A method for dynamically controlling the growth direction of a micron-sized single crystal

Abstract

The application provides a micron-scale single crystal growth crystal direction dynamic constraint regulation method, relates to the technical field of micron-scale single crystal growth, and comprises the following steps: identifying and characterizing each crystal face orientation exposed at the same time of a growth interface in an initial growth stage of micron-scale single crystal growth, forming a multi-orientation growth front crystal direction candidate set; calculating dominant potential of each candidate crystal direction, and obtaining a target crystal direction, a competitive crystal direction sequence and a competitive strength index according to the priority of the dominant potential; combining an engineering feasible constraint channel to generate a target crystal direction dominant right strengthening constraint condition set; determining whether the target crystal direction forms a unique dominant main crystal direction locking state; determining a crystal direction reference and an offset allowed band, and dynamically pulling back the constraint on slight offset in the single main crystal direction growth process, so as to accurately screen and lock the target crystal direction, avoid interface disturbance by grading regulation and constraint strength, and realize crystal direction stability in the whole single crystal growth cycle by dynamically pulling back and inhibiting the slight offset of the crystal direction.

Description

Technical Field

[0001] This invention relates to the field of micron-scale single crystal growth technology, and in particular to a method for dynamic constraint control of crystal orientation in micron-scale single crystal growth. Background Technology

[0002] As the requirements for crystal orientation accuracy of micron-scale single crystal materials continue to increase in fields such as semiconductors and microelectronics, crystal orientation control during single crystal growth has become a core technology.

[0003] In the initial growth stage of micron-sized single crystals with strong anisotropy, the growth front is prone to simultaneously exposing multiple near-equipotential crystal orientations, exhibiting interface evolution characteristics of multi-orientation parallel competition. Traditional crystal orientation control methods implicitly assume that the principal crystal orientation is predetermined and only undergoes continuous small-amplitude shifts. They can only suppress the small shifts of the existing principal crystal orientation and cannot substantially intervene in the allocation of the dominant weight of crystal orientations under multi-orientation competition. In near-equipotential scenarios, crystal orientation transitions are prone to occur, leading to the failure of crystal orientation constraints and making it difficult to meet the stable growth requirements of high-precision micron-sized single crystals.

[0004] Therefore, it is necessary to provide a method for dynamic constraint control of crystal orientation in micron-scale single crystal growth to solve the above-mentioned technical problems. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for dynamic constraint control of crystal orientation in micron-scale single crystal growth. This method solves the problem that in the initial growth of micron-scale single crystals, there is competition among multiple orientation crystal planes, the main crystal orientation is not unique and the dominance frequently switches, and traditional crystal orientation offset constraint methods are difficult to meet the stable growth requirements of high-precision micron-scale single crystals.

[0006] This invention provides a method for dynamic constraint control of crystal orientation in micron-scale single crystal growth, the method comprising: The orientations of each crystal plane simultaneously exposed at the growth interface during the initial stage of micron-scale single crystal growth are identified and characterized, forming a multi-orientation growth front crystal direction candidate set that includes the interface normal characteristics, growth extension trend characteristics, and spatial distribution range of each candidate crystal direction. Based on the candidate set of crystal orientations at the growth front of multiple orientations, the dominant potential of each candidate crystal orientation is calculated, and the target crystal orientation, the sequence of competing crystal orientations and the competition intensity index are obtained by sorting them according to the priority of the dominant potential. Based on the target crystal orientation, competing crystal orientation sequences and competition intensity indicators, combined with engineering-feasible constraint channels, a set of directional target crystal orientation dominance enhancement constraint conditions is generated. Apply a set of constraints to strengthen the dominance of the target crystal orientation, and quantitatively determine whether the target crystal orientation forms a unique dominant master crystal orientation locked state. Based on the principal crystal direction locked state, the crystal direction reference and offset allowable zone are determined, and the subtle offsets in the single principal crystal direction growth process are dynamically pulled back to constrain them.

[0007] Preferably, the identification and characterization of the orientations of each crystal plane simultaneously exposed at the growth interface during the initial stage of micron-scale single crystal growth, forming a multi-orientation growth front crystal orientation candidate set including the interface normal characteristics, growth extension trend characteristics, and spatial distribution range of each candidate crystal orientation, specifically includes: The growth interface measurement results and system calibration parameters of the initial stage of micron-scale single crystal growth are converted into the interface height field in the device coordinate system. After resampling and local smoothing, unusable areas are removed to generate an effective area mask. Based on the interface height field and the effective region mask, the three-directional gradient components and the unit normal component of the interface are calculated. After filtering out invalid points, the interface normal characteristics are obtained, including the interface normal component field and the interface normal stability index. Based on the interface normal component field and interface normal stability index, after screening out strong fluctuation regions, crystal plane plate set is divided, plate statistics are calculated, and candidate crystal directions are formed by clustering according to normal similarity. The corresponding growth extension trend characteristics are calculated based on the changes in the area ratio of each candidate crystal orientation within a short time window. By integrating the interface normal characteristics, growth extension trend characteristics, and spatial distribution range of each candidate crystal orientation, a multi-orientation growth front crystal orientation candidate set is obtained.

