and analysis, and comprises the following steps: generating an impurity traceable directed propagation graph based on a time sequence Raman spectrum data set containing spatial coordinates, deducing and screening a candidate impurity migration path, integrating a hierarchical impurity distribution and evolution network, obtaining a main defect cluster of impurities through physical segmentation, carrying out cross-growth cycle impurity concentration diffusion inversion on each defect cluster, quantifying an impurity contribution weight, and generating a structured detection and analysis report in combination with a crystal growth process database. The method constructs an impurity propagation relationship based on space-time spectrum data, realizes quantitative screening of a migration path and fine inversion of a defect cluster, accurately defines the contribution degree of impurities in different growth stages, and provides a complete analysis path for gallium oxide single crystal growth impurity detection.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor crystal detection and analysis technology, specifically a method for detecting and analyzing impurities in gallium oxide single crystal growth based on Raman spectroscopy. Background Technology

[0002] Existing methods for impurity detection and analysis during gallium oxide single crystal growth mostly employ single-point Raman spectroscopy, which can only obtain impurity spectral data at local locations in the crystal. The presence of impurities is determined through conventional data statistics, and the derivation of impurity migration paths relies on human experience. The spatial coordinate information of Raman spectra is not combined with temporal variation characteristics to construct a corresponding propagation correlation model, and impurity source tracing analysis remains at the level of local data interpretation.

[0003] Existing impurity detection and analysis technologies cannot construct directional propagation relationships for impurity origination based on spatiotemporal Raman spectral data, cannot forward extrapolate all potential migration paths of impurities from the introduction point to the defect state, and cannot achieve quantitative screening of paths through migration energy barriers and thermodynamic probability integrals. At the same time, they lack physical segmentation processing methods for impurity evolution networks and cannot decompose complex impurity-defect interactions into independent analysis units.

[0004] Existing technologies cannot perform impurity concentration diffusion inversion operations across growth cycles for segmented defect clusters, cannot accurately quantify the contribution weight of various impurities to the final defect state in different growth stages, and the impurity detection and analysis results cannot be correlated with the entire crystal growth process, making it difficult to form structured impurity detection and analysis conclusions. Summary of the Invention

[0005] This invention aims to solve at least one of the technical problems existing in the prior art;

[0006] Therefore, this invention proposes a method for detecting and analyzing impurities in gallium oxide single crystal growth based on Raman spectroscopy, comprising:

[0007] Based on a time-series Raman spectroscopy dataset containing spatial coordinate information, a directed propagation map for impurity source tracing is generated.

[0008] Based on the impurity source tracing directed propagation graph, all candidate impurity migration paths from the impurity introduction point to the current defect state are deduced in a forward manner.

[0009] For each candidate impurity migration path, calculate its migration energy barrier and thermodynamic probability integral, and sort and filter all candidate impurity migration paths based on the migration energy barrier and the thermodynamic probability integral.

[0010] All candidate impurity migration paths after sorting and screening are integrated to form a hierarchical impurity distribution and evolution network. Each node in the hierarchical impurity distribution and evolution network represents an impurity state or defect configuration, and each edge represents an impurity migration or reaction relationship.

[0011] The hierarchical impurity distribution and evolution network is physically segmented, and the complex network structure is decomposed into multiple impurity-dominated defect clusters, with each defect cluster focusing on a core impurity-defect interaction process.

[0012] For each of the defect clusters, an impurity concentration diffusion inversion analysis is performed across the growth cycle to quantify the contribution weight of each impurity to the final defect state at different growth stages.

[0013] Based on the contribution weight of each impurity and combined with the crystal growth process database, a structured gallium oxide single crystal growth impurity detection and analysis report is generated.

[0014] Furthermore, the generation of a directed propagation graph for impurity tracing based on the time-series Raman spectroscopy dataset containing spatial coordinate information includes:

[0015] During the growth of gallium oxide single crystals, in-situ laser Raman spectroscopy scanning is performed on the growth interface region to collect a time-series Raman spectral dataset containing spatial coordinate information.

[0016] Feature enhancement and noise stripping operations were performed on the time-series Raman spectroscopy dataset to separate the intrinsic peak feature streams related to gallium oxide lattice vibrations and the anomalous peak feature streams related to impurity defects;

[0017] Based on the separated intrinsic peak characteristic flow and the anomalous peak characteristic flow, a multidimensional impurity-stress-structure correlation tensor is constructed. The multidimensional impurity-stress-structure correlation tensor is used to characterize the coupling relationship between impurity type, local stress and lattice distortion.

[0018] The multidimensional impurity-stress-structure correlation tensor is input into a learnable physical law guidance network, which generates an impurity source tracing directed propagation graph by iteratively identifying spurious correlations and solidifying physical correlations.

[0019] Furthermore, feature enhancement and noise stripping operations are performed on the time-series Raman spectroscopy dataset to separate the intrinsic peak feature streams related to gallium oxide lattice vibrations and the anomalous peak feature streams related to impurity defects, including:

[0020] Background subtraction and intensity normalization are performed on each original spectrum in the time-series Raman spectroscopy dataset;

[0021] Continuous wavelet transform is performed on the normalized spectrum to extract its time-frequency features at different scales, forming a high-dimensional spectral feature sequence.

[0022] Independent principal component analysis was applied to the high-dimensional spectral feature sequence to separate several independent components with the largest variance contribution.

[0023] The independent components are matched with the theoretical Raman active phonon modes of gallium oxide standard crystals, and the successfully matched components are reconstructed as the intrinsic peak characteristic flow.

[0024] The remaining unmatched independent components, along with the characteristic peak components associated with known impurities or defects, are collectively reconstructed into the anomalous peak feature stream.

[0025] Furthermore, the multidimensional impurity-stress-structure correlation tensor is input into a learnable physical law guidance network. This network iteratively identifies spurious correlations and solidifies physical correlations to generate a directed propagation graph for impurity tracing, including:

[0026] Initialize a fully connected candidate correlation graph, wherein each physical quantity dimension in the multidimensional impurity-stress-structure correlation tensor corresponds to a node in the graph;

[0027] A physical constraint-based structure optimizer is used to learn the physical association strength and direction of each edge in the candidate association graph by minimizing a loss function that includes sparsity constraints, crystal symmetry constraints and thermodynamic feasibility constraints.

[0028] In each optimization iteration, the structure optimizer calculates the degree to which the current correlation graph satisfies the known physical laws of crystals;

[0029] Based on the degree of satisfaction, the edge weights that satisfy physical laws are dynamically increased, while edges that violate physical laws are reduced or deleted, and the final graph structure is ensured to not contain loops that violate the direction of the thermodynamic time arrow.

[0030] Once the loss function converges to a stable value, the graph structure output by the structure optimizer is defined as the impurity source tracing directed propagation graph, where the weights of the edges represent the rate constants of impurity migration or defect response.

[0031] Furthermore, based on the impurity source tracing directed propagation graph, all candidate impurity migration paths from the impurity introduction point to the current defect state are deduced in a forward manner, including:

[0032] In the impurity source tracing directed propagation diagram, all nodes corresponding to impurities introduced by crystal growth raw materials, atmosphere or equipment are identified, and the nodes are marked as source nodes;

[0033] Starting from each of the source nodes, a breadth-first search algorithm is used to traverse the impurity tracing directed propagation graph along the positive direction of the directed edges;

[0034] During the traversal, the complete sequence of nodes and edges traversed from any of the source nodes to the node representing the defect state detected by the current Raman spectrum is recorded. Each complete forward path constitutes a candidate impurity migration path.

[0035] For each candidate impurity migration path, verify whether each step of the reaction or migration meets the temperature and pressure conditions during the gallium oxide crystal growth process, and eliminate paths that do not meet the actual process conditions.

[0036] Further, for each of the candidate impurity migration paths, the migration energy barrier and thermodynamic probability integral of that path are calculated, including:

[0037] For a candidate impurity migration path, extract the reaction or migration rate constants of all edges on the candidate impurity migration path;

[0038] Based on a variation of the Arrhenius equation, the activation energy of each step in the path is calculated by back-calculating the reaction or migration rate constant, and the sum of the activation energies of all steps is taken as the migration energy barrier of the candidate impurity migration path.

[0039] Acquire real-time temperature and pressure data at each stage of gallium oxide single crystal growth;

[0040] Based on the temperature and pressure data, the standard Gibbs free energy change of each step of the reaction along the candidate impurity migration path is calculated;

[0041] The standard Gibbs free energy changes of all steps along the entire path are accumulated and substituted into the Boltzmann factor formula to obtain the thermodynamic probability integral of the corresponding path.

[0042] Furthermore, the integration of all candidate impurity migration paths after sorting and filtering forms a hierarchical impurity distribution and evolution network, including:

[0043] All candidate impurity migration paths that meet the preset upper limit of migration energy barrier and lower limit of thermodynamic probability integral are merged.

[0044] During the merging process, common intermediate state nodes and common reaction edges shared between different candidate impurity migration paths are identified;

[0045] Using the common intermediate state node as a hub, multiple candidate impurity migration paths are woven into a directed acyclic mesh topology;

[0046] Based on the growth stage of nodes in the impurity migration path, the nodes in the mesh topology are divided into an impurity introduction layer, a defect formation layer, and a defect stabilization layer, forming a hierarchical impurity distribution and evolution network with a clear time hierarchy.

[0047] Furthermore, the hierarchical impurity distribution and evolution network is physically segmented, decomposing the complex network structure into multiple impurity-dominated defect clusters, including:

[0048] Calculate the hierarchical impurity distribution and the reaction path distance between all nodes in the evolution network;

[0049] A clustering method based on reaction kinetics is used to divide nodes into different reaction groups according to the reaction path distance. Nodes within each reaction group are connected through fast reactions, and nodes in different reaction groups are connected through slow reactions.

[0050] Each reaction group and its internally connected reaction edges are extracted to form a physically independent sub-network, which is a defect cluster.

[0051] Each defect cluster is labeled with a defect type tag based on its core impurity type.

[0052] Furthermore, for each of the defect clusters, an impurity concentration diffusion inversion analysis across growth cycles is performed to quantify the contribution weight of each impurity to the final defect state at different growth stages, including:

[0053] Within one of the defect clusters, a stable defect state node located at the end of the growth phase is defined as an observation node;

[0054] Using an impurity concentration diffusion inversion model, starting from each initial impurity introduction node in the defect cluster, the process of impurity concentration diffusion and evolution along the reaction edge to the observation node during crystal growth is simulated.

[0055] During the simulation, the transport and reaction consumption of the diffused impurity concentration are calculated based on the rate constant of the reaction edge, and the impurity concentration fraction that finally reaches the observation node is recorded.

[0056] The contribution weight of the impurity at the corresponding growth stage of each initial impurity introduction node is obtained by dividing the final impurity concentration share contributed by each initial impurity introduction node by the total concentration share contributed by all initial impurity introduction nodes.

[0057] Furthermore, based on the contribution weight of each impurity and combined with a crystal growth process database, a structured gallium oxide single crystal growth impurity detection and analysis report is generated, including:

[0058] Impurities whose contribution weight exceeds a preset threshold are marked as critical control impurities;

[0059] From the crystal growth process database, retrieve the raw material purity standards, sensitive ranges of process parameters, and historical control schemes related to each key controlled impurity;

[0060] The key control impurities are arranged in descending order of their contribution weights.

[0061] For each critical control impurity, list in detail its growth stage, the defect cluster to which it belongs, its corresponding contribution weight, the raw materials or process steps it was introduced into, and the recommended process control direction.

[0062] All information is organized and filled according to a predefined analysis report template to generate the final structured gallium oxide single crystal growth impurity detection and analysis report.

[0063] Compared with the prior art, the beneficial effects of the present invention are:

[0064] Based on a temporal Raman spectroscopy dataset containing spatial coordinate information, a directed propagation map for impurity tracing is generated. Using this map, all candidate impurity migration paths from the impurity introduction point to the current defect state are deduced forward. The migration energy barrier and thermodynamic probability integral are calculated for each candidate impurity migration path, and sorting and filtering are performed. This transforms discrete spatiotemporal Raman spectroscopy data into logically oriented propagation relationships, fully covering all potential impurity migration paths. Quantitative calculations of physical parameters distinguish the rationality of different migration paths, eliminating paths that do not conform to thermodynamic laws, and clarifying the associated nodes and transformation relationships in the impurity migration process.