[0008] Preferably, the formula for calculating the three-directional gradient components of the interface is as follows:

[0009] In the formula, Represents the three-directional gradient components of the interface; This represents the height value of the interface height field at coordinates (x, y, z); Indicates the sampling step size in the x and y directions; The formula for calculating the unit normal component of the interface is as follows:

[0010] In the formula, The normal component represents the unit normal component of the interface; den represents the normalized denominator. The formula for calculating the area ratio of a district is as follows:

[0011] In the formula, This represents the area percentage of the i-th candidate crystal orientation; This represents the total area of ​​the region corresponding to the i-th candidate crystal orientation; Indicates the total area of ​​the effective region; A constant that prevents division by zero; The formula for calculating the growth extension trend characteristics is as follows:

[0012] In the formula, This represents the growth extension trend characteristics of the i-th candidate crystal orientation. Indicates orientation expansion, Indicates oriented contraction; These represent the i-th candidate crystal orientation at time t. The total area of ​​the district.

[0013] Preferably, the step of calculating the dominant potential of each candidate crystal direction based on the multi-orientation growth front crystal direction candidate set, and sorting them according to the priority of dominant potential to obtain the target crystal direction, the sequence of competing crystal directions, and the competition intensity index, specifically includes: Based on the candidate set of crystal orientations at the growth front of multiple orientations, the growth extension trend characteristics of each candidate crystal orientation are extracted. Combined with the corresponding area ratio, the spatial continuity coefficient is calculated to form a set of basic characterization quantities. Based on the set of basic characterization quantities, dimensionless proportion terms, expansion terms, and contiguous terms are constructed and normalized to obtain the set of dominant potential component terms. Dominant potential is generated by weighting the set of dominant potential components, and a competition intensity index is calculated to identify near-equipotential competition scenarios. Based on the dominant potential, all candidate crystal directions are sorted from largest to smallest to obtain a preliminary sorting sequence of candidate crystal directions. Based on the preliminary sorting sequence of candidate crystal directions and the competition intensity index, the competition mode is marked, and the sorting results of the target crystal direction, the competing crystal direction sequence, and the competition intensity index are obtained by encapsulation.

[0014] Preferably, the formula for calculating the spatial continuity coefficient is as follows:

[0015] In the formula, Let represent the spatial continuity coefficient of the i-th candidate crystal orientation, and The larger the value, the stronger the directional continuity. Let represent the perimeter of the outer boundary of the region union of the i-th candidate crystal orientation; The formula for calculating the expansion term is as follows:

[0016] In the formula, This represents the expansion term for the i-th candidate crystal orientation; The saturation scale constant represents the expansion term; The formula for calculating contiguous items is as follows:

[0017] In the formula, This represents the lamination term for the i-th candidate crystal orientation; Represents the maximum spatial continuity coefficient for all candidate crystal orientations; Represents the minimum spatial continuity coefficient for all candidate crystal orientations; The formula for calculating dominant potential is as follows:

[0018] In the formula, This represents the dominant potential of the i-th candidate crystal orientation; These represent the weights of the percentage item, the expansion item, and the contiguous item, respectively. This represents the proportion of the i-th candidate crystal orientation; The formula for calculating the competition intensity index is as follows:

[0019] In the formula, Let represent the competition intensity index of the i-th candidate crystal orientation, and The closer the value is to 1, the stronger the competition is; This indicates the greatest potential for dominance; This indicates the second largest potential dominant force; This represents the difference scale constant.

[0020] Preferably, the step of generating a set of dominance enhancement constraint conditions for the target crystal orientation based on the target crystal orientation, competing crystal orientation sequences, and competition intensity indices, combined with engineering-feasible constraint channels, specifically includes: Based on the ranking results of the target crystal orientation, competing crystal orientation sequence and competition intensity index, the dominance enhancement target amount is calculated, and the dominance enhancement target amount is mapped to the dominance enhancement level in the range of 0 to 1 to characterize the constraint bias strength requirement. Based on the target amount and level of dominance enhancement, the directional growth bias is calculated, and the directional growth bias is allocated to three types of engineering constraint channels: thermal field, interface morphology, and solute transport, and the corresponding allocation coefficients are determined. Based on the directional growth bias and the thermal field channel allocation coefficient, the thermal field bias amplitude is calculated, and thermal field orientation constraint conditions containing temperature gradient range and thermal asymmetry limit are generated. Based on the directional growth bias and the morphology channel allocation coefficient, the morphology bias amplitude is calculated, and interface morphology orientation constraints containing curvature intervals and step density limits are generated. By integrating thermal field orientation constraints, interface morphology orientation constraints, and solute transport orientation constraints, a set of dominance enhancement constraints for the target crystal orientation is encapsulated.

[0021] Preferably, the formula for calculating the dominant power reinforcement target quantity is as follows:

[0022] In the formula, This indicates that the dominance of the target crystal orientation strengthens the target quantity; This indicates the dominant potential of the target crystal orientation; This indicates the dominant potential of the secondary competitive crystal orientation; An index representing the intensity of competition for a target crystal orientation; Indicates the strong competition threshold; 'a' represents the target quantity proportionality coefficient. The formula for calculating the dominance enhancement level is as follows:

[0023] In the formula, Indicates the level of dominance enhancement in the target crystal orientation. The closer to 1, the stronger the required constraint bias; exp represents an exponential function with the natural constant e as the base; b represents the level slope constant; The formula for calculating the directional growth bias is as follows:

[0024] In the formula, Indicates the directional growth bias of the target crystal orientation; This represents the bias gain constant; The formula for calculating the thermal field offset amplitude is as follows:

[0025] In the formula, Indicates the magnitude of thermal field offset; Indicates the thermal field reference offset; This represents the proportionality constant of the thermal field channels; Indicates the thermal field channel distribution coefficient; The formula for calculating the topographic offset magnitude is as follows:

[0026] In the formula, Indicates the magnitude of topographic offset; Indicates the topographic reference offset; This represents the scaling constant of the morphology channel; This represents the morphology channel allocation coefficient.