[0065] The integrated screening of candidate impurity migration paths forms a hierarchical impurity distribution and evolution network. This network is physically segmented to obtain multiple impurity-dominated defect clusters. For each defect cluster, a cross-growth cycle impurity concentration diffusion inversion analysis is performed to quantify the contribution weight of each impurity to the final defect state at different growth stages. This decomposes the complex network structure into analytical units that focus on a single core role, simplifying the analytical dimensions of impurity-defect interactions. Through cross-cycle inversion analysis, the correlation characteristics between impurity concentration changes and defect states are directly identified, distinguishing the differences in the role of impurities in different growth stages and achieving a refined numerical definition of the degree of impurity contribution. Attached Figure Description

[0066] Figure 1 This is a flowchart illustrating the steps of the gallium oxide single crystal growth impurity detection and analysis method based on Raman spectroscopy described in this invention.

[0067] Figure 2 The flowchart shows the feature enhancement and noise stripping operations;

[0068] Figure 3 A comparative analysis of the contribution weight of impurities and the migration barrier;

[0069] Figure 4 A thermal map of reaction path distances;

[0070] Figure 5 This is a line graph showing how the degree of impurity migration changes with the growth stage. Detailed Implementation

[0071] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0072] See Figure 1 Based on a time-series Raman spectroscopy dataset containing spatial coordinate information, a directed propagation graph for impurity source tracing is generated. According to this graph, all candidate impurity migration paths from the impurity introduction point to the current defect state are forward deduced. The migration barrier and thermodynamic probability integral of each candidate impurity migration path are calculated, and all paths are sorted and filtered based on these parameters. All sorted and filtered candidate impurity migration paths are integrated to form a hierarchical impurity distribution and evolution network. Each node in this network represents an impurity state or defect configuration, and each edge represents an impurity migration or reaction relationship. The hierarchical network is physically segmented, decomposing the complex network structure into multiple impurity-dominated defect clusters, each focusing on a core impurity-defect interaction process. For each defect cluster, a cross-growth cycle impurity concentration diffusion inversion analysis is performed to quantify the contribution weight of each impurity at different growth stages to the final defect state. Based on the contribution weight of each impurity and combined with the crystal growth process database, a structured gallium oxide single crystal growth impurity detection and analysis report is generated.

[0073] In one embodiment of the present invention, in-situ laser Raman spectroscopy scanning is performed on the growth interface region during the growth process of gallium oxide single crystal. The scanning is performed at a set time interval and on a spatial grid. The Raman spectral data collected at each scanning point is bound to its collection time point and three-dimensional spatial coordinates on the crystal sample to form a time-series Raman spectral dataset containing spatial coordinate information. Each spectral data contains Raman shift and intensity information.

[0074] In specific implementation, please refer to Figure 2Feature enhancement and noise stripping operations are performed on the time-series Raman spectroscopy dataset. The first step is to perform background subtraction and intensity normalization on each original spectrum in the dataset. Background subtraction is achieved by fitting the non-Raman scattering background of the spectrum and subtracting this background. Intensity normalization is to scale the intensity values ​​of the spectrum after background subtraction to a standard intensity range. Next, continuous wavelet transform is performed on each normalized spectrum within a preset scale range to extract the time-frequency features of the spectrum at different scales. These features constitute a high-dimensional spectral feature sequence, the dimension of which is determined by the number of selected wavelet scales. Then, independent principal component analysis is applied to the high-dimensional spectral feature sequence. The goal is to separate statistically independent components from the mixed high-dimensional features. The algorithm iteratively finds an unmixing matrix that maximizes the independence of the output components, ultimately separating several independent components with the largest variance contribution. Subsequently, the isolated independent components are matched with the theoretical Raman active phonon modes of the gallium oxide standard crystal. The matching process involves comparing the frequency peaks, peak widths, and relative intensities of the independent components with the corresponding parameters of the theoretical phonon modes. The successfully matched independent components—those whose frequencies and line shapes are consistent with the intrinsic lattice vibration modes of gallium oxide within the allowable error range—are reconstructed as intrinsic peak characteristic flows related to gallium oxide lattice vibrations. It can be understood that the remaining independent components that cannot match any theoretical phonon mode, along with those characteristic peak components that, although they can match phonon modes, have peak positions or line shapes related to known impurities or defects, collectively constitute anomalous peak characteristic flows related to gallium oxide impurities and defects. These anomalous peak characteristic flows are reconstructed separately.

[0075] In practical implementation, a multidimensional impurity-stress-structure correlation tensor is constructed based on the separated intrinsic peak characteristic flow and anomalous peak characteristic flow. The construction process involves defining a multidimensional array where each dimension corresponds to a different physical quantity, including the intensity of different impurity characteristic peaks resolved from the anomalous peak characteristic flow, the intrinsic peak frequency shift and full width at half maximum (FWHM) variation calculated from the intrinsic peak characteristic flow, the local stress components obtained by inversion from the frequency shift using a spectral stress model, and the lattice symmetry distortion parameters inferred from the intrinsic peak position and line shape variations. Each element value in the multidimensional impurity-stress-structure correlation tensor is the numerical value of the aforementioned physical quantities at a specific spatial coordinate and time point. This multidimensional correlation tensor is used to characterize the coupling relationship between impurity type, local stress, and lattice distortion. Optionally, the multidimensional impurity-stress-structure correlation tensor can further include temperature, pressure, and growth rate information at the corresponding spatiotemporal points obtained from a crystal growth process parameter database as additional dimensions.

[0076] In practice, the multidimensional impurity-stress-structure correlation tensor is input into a learnable physical law guidance network. The goal of this network is to generate a directed propagation graph for impurity source tracing. This can be understood as the network initializing a fully connected candidate correlation graph, where each physical quantity dimension of the multidimensional impurity-stress-structure correlation tensor corresponds to a node in the graph. A directed edge exists between every two nodes, and each edge is initialized with a random weight representing the strength and direction of the candidate physical correlation. Internally, the physical law guidance network uses a physically constrained structure optimizer. This optimizer learns the strength and direction of the physical correlation for each edge in the candidate correlation graph by minimizing a loss function. The loss function is... Defined as:

[0077]

[0078] in: It is the edge weight matrix of Norms impose sparsity constraints to encourage simple graph structures; It is a crystal symmetry constraint term that penalizes operations that violate the point group symmetry of gallium oxide crystals (matrix). (represents) associated edges; It is a thermodynamic feasibility constraint that penalizes those directions that change from the standard Gibbs free energy. The calculated thermodynamic driving force is opposite in direction on the side; , , These are the weight coefficients of each term. In each optimization iteration, the structure optimizer calculates the degree to which the current correlation graph satisfies the known physical laws of the crystal, which is achieved by evaluating the values ​​of each term in the loss function. Based on the degree of satisfaction, the structure optimizer dynamically adjusts the network parameters to enhance the weights of edges that satisfy the physical laws, while reducing or deleting edges that violate the physical laws. During the optimization process, the algorithm design ensures that the final generated graph structure does not contain loops that violate the direction of the thermodynamic time arrow, i.e., reverse edges from high-energy states to low-energy states are suppressed. Optionally, the optimization process can set an early stopping criterion, stopping iteration when the change in the loss function value is lower than a threshold for several consecutive iterations. When the loss function converges to a stable value, the graph structure output by the structure optimizer is defined as a directed propagation graph for impurity tracing, where the final weight of each directed edge represents the rate constant of migration or reaction from the physical state of the source node to the physical state of the target node.

[0079] In one embodiment of the present invention, forward inference is performed based on a generated impurity source tracing directed propagation graph. The impurity source tracing directed propagation graph is a directed graph data structure where each node represents a physical state identifiable in the spectrum, each directed edge represents a possible physical or chemical reaction path, and the weight value on the edge represents the rate constant of that path. In a specific implementation, all nodes corresponding to impurities introduced by the crystal growth raw materials, atmosphere, or equipment are identified in the impurity source tracing directed propagation graph. The identification process is based on the metadata attributes of the nodes in the impurity source tracing directed propagation graph. The metadata attributes of the nodes include a state type description, such as labeled "silicon interstitial impurity Si introduced by raw materials". i "or "Atmosphere-introduced hydroxide ions OH" - The nodes marked with "" are identified as source nodes of impurities. In some embodiments, the identification of source nodes can be aided by a crystal growth process database, which stores information on raw material purity, atmosphere composition, and equipment materials. Nodes in the impurity tracing directed propagation graph associated with known impurity elements or groups in this information are marked as source nodes.

[0080] In practice, starting from each marked source node, a breadth-first search algorithm is used to traverse the entire graph structure along the forward direction of the directed edges in the impurity tracing directed propagation graph. The implementation of the breadth-first search algorithm begins with a selected source node, visiting all its direct successor nodes (i.e., all nodes reachable in one step from the source node along the directed edges). These successor nodes are then added to a queue to be visited, and the path from the source node to each successor node is recorded, i.e., the sequence of nodes consisting of the source node and its successors, along with the directed edges connecting them. In practice, the breadth-first search algorithm continuously removes a node from the head of the queue, visits all its direct successor nodes that have not yet been visited in the current search path, and adds these newly visited successor nodes to the tail of the queue. Simultaneously, the search path is extended from the current node to these successor nodes, forming a longer path. During the traversal, the complete sequence of nodes and edges traversed from any source node to the defect state node detected by the current Raman spectrum is recorded. Defect state nodes are determined by finding nodes in the impurity source-tracing directed propagation graph that match the characteristic flow of the abnormal peaks in the measured Raman spectrum. Each complete forward path starting from a source node and ending at a defect state node constitutes a candidate impurity migration path. It can be understood that the impurity source-tracing directed propagation graph may contain multiple defect state nodes. For each defect state node, the breadth-first search algorithm needs to start from all source nodes and find all forward paths that can reach that defect state node.

[0081] In practical implementation, for each candidate impurity migration path obtained through the breadth-first search algorithm, it is necessary to verify whether each reaction or migration step on the path meets the actual temperature and pressure conditions during gallium oxide crystal growth. The verification process involves obtaining the physical or chemical processes corresponding to each reaction or migration step on the candidate impurity migration path and querying the actual process parameters recorded in the crystal growth process database. The verification process requires calculating the thermodynamic feasibility of each reaction or migration step under the real-time temperature and pressure conditions of the growth stage corresponding to the current step (determined by the temporal attributes of the intermediate state node in the impurity source propagation graph). The thermodynamic feasibility calculation formula is:

[0082]

[0083] in: Indicates the current temperature and pressure Gibbs free energy change under certain conditions Indicates the enthalpy change of the reaction. This represents the entropy change of the reaction. This represents the volume change during the reaction process. This represents the reference pressure. If, for a certain step in the candidate impurity migration path, the calculated... If the value is greater than zero, the step is considered thermodynamically infeasible under the current process conditions, and the entire candidate impurity migration path will be eliminated. In some embodiments, in addition to thermodynamic feasibility, the verification process may also include a kinetic feasibility assessment. For example, by comparing the reaction timescale corresponding to the edge weights of the impurity source tracing directed propagation graph with the actual residence time of that stage of crystal growth, if the reaction time required is much greater than the residence time provided by the process, the candidate impurity migration path is also considered to not meet the actual process conditions and is eliminated. Optionally, the verification process can be designed as a screening function that iterates through each step of the candidate impurity migration path, applying thermodynamic and kinetic judgment conditions in sequence. Only candidate impurity migration paths that pass all steps of the verification will be retained for subsequent analysis.

[0084] In one embodiment of the present invention, for each candidate impurity migration path retained after forward derivation from the impurity source tracing directed propagation graph and verification of process conditions, its migration energy barrier and thermodynamic probability integral are calculated. In a specific implementation, for a candidate impurity migration path, the reaction or migration rate constants of all edges on the candidate impurity migration path are extracted. The extraction operation reads the rate constant attribute values ​​stored on each directed edge constituting the candidate impurity migration path from the data structure of the impurity source tracing directed propagation graph. The rate constants are expressed as... It indicates that the subscript Indicates the first position on the path Step reaction or migration.