[0027] Preferably, the application of the target crystal orientation dominance enhancement constraint set, and the quantitative determination of whether the target crystal orientation forms a uniquely dominant principal crystal orientation locked state, specifically includes: The set of target crystal orientation dominance enhancement constraint conditions is sent to the execution component of the growth system to determine the set of execution window parameters for constraint application duration, constraint update cycle and constraint perturbation bandwidth; Based on the execution window parameter set and the real-time extracted multi-orientation growth front crystal direction candidate set, the advance difference, bridging difference and comprehensive advantage index between the target crystal direction and the competing crystal direction are calculated. Based on the difference in advancement, comprehensive advantage indicators, and execution window parameter set, the constraint execution amplitude is adjusted, and the percentage decrease rate of the competing crystal orientation and the percentage increase rate of the target crystal orientation are calculated. Based on the decreasing rate of the proportion of competing crystal orientations, the increasing rate of the proportion of the target crystal orientation, and comprehensive advantage indicators, a stable main crystal orientation locked state is determined according to preset criteria. By encapsulating the unique dominant marker of the target crystal orientation, the locking duration, the upper limit of the residual competition ratio, and the crystal orientation reference parameters, the main crystal orientation locked state is obtained.

[0028] Preferably, the formula for calculating the propulsion difference is as follows:

[0029] In the formula, This represents the difference in advancement of the target crystal orientation relative to the competing crystal orientation; This indicates the growth and extension trend characteristics of the target crystal orientation; The formula for calculating the difference between consecutive pieces is as follows:

[0030] In the formula, This indicates the lamination difference between the target crystal orientation and the competing crystal orientation; Indicates the spatial continuity coefficient of the target crystal orientation; The formula for calculating the comprehensive advantage index is as follows:

[0031] In the formula, The index represents the overall advantage of the target crystal orientation; n represents the number of competing crystal orientations; q represents the index weighting constant. The formula for calculating the percentage decrease rate of competing crystal orientations is as follows:

[0032] In the formula, This indicates the rate of decrease in the proportion of competing crystal orientations; These represent the competing crystal orientations at time [time]. The area percentage; The formula for calculating the percentage increase of the target crystal orientation is as follows:

[0033] In the formula, This indicates the percentage increase in the proportion of the target crystal orientation; These represent the target crystal orientation at time [time]. The area percentage.

[0034] Preferably, the step of determining the crystal orientation reference and offset allowable zone based on the principal crystal orientation locked state, and dynamically pulling back the fine offsets during the single principal crystal orientation growth process, specifically includes: The unit normal component of the target crystal direction is extracted based on the principal crystal direction locked state and used as the crystal direction reference. A crystal direction offset angle threshold is set to form an offset allowable band. Based on the crystal orientation reference, the offset allowable band and the real-time interface unit normal component, the crystal orientation offset angle is calculated, and the offset trend term is extracted by the change of offset angle within a short time window. Compare the crystal orientation offset angle, offset trend term, and offset allowable zone to determine whether dynamic pullback constraint needs to be applied. Based on the constraint trigger determination result, the pullback strength and constraint execution duration in the interval from 0 to 1 are calculated to form dynamic pullback constraint parameters; Based on the dynamic pullback constraint parameters, a dynamic pullback constraint instruction set that can be sent to the growth system is encapsulated to achieve reverse fine-tuning of crystal orientation shift.

[0035] The formula for calculating the crystal orientation offset angle is as follows:

[0036] In the formula, The unit normal component representing the crystal orientation reference; The formula for calculating the offset trend term is as follows:

[0037] In the formula, V represents the offset trend term; Indicates time Crystal orientation offset angle; The formula for calculating pullback strength is as follows:

[0038] In the formula, Y represents the pullback strength; This represents the pullback ratio constant; This indicates the threshold for the crystal orientation offset angle.

[0039] Compared with related technologies, the method for dynamic constraint control of crystal orientation in micron-scale single crystal growth provided by this invention has the following beneficial effects: This invention identifies and characterizes the orientations of all crystal planes simultaneously exposed at the growth interface during the initial stage of micron-scale single crystal growth, forming a multi-orientation growth front crystal direction candidate set that includes the interface normal characteristics, growth extension trend characteristics, and spatial distribution range of each candidate crystal direction. Based on the multi-orientation growth front crystal direction candidate set, the dominance potential of each candidate crystal direction is calculated, and the target crystal direction, competing crystal direction sequence, and competition intensity index are obtained by prioritizing the dominance potential. Based on the target crystal direction, competing crystal direction sequence, and competition intensity index, combined with engineering-feasible constraint channels, a set of directional target crystal direction dominance enhancement constraint conditions is generated. The target crystal direction dominance enhancement constraint condition set is applied to quantitatively determine whether the target crystal direction forms a unique dominant master crystal direction locked state. Based on the master crystal direction locked state, the crystal direction reference and offset allowable band are determined, and the subtle offsets in the single master crystal direction growth process are dynamically pulled back to constrain them. This allows for precise screening and locking of the target crystal direction, hierarchical control of the constraint intensity to avoid interface disturbances, and suppression of subtle crystal direction offsets through dynamic pull-back, achieving crystal direction stability throughout the entire growth cycle of the single crystal, significantly improving crystal direction consistency, and solving the problem of crystal direction constraint failure under multi-orientation competition.