[0085] In practice, based on a variation of the Arrhenius equation, the activation energy at each step along the path is calculated by back-calculating the reaction or migration rate constant. The standard form of the Arrhenius equation is... ,in It is the rate constant. It refers to the pre-factor. It is activation energy. It is the molar gas constant. It is absolute temperature. From the known rate constant... Activation energy When doing so, the corresponding temperature needs to be specified. and pre-exponential factors ,temperature The real-time temperature corresponding to the growth stage at which this reaction occurs, taken from the crystal growth process database, and the pre-exponential factor. The activation energy can be calculated theoretically, empirically, or learned from the process of constructing a directed propagation graph of impurity sources. In practical implementation, the activation energy... The calculation formula is expressed as follows:

[0086]

[0087] in: Indicates the first impurity in the migration path Activation energy of the step It is the molar gas constant. It is the first The absolute temperature at which the first reaction occurs. It is the first The rate constant of the step, It is the first The pre-exponential factor of the step. The activation energy at each step along the candidate impurity migration path is calculated. Then, the activation energy of all steps The results are summed and defined as the migration barrier of the candidate impurity migration path. In some embodiments, if some steps in the candidate impurity migration path are reversible reactions, only the activation energy of the forward reaction is considered when calculating the migration barrier.

[0088] In practice, real-time temperature and pressure data are acquired for each stage of gallium oxide single crystal growth. This data is stored in a crystal growth process database, where each record includes a timestamp, temperature value, pressure value, and growth stage identifier. The standard Gibbs free energy change for each reaction step along the candidate impurity migration path is calculated. Step reaction, its standard Gibbs free energy change The calculations rely on standard Gibbs free energy of formation data for the reactants and products involved in this reaction step, which can be obtained from materials thermodynamics databases. Combining real-time temperature and pressure data obtained from crystal growth process databases, the Gibbs free energy change of each reaction step along the candidate impurity migration path under actual process conditions is calculated. The calculation formula is: ,in It is the reaction quotient of this step of the reaction. This is the absolute temperature at which the reaction occurs. In practice, it refers to the actual Gibbs free energy change for all steps along the entire candidate impurity migration path. By summing the results, we obtain the total Gibbs free energy change along the path. The total Gibbs free energy variation Substituting into the Boltzmann factor formula for calculation, the Boltzmann factor formula is: ,in It is the weighted average of the temperatures of each stage experienced by the candidate impurity migration path. The calculated result is defined as the thermodynamic probability integral of the corresponding candidate impurity migration path. The thermodynamic probability integral is a dimensionless value, and its magnitude reflects the thermodynamic relative probability of the candidate impurity migration path occurring at a given temperature.

[0089] See Figure 3 This is a comparative analysis chart of impurity contribution weights and migration barriers, showing the correspondence between the contribution weights and migration barriers of different impurity types during gallium oxide single crystal growth. Silicon impurities contribute the most to the final defect state, followed by carbon impurities, with the two combined contributing over 60%. Metal impurities have the lowest contribution weights and the least impact on defect formation. Oxygen vacancies have the highest migration barrier, indicating that they are the most difficult to migrate in the crystal and the least kinetically active. Hydrogen impurities have the lowest migration barrier and are the easiest to diffuse and migrate within the crystal. There is no strict positive correlation between contribution weights and migration barriers. Silicon impurities contribute the most, but their migration barrier is not the highest, indicating that their defect impact mainly stems from high initial concentration or strong reactivity, rather than diffusion ability. Although oxygen vacancies have the highest migration barrier, they still have a certain contribution weight, suggesting that they may form stable defects in local regions, having a key impact on crystal performance.

[0090] In one embodiment of the present invention, all candidate impurity migration paths that satisfy a preset upper limit of migration barrier and a lower limit of thermodynamic probability integral are merged. The preset upper limit of migration barrier refers to a threshold of the sum of maximum activation energies, and the preset lower limit of thermodynamic probability integral refers to a threshold of the minimum Boltzmann factor product. Only candidate impurity migration paths whose calculated migration barrier is lower than or equal to the upper limit of migration barrier and whose calculated thermodynamic probability integral is higher than or equal to the lower limit of thermodynamic probability integral are included in the merging process. In specific implementation, the merging process imports the node and edge information of all qualified candidate impurity migration paths into a unified network data structure. During the merging process, common intermediate state nodes and common reaction edges shared between different candidate impurity migration paths are identified. Common intermediate state nodes refer to nodes that appear in multiple candidate impurity migration paths and represent the same physical or chemical state. Common reaction edges refer to directed edges that exist in multiple candidate impurity migration paths and connect the same two nodes. The method for identifying common intermediate state nodes and common reaction edges is to compare the unique identifiers of nodes and edges; nodes or edges with the same identifier are considered the same entity. In practical implementation, a common intermediate state node serves as the hub, weaving multiple candidate impurity migration paths into a directed acyclic network topology. The weaving process involves merging all nodes and edges of all paths. When encountering a common intermediate state node, edges from different paths connect to this unique node, thus forming a merged network starting from the source node and ending at nodes representing different defect states. It can be understood that since the impurity source tracing directed propagation graph itself does not contain loops violating the thermodynamic time arrow direction, and the candidate impurity migration paths are along the positive direction, the resulting network topology must also be a directed acyclic graph. In practical implementation, based on the growth stage in which nodes appear in the candidate impurity migration paths, the nodes in the network topology are divided into an impurity introduction layer, a defect formation layer, and a defect stabilization layer. The division of growth stages is based on the time axis definition in the crystal growth process database. Nodes in the impurity introduction layer correspond to the initial state of impurities introduced in the early growth stage; nodes in the defect formation layer correspond to the intermediate defect states formed by the interaction between impurities and the lattice in the middle growth stage; and nodes in the defect stabilization layer correspond to the final stable defect configuration formed at the end of the growth stage. Each node in the mesh topology is assigned to a corresponding level based on its state and the corresponding process time point, forming a hierarchical impurity distribution and evolution network with a clear time hierarchy.