[0040] This invention designs a dynamic constraint control method for crystal orientation in multi-orientation competition scenarios. First, it constructs a candidate set of crystal orientations and evaluates their dominance potential to accurately screen target crystal orientations. Then, it generates dynamic dominance strengthening constraints based on the competition intensity, achieving stable locking of the target crystal orientation and completely solving the core problem of constraint failure in traditional methods. Furthermore, the constraint strength is adjusted in stages according to the degree of competition, avoiding excessive bias leading to interface disturbances or insufficient bias causing crystal orientation loss of control, thus improving the adaptability and accuracy of the control. After the main crystal orientation is locked, dynamic pull-back constraints suppress minor deviations, ensuring crystal orientation stability throughout the entire growth cycle of the single crystal, effectively weakening the influence of competing crystal orientations, and significantly improving the growth quality and crystal orientation consistency of micron-scale single crystals, adapting to the engineering application needs of high-precision single crystal materials. Attached Figure Description

[0041] Figure 1 A flowchart of a method for dynamically constraining and controlling the crystal orientation of micron-scale single crystal growth provided in an embodiment of the present invention; Figure 2 The image shows a micron-sized single crystal grown using a method for dynamically constraining and controlling the crystal orientation of a micron-sized single crystal, as provided in an embodiment of the present invention. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] like Figure 1 The diagram shown is a flowchart of a method for dynamically constraining and controlling the crystal orientation of a micron-scale single crystal growth according to an embodiment of the present invention. Figure 1 The execution entity of the method shown can be a software and / or hardware device. The execution entity of this application can include, but is not limited to, at least one of the following: user equipment, network equipment, etc. User equipment can include, but is not limited to, computers, smartphones, personal digital assistants (PDAs), and the aforementioned electronic devices. Network equipment can include, but is not limited to, a single network server, a server group consisting of multiple network servers, or a cloud based on cloud computing consisting of a large number of computers or network servers. Cloud computing is a type of distributed computing, consisting of a super virtual computer composed of a group of loosely coupled computers. This embodiment does not limit this. Steps S1 to S5 are detailed as follows: S1 identifies and characterizes the orientations of each crystal plane simultaneously exposed at the growth interface during the initial stage of micron-scale single crystal growth, forming a multi-orientation growth front crystal direction candidate set that includes the interface normal characteristics, growth extension trend characteristics, and spatial distribution range of each candidate crystal direction. S2, based on the candidate crystal orientation set of multi-orientation growth front, calculate the dominant potential of each candidate crystal orientation, and sort them according to the priority of dominant potential to obtain the target crystal orientation, the sequence of competing crystal orientations and the competition intensity index. S3, based on the target crystal orientation, competing crystal orientation sequence and competition intensity index, combined with engineering feasible constraint channels, generates a set of directional target crystal orientation dominance enhancement constraint conditions; S4, apply the target crystal orientation dominance strengthening constraint set, and quantitatively determine whether the target crystal orientation forms a unique dominant master crystal orientation locked state; S5 determines the crystal orientation reference and offset allowable zone based on the principal crystal orientation locked state, and dynamically pulls back the slight offset during the growth process of a single principal crystal orientation.

[0044] like Figure 2 The image shown is of a micron-sized single crystal, representing a method for dynamic constraint control of crystal orientation in micron-sized single crystal growth according to an embodiment of the present invention. In the initial growth stage of the micron-sized single crystal, the measured data of the growth interface and system calibration parameters are first converted into an interface height field in the device coordinate system. After resampling, local smoothing, and removal of invalid regions, an effective region mask is formed. Then, the interface normal features are obtained through gradient calculation, and strong fluctuation regions are screened out. Crystal plane lamellae are divided and normal clustering is performed on the effective region to determine candidate crystal orientations. Finally, the spatial distribution range of each candidate crystal orientation is extracted, and its growth extension trend is monitored and analyzed through a short time window. Ultimately, a multi-orientation crystal orientation candidate set containing three core features—interface normal, growth extension trend, and spatial distribution range—is encapsulated.

[0045] The area ratio, growth extension trend, and spatial continuity are extracted from the candidate crystal orientation as basic characterization quantities. These are normalized into three dimensionless components: ratio, expansion, and bridging. The dominant potential parameters of each candidate crystal orientation are then weighted according to engineering requirements. At the same time, the near-equipotential competition scenario is identified by the potential difference between the top two candidate crystal orientations, and the competition intensity index is obtained. Subsequently, the target crystal orientation and the sequence of competing crystal orientations are determined by sorting them from high to low dominant potential.

[0046] Based on the potential difference and competition intensity between the target crystal orientation and the secondary competing crystal orientation, the target amount of dominance enhancement is calculated and mapped to a quantified enhancement level to determine the directional growth bias. The bias is then allocated to three types of engineering-implementable constraint channels: thermal field, interface morphology, and solute transport. For each channel, directional constraint conditions containing specific control ranges and limits are generated. Finally, the constraint conditions of each channel are integrated and encapsulated into a set of target crystal orientation dominance enhancement constraint conditions that can be directly issued and executed.

[0047] The enhanced constraint set is distributed to the execution component of the single crystal growth system, and an execution window including application duration, update cycle, and perturbation bandwidth is established to limit the constraint application rhythm. Real-time crystal orientation data of the growth front is extracted, and the advance difference, lamination difference, and comprehensive advantage index of the target crystal orientation relative to the competing crystal orientation are calculated. The constraint execution amplitude is dynamically adjusted to achieve the control of the decreasing proportion of the competing crystal orientation and the increasing proportion of the target crystal orientation. Finally, according to the preset quantitative criteria, it is determined whether a stable master crystal orientation locked state with the target crystal orientation as the sole dominant state has been formed.