[0091] In practice, the hierarchical impurity distribution and evolution network is physically segmented, and the reaction path distances between all nodes in the hierarchical impurity distribution and evolution network are calculated. (Reaction path distance) The definition is based on connecting two nodes and The reciprocal of the sum of the rate constants on all possible paths is calculated using the following formula:

[0092]

[0093] in: Represents a node To the node The reaction path distance, Indicates from node To the node The set of all directed paths, It is a set A specific path in it, It is a path A directed edge on, This is the weight (i.e., rate constant) of the directed edge. Reaction path distance. The smaller the value, the greater the likelihood that two nodes are connected via a rapid reaction. A reaction kinetics-based clustering method is used to divide the hierarchical impurity distribution and nodes in the evolutionary network into different reaction groups based on the calculated reaction path distance matrix. The clustering method employs a hierarchical clustering algorithm, using reaction path distance as a measure of dissimilarity between nodes, and a reaction path distance threshold is set. To divide the group, when the reaction path distance between two nodes is... At this time, they are grouped into the same reaction group. Nodes within a reaction group are connected by fast reactions, with fast reactions corresponding to edges with short reaction path distances; nodes between different reaction groups are connected by slow reactions, with slow reactions corresponding to edges with long reaction path distances. In specific implementation, each reaction group and all its internally connected reaction edges are extracted from the hierarchical impurity distribution and evolution network to form a physically relatively independent sub-network. This sub-network is a defect cluster, and each defect cluster contains a relatively compact impurity migration and reaction network. Each defect cluster is labeled with a defect type tag based on its core impurity type. The labeling process involves analyzing the impurity element or group information contained in the state descriptions of all nodes within the defect cluster, taking the most frequently occurring impurity type as the core impurity type of the defect cluster, and generating a tag in the form of "impurity element-defect type", such as "silicon-interstitial cluster" or "oxygen-vacancy complex".

[0094] In practice, the defect cluster information formed by clustering and segmenting a hierarchical impurity distribution and evolution network can be recorded in a table, see Table 1.

[0095] Table 1: Example of Defect Cluster Partition Results

[0096]

[0097] In the example of defect cluster partitioning results, the defect cluster number is a unique identifier, the number of nodes refers to the total number of nodes in the defect cluster subnetwork, the core impurity type is the main impurity element statistically derived from node state information, the defect type label is a descriptive label defined based on the core impurity type and defect morphology, and the hierarchy indicates which time level(s) of the hierarchical impurity distribution and evolution network most nodes in the defect cluster are distributed in. It can be understood that the partitioning of defect clusters decomposes the complex hierarchical impurity distribution and evolution network into multiple sub-modules that are easier to analyze and understand, with each defect cluster focusing on a core impurity-defect interaction process.

[0098] See Figure 4 This is a reaction path distance heatmap used to illustrate the reaction path distance between source nodes and target nodes in the gallium oxide single-crystal growth impurity evolution network. Red represents high reaction path distances, and blue represents low reaction path distances. The dark red blocks at source node 5 and target nodes 7 and 8 indicate extremely long reaction paths between them, belonging to different defect clusters. High-distance regions also exist between source node 10 and target nodes 11 and 12, similarly belonging to physically segmented independent sub-networks. The diagonal and adjacent areas are mostly blue / light orange, representing short reaction paths and tight connections within the same cluster. Cross-cluster node pairs are mostly orange / red, indicating that different defect clusters are connected through slow reactions, exhibiting an overall block-structured distribution, verifying that the hierarchical impurity evolution network is segmented into multiple physically independent defect clusters.

[0099] In one embodiment of the present invention, for each defect cluster obtained after physical segmentation, an impurity concentration diffusion inversion analysis across growth cycles is performed. Within a defect cluster, a stable defect state node located at the end of growth is defined as an observation node. The observation node is defined based on the node being marked as belonging to the defect stability layer in the hierarchical impurity distribution and evolution network, and the physical state description of the node matching the main defect characteristic peaks finally observed in the Raman spectrum. In a specific implementation, an impurity concentration diffusion inversion model is used to simulate the diffusion and evolution of impurity concentration along the reaction edge to the observation node from each initial impurity introduction node in the defect cluster as the crystal grows. The initial impurity introduction node refers to a node located inside the defect cluster and belonging to the impurity introduction layer or defect formation layer, representing the initial impurity introduction state. The impurity concentration diffusion inversion model is a mathematical model based on reaction kinetics and the law of conservation of mass. The model treats the defect cluster as a reaction network, where nodes represent the concentrations of different impurity or defect states, edges represent the transition reactions between states, and each edge has a rate constant determined by the impurity source-tracing directed propagation graph.

[0100] In practice, at the start of the simulation, an initial concentration value is assigned to each initial impurity introduction node in the defect cluster. This initial concentration value can be obtained based on the impurity content of the crystal growth raw materials, the partial pressure of impurities in the atmosphere, or statistical analysis from historical data. During the simulation, the transport and reaction consumption of the diffused impurity concentration are calculated based on the rate constant of the reaction edge. For connecting nodes... and nodes The directed reaction edge, its reaction rate The calculation formula, derived from the law of mass action, is as follows:

[0101]

[0102] in: It is the reaction rate constant of that edge obtained from the directed propagation graph of impurity source tracing. Reactant nodes In simulating the concentration at the current moment, This is the reaction order, typically set to 1 for unimolecular reaction steps. Within each simulation time step, the model calculates the net change in concentration at each node based on the rates of all reaction edges and updates the node concentration. The simulation time covers the entire crystal growth cycle, and the time step setting must ensure the stability of the numerical solution. During the simulation, the model records the impurity concentration share that finally reaches the observation node. This concentration share refers to the concentration of impurities originating from a specific initial impurity introduction node, after a series of reactions and transports, existing at the end of the simulation in the form of the defect state represented by the observation node. In practice, the final impurity concentration share contributed by each initial impurity introduction node is divided by the total concentration share contributed by all initial impurity introduction nodes to obtain the contribution weight of the impurity corresponding to the initial impurity introduction node at the corresponding growth stage. Contribution Weight The calculation formula is:

[0103]

[0104] in: This indicates the introduction of nodes from a specific initial impurity. The contribution weight of the impurities at the starting point to the defect state of the final observed node. When the simulation ends, it is controlled by the nodes. The concentration of introduced impurities at the observation node. At the end of the simulation, all within the defect cluster The total concentration of impurities introduced at each initial impurity introduction node at the observation node. This can be understood as the contribution weight. This is a value between 0 and 1, where the sum of the contribution weights of all initial impurity introduction nodes is 1. In some embodiments, the impurity concentration diffusion inversion model can be described by a system of ordinary differential equations and solved using numerical integration methods such as the Runge-Kutta method. The effect of temperature and pressure changes on the reaction rate constant during crystal growth can be simulated by updating the temperature parameter in the Arrhenius equation at each time step.