[0048] Using the target crystal orientation normal component in the main crystal orientation locked state as the crystal orientation reference, a crystal orientation offset angle threshold that is allowed for micron-level growth is defined to form an offset allowable zone. The crystal orientation offset angle of the current interface normal relative to the reference is calculated in real time, and the offset trend term is extracted by monitoring through a short time window to distinguish between instantaneous disturbances and continuous drift. For continuous drift that exceeds the offset allowable zone, the dynamic pullback constraint strength and execution time are calculated, a pullback constraint command is generated and applied, and the crystal orientation offset is brought back to the allowable range through reverse fine adjustment to ensure the continuous stability of the crystal orientation during the growth of a single main crystal orientation.

[0049] In the specific implementation process, the identification and characterization of the orientations of each crystal plane simultaneously exposed at the growth interface during the initial stage of micron-scale single crystal growth are performed to form a multi-orientation growth front crystal orientation candidate set containing the interface normal characteristics, growth extension trend characteristics, and spatial distribution range of each candidate crystal orientation. Specifically, this includes: The growth interface measurement results and system calibration parameters of the initial stage of micron-scale single crystal growth are converted into the interface height field in the device coordinate system. After resampling and local smoothing, unusable areas are removed to generate an effective area mask. Based on the interface height field and the effective region mask, the three-directional gradient components and the unit normal component of the interface are calculated. After filtering out invalid points, the interface normal characteristics are obtained, including the interface normal component field and the interface normal stability index. Based on the interface normal component field and interface normal stability index, after screening out strong fluctuation regions, crystal plane plate set is divided, plate statistics are calculated, and candidate crystal directions are formed by clustering according to normal similarity. The corresponding growth extension trend characteristics are calculated based on the changes in the area ratio of each candidate crystal orientation within a short time window. By integrating the interface normal characteristics, growth extension trend characteristics, and spatial distribution range of each candidate crystal orientation, a multi-orientation growth front crystal orientation candidate set is obtained.

[0050] The formulas for calculating the three-directional gradient components of the interface are as follows:

[0051] In the formula, Represents the three-directional gradient components of the interface; where, Indicates the slope of the interface in the x and y directions. A fixed value of 1 is used to unify the slope of each interface to the same scale; This represents the height value of the interface height field at coordinates (x, y, z); Indicates the sampling step size in the x and y directions; The formula for calculating the unit normal component of the interface is as follows:

[0052] In the formula, The normal component represents the unit normal component of the interface; den represents the normalized denominator. The formula for calculating the area ratio of a district is as follows:

[0053] In the formula, This represents the area percentage of the i-th candidate crystal orientation; This represents the total area of ​​the region corresponding to the i-th candidate crystal orientation; Indicates the total area of ​​the effective region; A constant that prevents division by zero; The formula for calculating the growth extension trend characteristics is as follows:

[0054] In the formula, This represents the growth extension trend characteristics of the i-th candidate crystal orientation. Indicates orientation expansion, Indicates oriented contraction; These represent the i-th candidate crystal orientation at time t. The total area of ​​the district.

[0055] In practical applications, the measured interface data and system calibration parameters of the initial growth stage of single crystal are uniformly transformed into the device coordinate system to generate an interface height field. The scale uniformity of the spatial resolution of the height field is achieved through resampling. Then, the height field is locally smoothed to suppress micro-noise at the interface while retaining the mid-to-low frequency morphological fluctuations of the crystal plane steps. Subsequently, unusable areas such as strong edge reflections and shadow occlusions are removed to generate an effective area mask, which defines the effective range for subsequent crystal orientation analysis.

[0056] Based on the constructed interface height field and effective region mask, the three-dimensional gradient components of the interface are calculated within the effective analysis range. After normalization, the unit normal component of the interface is obtained. During the process, invalid measurement points that do not meet the threshold of the normalization denominator are screened out. Finally, a normal component field that can distinguish crystal plane orientation is formed. At the same time, the normal stability index is calculated, which together constitute the interface normal characteristics.

[0057] Based on the interface normal component field and normal stability index, rough amorphous surface regions with strong normal fluctuations are first screened out. The remaining effective regions are divided into connected regions. The average normal and region area of ​​each region are calculated. Then, clustering is performed according to normal similarity, and regions with consistent normal characteristics are merged to form several candidate crystal orientation categories, i.e., candidate crystal orientations.

[0058] A short time window is selected to continuously identify crystal orientations and analyze regions at the growth interface. The total area of ​​each candidate crystal orientation at different times within the time window is obtained. By analyzing the dynamic changes in the proportion of region area, the growth extension trend characteristics of each candidate crystal orientation are quantified. This characteristic can directly reflect the expansion or contraction state of the candidate crystal orientation and intuitively demonstrate its growth promotion capability.

[0059] The interface normal features of each candidate crystal orientation, the growth extension trend features obtained through short time window analysis, and the spatial distribution range features such as the outer boundary of the region, the centroid position, and the coverage bandwidth corresponding to each candidate crystal orientation are extracted. The three types of core features are systematically integrated and finally encapsulated to form a candidate set of multi-orientation growth front crystal orientations. This candidate set fully characterizes the crystal orientation state of multi-orientation parallel competition in the initial growth stage of a single crystal.