[0105] In practice, a structured gallium oxide single crystal growth impurity detection and analysis report is generated based on the contribution weight of each impurity and in conjunction with the crystal growth process database. Impurities with contribution weights exceeding a preset threshold are marked as critical control impurities. The preset threshold is an empirical value, such as 0.1 or 0.05, meaning that impurities contributing more than 10% or 5% to the final defect state are identified as critical control impurities requiring focused control. The crystal growth process database is retrieved to identify raw material purity standards, sensitive ranges of process parameters, and historical control schemes related to each critical control impurity. The database stores the chemical composition specifications of raw materials, temperature and pressure ranges of process steps and their control history, as well as records of measures taken to reduce specific impurities in the past. Critical control impurities are sorted in descending order of contribution weight, with those having higher contribution weights appearing earlier in the report. For each critical control impurity, the report details its origin, growth stage, defect cluster, corresponding contribution weight, introduced raw material or process step, and suggested process control direction. Information on introduced raw materials or process steps is extracted from the metadata of the initial impurity introduction node or obtained through correlation queries from the crystal growth process database. The suggested process control directions are based on a comprehensive analysis of contribution weights, impurity sources, and historical control schemes. For example, for impurities with high contribution weights that originate from raw materials, the control direction is to improve the purity of the raw materials; for impurities with high contribution weights that are sensitive to a certain process parameter, the control direction is to optimize the control range of that parameter.

[0106] See Figure 5This is a line graph showing the migration rate of impurities as the growth process progresses, illustrating the migration patterns of Si, Fe, and Cu impurities throughout the entire gallium oxide single crystal growth process. The migration rates of all three impurities continuously increase with each growth stage, indicating that impurities diffuse and redistribute within the crystal throughout the entire process from raw material to finished product. Si impurities exhibit the strongest migration ability, while Cu impurities have the weakest. During the crystal growth stage, Si impurities migrate at the fastest rate, followed by Fe, and then Cu at the slowest, consistent with the high diffusion coefficient of Si in the gallium oxide lattice at high temperatures. During the annealing stage, the migration rates of all three impurities significantly increase, with Si showing the most pronounced increase. The high-temperature environment of annealing provides ample kinetics for impurity diffusion. During the cooling stage, the migration rate of Fe impurities surpasses that of Si, possibly related to the enhanced segregation effect of Fe during cooling. In the finished product inspection stage, the migration rate of Si impurities remains the highest, indicating that its distribution in the final crystal is the most uneven and is one of the main sources of defects.

[0107] The above embodiments are only used to illustrate the technical methods of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical methods of the present invention without departing from the spirit and scope of the technical methods of the present invention.

Claims

1. A method for detecting and analyzing impurities in gallium oxide single crystal growth based on Raman spectroscopy, characterized in that, include: Based on a time-series Raman spectroscopy dataset containing spatial coordinate information, a directed propagation map for impurity source tracing is generated, including: During the growth of gallium oxide single crystals, in-situ laser Raman spectroscopy scanning is performed on the growth interface region to collect a time-series Raman spectral dataset containing spatial coordinate information. Feature enhancement and noise stripping operations were performed on the time-series Raman spectroscopy dataset to separate the intrinsic peak feature streams related to gallium oxide lattice vibrations and the anomalous peak feature streams related to impurity defects; Based on the separated intrinsic peak characteristic flow and the anomalous peak characteristic flow, a multidimensional impurity-stress-structure correlation tensor is constructed. The multidimensional impurity-stress-structure correlation tensor is used to characterize the coupling relationship between impurity type, local stress and lattice distortion. The multidimensional impurity-stress-structure correlation tensor is input into a learnable physical law guidance network, which generates an impurity source tracing directed propagation graph by iteratively identifying spurious correlations and solidifying physical correlations. Based on the impurity source tracing directed propagation graph, all candidate impurity migration paths from the impurity introduction point to the current defect state are deduced in a forward manner. For each candidate impurity migration path, calculate its migration energy barrier and thermodynamic probability integral, and sort and filter all candidate impurity migration paths based on the migration energy barrier and the thermodynamic probability integral. All candidate impurity migration paths after sorting and screening are integrated to form a hierarchical impurity distribution and evolution network. Each node in the hierarchical impurity distribution and evolution network represents an impurity state or defect configuration, and each edge represents an impurity migration or reaction relationship. The hierarchical impurity distribution and evolution network is physically segmented, and the complex network structure is decomposed into multiple impurity-dominated defect clusters, with each defect cluster focusing on a core impurity-defect interaction process. For each of the defect clusters, an impurity concentration diffusion inversion analysis across the growth cycle is performed to quantify the contribution weight of each impurity to the final defect state at different growth stages. Based on the contribution weight of each impurity and combined with the crystal growth process database, a structured gallium oxide single crystal growth impurity detection and analysis report is generated.

2. The method for detecting and analyzing impurities in gallium oxide single crystal growth based on Raman spectroscopy as described in claim 1, characterized in that, Feature enhancement and noise stripping operations are performed on the time-series Raman spectroscopy dataset to separate the intrinsic peak feature streams related to gallium oxide lattice vibrations and the anomalous peak feature streams related to impurity defects, including: Background subtraction and intensity normalization are performed on each original spectrum in the time-series Raman spectroscopy dataset; Continuous wavelet transform is performed on the normalized spectrum to extract its time-frequency features at different scales, forming a high-dimensional spectral feature sequence. Independent principal component analysis was applied to the high-dimensional spectral feature sequence to separate several independent components with the largest variance contribution. The independent components are matched with the theoretical Raman active phonon modes of gallium oxide standard crystals, and the successfully matched components are reconstructed as the intrinsic peak characteristic flow. The remaining unmatched independent components, along with the characteristic peak components associated with known impurities or defects, are collectively reconstructed into the anomalous peak feature stream.