[0060] The process involves calculating the dominant potential of each candidate crystal orientation based on a multi-orientation growth front crystal orientation candidate set, and ranking them according to the priority of the dominant potential to obtain the target crystal orientation, the sequence of competing crystal orientations, and the competition intensity index. Specifically, this includes: Based on the candidate set of crystal orientations at the growth front of multiple orientations, the growth extension trend characteristics of each candidate crystal orientation are extracted. Combined with the corresponding area ratio, the spatial continuity coefficient is calculated to form a set of basic characterization quantities. Based on the set of basic characterization quantities, dimensionless proportion terms, expansion terms, and contiguous terms are constructed and normalized to obtain the set of dominant potential component terms. Dominant potential is generated by weighting the set of dominant potential components, and a competition intensity index is calculated to identify near-equipotential competition scenarios. Based on the dominant potential, all candidate crystal directions are sorted from largest to smallest to obtain a preliminary sorting sequence of candidate crystal directions. Based on the preliminary sorting sequence of candidate crystal directions and the competition intensity index, the competition mode is marked, and the sorting results of the target crystal direction, the competing crystal direction sequence, and the competition intensity index are obtained by encapsulation.

[0061] The formula for calculating the spatial continuity coefficient is as follows:

[0062] In the formula, Let represent the spatial continuity coefficient of the i-th candidate crystal orientation, and The larger the value, the stronger the directional continuity. Let represent the perimeter of the outer boundary of the region union of the i-th candidate crystal orientation; The formula for calculating the expansion term is as follows:

[0063] In the formula, This represents the expansion term for the i-th candidate crystal orientation; The saturation scale constant represents the expansion term; The formula for calculating contiguous items is as follows:

[0064] In the formula, This represents the lamination term for the i-th candidate crystal orientation; Represents the maximum spatial continuity coefficient for all candidate crystal orientations; Represents the minimum spatial continuity coefficient for all candidate crystal orientations; The formula for calculating dominant potential is as follows:

[0065] In the formula, This represents the dominant potential of the i-th candidate crystal orientation; These represent the weights of the percentage item, the expansion item, and the contiguous item, respectively. This represents the proportion of the i-th candidate crystal orientation; The formula for calculating the competition intensity index is as follows:

[0066] In the formula, Let represent the competition intensity index of the i-th candidate crystal orientation, and The closer the value is to 1, the stronger the competition is; This indicates the greatest potential for dominance; This indicates the second largest potential dominant force; This represents the difference scale constant.

[0067] Understandably, from the existing pool of candidate crystal orientations for multi-orientation growth fronts, the growth extension trend characteristics and area proportions of each candidate crystal orientation are extracted. Simultaneously, the spatial continuity coefficient is calculated by combining the geometric characteristics of the lamellae in each crystal orientation. This coefficient is a core indicator characterizing the degree of lamination of crystal orientation lamellae; a higher value indicates stronger spatial lamination of the crystal orientation lamellae, effectively distinguishing between fragmented orientations and lamination-progressing orientations of the same area. Integrating these three types of indicators—growth extension trend, area proportion, and spatial continuity coefficient—forms a set of basic characterizing quantities for each candidate crystal orientation, achieving unified and comparable characteristic characterization among different crystal orientations.

[0068] The three types of indicators in the basic characterization set are transformed into dimensionless proportion terms, expansion terms, and contiguous terms, respectively, forming a set of dominant potential components. The proportion term is obtained by processing the area proportion, which removes noise from extremely small areas to ensure effectiveness; the expansion term is saturated and mapped to the growth extension trend to avoid misjudgment of advantages caused by short-term surges, while also quantifying the penalty for shrinkage orientation; the contiguous term is relatively normalized to the spatial continuity coefficient, bringing the contiguous characteristics of different crystal orientations to the same dimension, ensuring that the three components can be weighted and synthesized.

[0069] Based on the engineering requirements for the initial growth of micron-scale single crystals, appropriate weights are assigned to the proportion, expansion, and lamination terms. The weighting emphasizes expansion and lamination characteristics, avoiding the reliance solely on the current area proportion to determine crystal orientation dominance. A weighted synthesis is used to generate unique dominant potential parameters for each candidate crystal orientation. Among these, the proportion term ( : 0.2~0.4), expansion term ( : 0.3~0.5), contiguous items ( (0.2~0.4) The core principle of weight allocation follows the principle of adapting to growth requirements while balancing accuracy and efficiency. The expansion term is given the highest weight because it directly reflects the thermodynamic and kinetic advantages of the crystal orientation and is key to locking in potential crystal orientations in multi-orientation competition; the proportion term has a moderate weight, used to consider the current spatial dominance and exclude noisy areas; the continuity term has a weight comparable to the proportion term, ensuring spatial continuity of the crystal orientation and adapting to high-precision scenarios. The weights need to be fine-tuned according to the actual scenario: for strongly anisotropic crystals and high-precision applications, the weights of the expansion and continuity terms can be increased; for low-noise environments and general-purpose single crystals, the weight of the proportion term can be appropriately increased to ensure... Simultaneously, a competition intensity index is calculated. This index is a core parameter characterizing the intensity of competition between crystal orientations. The closer the value is to 1, the more similar the dominant potential of the top two candidate crystal orientations, and the more significant the near-equipotential competition characteristics, so as to achieve accurate identification of near-equipotential competition scenarios.

[0070] All candidate crystal orientations are sorted based on their dominant potential, from largest to smallest, to obtain a preliminary sorting sequence. This sequence can be used to initially distinguish the growth advantage levels of each candidate crystal orientation and clarify the initial advantage differences of each crystal orientation in the growth process.