3. The method for detecting and analyzing impurities in gallium oxide single crystal growth based on Raman spectroscopy as described in claim 2, characterized in that, The multidimensional impurity-stress-structure correlation tensor is input into a learnable physical law guidance network. This network iteratively identifies spurious correlations and solidifies the physical correlations, generating a directed propagation graph for impurity tracing, including: Initialize a fully connected candidate correlation graph, wherein each physical quantity dimension in the multidimensional impurity-stress-structure correlation tensor corresponds to a node in the graph; A physical constraint-based structure optimizer is used to learn the physical association strength and direction of each edge in the candidate association graph by minimizing a loss function that includes sparsity constraints, crystal symmetry constraints and thermodynamic feasibility constraints. In each optimization iteration, the structure optimizer calculates the degree to which the current correlation graph satisfies the known physical laws of crystals; Based on the degree of satisfaction, the edge weights that satisfy physical laws are dynamically increased, while edges that violate physical laws are reduced or deleted, and the final graph structure is ensured to not contain loops that violate the direction of the thermodynamic time arrow. Once the loss function converges to a stable value, the graph structure output by the structure optimizer is defined as the impurity source tracing directed propagation graph, where the weights of the edges represent the rate constants of impurity migration or defect response.

4. The method for detecting and analyzing impurities in gallium oxide single crystal growth based on Raman spectroscopy as described in claim 3, characterized in that, Based on the impurity source tracing directed propagation graph, all candidate impurity migration paths from the impurity introduction point to the current defect state are deduced in a forward manner, including: In the impurity source tracing directed propagation diagram, all nodes corresponding to impurities introduced by crystal growth raw materials, atmosphere or equipment are identified, and the nodes are marked as source nodes; Starting from each of the source nodes, a breadth-first search algorithm is used to traverse the impurity tracing directed propagation graph along the positive direction of the directed edges; During the traversal, the complete sequence of nodes and edges traversed from any of the source nodes to the node representing the defect state detected by the current Raman spectrum is recorded. Each complete forward path constitutes a candidate impurity migration path. For each candidate impurity migration path, verify whether each step of the reaction or migration meets the temperature and pressure conditions during the gallium oxide crystal growth process, and eliminate paths that do not meet the actual process conditions.

5. The method for detecting and analyzing impurities in gallium oxide single crystal growth based on Raman spectroscopy as described in claim 4, characterized in that, For each of the candidate impurity migration paths, the migration barrier and thermodynamic probability integral of the path are calculated, including: For a candidate impurity migration path, extract the reaction or migration rate constants of all edges on the candidate impurity migration path; Based on a variation of the Arrhenius equation, the activation energy of each step in the path is calculated by back-calculating the reaction or migration rate constant, and the sum of the activation energies of all steps is taken as the migration energy barrier of the candidate impurity migration path. Acquire real-time temperature and pressure data at each stage of gallium oxide single crystal growth; Based on the temperature and pressure data, the standard Gibbs free energy change of each step of the reaction along the candidate impurity migration path is calculated; The standard Gibbs free energy changes of all steps along the entire path are accumulated and substituted into the Boltzmann factor formula to obtain the thermodynamic probability integral of the corresponding path.

6. The method for detecting and analyzing impurities in gallium oxide single crystal growth based on Raman spectroscopy as described in claim 5, characterized in that, The integration of all candidate impurity migration paths after sorting and filtering forms a hierarchical impurity distribution and evolution network, including: All candidate impurity migration paths that meet the preset upper limit of migration energy barrier and lower limit of thermodynamic probability integral are merged. During the merging process, common intermediate state nodes and common reaction edges shared between different candidate impurity migration paths are identified; Using the common intermediate state node as a hub, multiple candidate impurity migration paths are woven into a directed acyclic mesh topology; Based on the growth stage of nodes in the impurity migration path, the nodes in the mesh topology are divided into an impurity introduction layer, a defect formation layer, and a defect stabilization layer, forming a hierarchical impurity distribution and evolution network with a clear time hierarchy.

7. The method for detecting and analyzing impurities in gallium oxide single crystal growth based on Raman spectroscopy as described in claim 6, characterized in that, The hierarchical impurity distribution and evolution network is physically segmented, decomposing the complex network structure into multiple impurity-dominated defect clusters, including: Calculate the hierarchical impurity distribution and the reaction path distance between all nodes in the evolution network; A clustering method based on reaction kinetics is used to divide nodes into different reaction groups according to the reaction path distance. Nodes within each reaction group are connected through fast reactions, and nodes in different reaction groups are connected through slow reactions. Each reaction group and its internally connected reaction edges are extracted to form a physically independent sub-network, which is a defect cluster. Each defect cluster is labeled with a defect type tag based on its core impurity type.

8. The method for detecting and analyzing impurities in gallium oxide single crystal growth based on Raman spectroscopy as described in claim 7, characterized in that, For each of the aforementioned defect clusters, an impurity concentration diffusion inversion analysis across growth cycles is performed to quantify the contribution weight of each impurity to the final defect state at different growth stages, including: Within one of the defect clusters, a stable defect state node located at the end of the growth phase is defined as an observation node; Using an impurity concentration diffusion inversion model, starting from each initial impurity introduction node in the defect cluster, the process of impurity concentration diffusion and evolution along the reaction edge to the observation node during crystal growth is simulated. During the simulation, the transport and reaction consumption of the diffused impurity concentration are calculated based on the rate constant of the reaction edge, and the impurity concentration fraction that finally reaches the observation node is recorded. The contribution weight of the impurity at the corresponding growth stage of each initial impurity introduction node is obtained by dividing the final impurity concentration share contributed by each initial impurity introduction node by the total concentration share contributed by all initial impurity introduction nodes.

9. The method for detecting and analyzing impurities in gallium oxide single crystal growth based on Raman spectroscopy as described in claim 8, characterized in that, Based on the contribution weight of each impurity and combined with the crystal growth process database, a structured gallium oxide single crystal growth impurity detection and analysis report is generated, including: Impurities whose contribution weight exceeds a preset threshold are marked as critical control impurities; From the crystal growth process database, retrieve the raw material purity standards, sensitive ranges of process parameters, and historical control schemes related to each key controlled impurity; The key control impurities are arranged in descending order of their contribution weights. For each critical control impurity, list in detail its growth stage, the defect cluster to which it belongs, its corresponding contribution weight, the raw materials or process steps it was introduced into, and the recommended process control direction. All information is organized and filled according to a predefined analysis report template to generate the final structured gallium oxide single crystal growth impurity detection and analysis report.

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