[0071] By combining the preliminary ranking sequence of candidate crystal directions with the competition intensity index, the competition mode of the current growth interface is determined and marked. If the competition intensity index reaches a preset threshold, it is marked as a strong competition mode, indicating that stronger orientation constraints need to be applied subsequently. The crystal direction ranked first in the preliminary ranking is determined as the target crystal direction, and the remaining crystal directions form a competition crystal direction sequence according to the ranking. At the same time, the competition intensity index is integrated to complete the systematic encapsulation of the ranking results, and finally the target crystal direction, the competition crystal direction sequence, and the competition intensity index are output.

[0072] Based on the target crystal orientation, competing crystal orientation sequences, and competition intensity indices, and combined with engineering-feasible constraint channels, a set of dominance enhancement constraint conditions for the target crystal orientation is generated, specifically including: Based on the ranking results of the target crystal orientation, competing crystal orientation sequence and competition intensity index, the dominance enhancement target amount is calculated, and the dominance enhancement target amount is mapped to the dominance enhancement level in the range of 0 to 1 to characterize the constraint bias strength requirement. Based on the target amount and level of dominance enhancement, the directional growth bias is calculated, and the directional growth bias is allocated to three types of engineering constraint channels: thermal field, interface morphology, and solute transport, and the corresponding allocation coefficients are determined. Based on the directional growth bias and the thermal field channel allocation coefficient, the thermal field bias amplitude is calculated, and thermal field orientation constraint conditions containing temperature gradient range and thermal asymmetry limit are generated. Based on the directional growth bias and the morphology channel allocation coefficient, the morphology bias amplitude is calculated, and interface morphology orientation constraints containing curvature intervals and step density limits are generated. By integrating thermal field orientation constraints, interface morphology orientation constraints, and solute transport orientation constraints, a set of dominance enhancement constraints for the target crystal orientation is encapsulated.

[0073] The formula for calculating the dominant power reinforcement target quantity is as follows:

[0074] In the formula, This indicates that the dominance of the target crystal orientation strengthens the target quantity; This indicates the dominant potential of the target crystal orientation; This indicates the dominant potential of the secondary competitive crystal orientation; An index representing the intensity of competition for a target crystal orientation; Indicates a strong contention threshold; The value is 0.6~0.85. For strongly anisotropic crystals (such as silicon single crystals) or high-precision scenarios, the value is 0.75~0.85 to accurately identify near-equipotential competition. For weakly anisotropic crystals or general scenarios, the value is 0.6~0.7 to avoid over-judging strong competition. It is based on the distribution of potential differences in crystal orientation to ensure that strong constraints are triggered when the competition intensity index is close to 1, thus balancing the control sensitivity and stability. 'a' represents the target quantity proportional coefficient. The formula for calculating the dominance enhancement level is as follows:

[0075] In the formula, Indicates the level of dominance enhancement in the target crystal orientation. The closer to 1, the stronger the required constraint bias; exp represents an exponential function with the natural constant e as the base; b represents the level slope constant; The formula for calculating the directional growth bias is as follows:

[0076] In the formula, Indicates the directional growth bias of the target crystal orientation; This represents the bias gain constant; The formula for calculating the thermal field offset amplitude is as follows:

[0077] In the formula, Indicates the magnitude of thermal field offset; Indicates the thermal field reference offset; This represents the proportionality constant of the thermal field channels; Indicates the thermal field channel distribution coefficient; The formula for calculating the topographic offset magnitude is as follows:

[0078] In the formula, Indicates the magnitude of topographic offset; Indicates the topographic reference offset; This represents the scaling constant of the morphology channel; This represents the morphology channel allocation coefficient.

[0079] Based on the ranking results of the target crystal orientation, competing crystal orientation sequences, and competition intensity indices, the dominance enhancement target amount is calculated by comprehensively considering the difference in dominance potential between the target crystal orientation and the secondary competing crystal orientation, and the difference between the actual competition intensity and the strong competition threshold. This index intuitively reflects the dominance enhancement requirement of the target crystal orientation. Subsequently, this target amount is mapped to the range of 0 to 1 to obtain the dominance enhancement level. The closer the level value is to 1, the more intense the current near-equipotential competition among multiple orientations, and the higher the required constraint bias strength.

[0080] Based on the target amount and enhancement level of the dominance enhancement, the directional growth bias is calculated comprehensively. This index provides a core benchmark for setting the intensity of various subsequent constraints. The directional growth bias is allocated to three types of engineering-feasible constraint channels: thermal field, interface morphology, and solute transport. The allocation coefficient of each channel is determined according to the actual growth scenario. In the case of strong competition, thermal field and morphology channels are given priority. In multi-component doped growth, the proportion of solute transport channels is increased. The sum of the allocation coefficients of each channel is 1 to ensure the complete allocation of the bias.

[0081] The thermal field bias amplitude is calculated by combining the directional growth bias and the thermal field channel allocation coefficient, and a thermal field orientation constraint condition is generated. This condition clearly defines the target control range of the axial and radial temperature gradients near the interface, and sets a limit on the asymmetry of the local heat flux at the interface. Through the directional control of the thermal field, the growth region corresponding to the target crystal orientation obtains a stable and conducive temperature gradient environment, while slightly disturbing the regions prone to competing crystal orientations, thus breaking the near-equipotential competitive equilibrium.

[0082] The morphology bias amplitude is calculated based on the directional growth bias and the interface morphology channel allocation coefficient, and interface morphology orientation constraints are generated. These constraints distinguish the morphology control requirements of the target crystal orientation and competing crystal orientations, clarify the curvature allowable range of the target crystal orientation lamination region and the curvature suppression range of the competing crystal orientation prone region, and set an upper limit for the interface step density. Through morphology control, the step orientation and local concave-convex replication of competing crystal orientations are suppressed, ensuring the interface structure requirements of the target crystal orientation lamination growth are met.

[0083] The generated thermal field and interface morphology orientation constraints are systematically integrated with the solute transport orientation constraints generated based on the solute transport channel allocation coefficient (this constraint is removed for pure single crystal growth), and finally encapsulated into a unified set of target crystal orientation dominance enhancement constraints. This set can be directly connected to the execution components of the growth system, providing a standardized and integrated constraint execution basis for subsequent crystal orientation dominance locking.

[0084] It should be noted that the target quantity proportionality coefficient (a: 0.2~1.5) is used to adapt to the requirements of competition intensity for strengthening dominance, balancing the influence weight of potential difference and competition intensity. For strongly anisotropic crystals (such as silicon single crystals) or high-precision scenarios, a coefficient of 1.0~1.5 is used to amplify the gain of competition intensity on the strengthening target; for weakly anisotropic crystals or general scenarios, a coefficient of 0.2~0.8 is used to avoid over-strengthening leading to regulatory imbalance. The level slope constant (b: 2~20) is used to control the response sensitivity of the dominance strengthening level to the target quantity. For high-precision scenarios such as single crystals used in semiconductor chips, a coefficient of 10~20 is used to allow the level to saturate rapidly with the target quantity, quickly triggering strong constraints; for general-purpose single crystal growth, a coefficient of 2~8 is used to achieve a smooth level transition and avoid abrupt constraints. For the bias gain constant ( : 0.2~3), Focusing on the impact of the potential difference, Emphasis is placed on strengthening the weight of the level. Highly competitive scenarios (competition intensity index > 0.7). Take 2~3 Using values ​​of 1.5 to 3 highlights its adaptability to competition; in scenarios with weak competition, Take a value of 0.2~1.0. Use a value of 0.5~1.5 to ensure a mild and controllable bias. Thermal channel proportionality constant ( (0.5~30K / mm) is used to adapt to the thermal sensitivity of materials and the furnace type control capability. For high-melting-point crystals (such as silicon carbide), 10~30K / mm is used to improve the thermal field bias adjustment range; for low-melting-point crystals (such as certain oxides), 0.5~5K / mm is used to avoid thermal shock. Thermal field channel allocation coefficient ( The constant for morphology channels is 0.4~0.8, used to prioritize the basic control function of the thermal field channels. In scenarios with strong competition or pure material growth, a constant of 0.6~0.8 is used to enhance the guiding effect of the thermal field on crystal orientation; in multi-component doped growth, a constant of 0.4~0.6 is used to reserve weight for solute transport channels. The coefficient (0.05~1.51 / µm) is used to match the sensitivity of material interface morphology. For crystals sensitive to step density (such as optical single crystals), a coefficient of 0.8~1.51 / µm is used to strictly control morphology fluctuations; for crystals with higher tolerance for interface roughness, a coefficient of 0.05~0.51 / µm is used to reduce the complexity of adjustment. This is specifically for the morphology channel allocation coefficient (…). 0.2~0.5), in strong competition or high-precision scenarios (such as optical single crystals), take 0.3~0.5 to enhance the suppression of competing crystal orientations by morphology; in weak competition or general scenarios, take 0.2~0.3 to prioritize the dominance of thermal field regulation.

[0085] The set of constraint conditions for strengthening the dominance of the target crystal orientation is applied to quantitatively determine whether the target crystal orientation forms a uniquely dominant master crystal orientation locked state, specifically including: The set of target crystal orientation dominance enhancement constraint conditions is sent to the execution component of the growth system to determine the set of execution window parameters for constraint application duration, constraint update cycle and constraint perturbation bandwidth; Based on the execution window parameter set and the real-time extracted multi-orientation growth front crystal direction candidate set, the advance difference, bridging difference and comprehensive advantage index between the target crystal direction and the competing crystal direction are calculated. Based on the difference in advancement, comprehensive advantage indicators, and execution window parameter set, the constraint execution amplitude is adjusted, and the percentage decrease rate of the competing crystal orientation and the percentage increase rate of the target crystal orientation are calculated. Based on the decreasing rate of the proportion of competing crystal orientations, the increasing rate of the proportion of the target crystal orientation, and comprehensive advantage indicators, a stable main crystal orientation locked state is determined according to preset criteria. By encapsulating the unique dominant marker of the target crystal orientation, the locking duration, the upper limit of the residual competition ratio, and the crystal orientation reference parameters, the main crystal orientation locked state is obtained.

[0086] The formula for calculating the propulsion difference is as follows:

[0087] In the formula, This represents the difference in advancement of the target crystal orientation relative to the competing crystal orientation; This indicates the growth and extension trend characteristics of the target crystal orientation; The formula for calculating the difference between consecutive pieces is as follows:

[0088] In the formula, This indicates the lamination difference between the target crystal orientation and the competing crystal orientation; Indicates the spatial continuity coefficient of the target crystal orientation; The formula for calculating the comprehensive advantage index is as follows:

[0089] In the formula, The index represents the overall advantage of the target crystal orientation; n represents the number of competing crystal orientations; q represents the index weighting constant. The formula for calculating the percentage decrease rate of competing crystal orientations is as follows:

[0090] In the formula, This indicates the rate of decrease in the proportion of competing crystal orientations; These represent the competing crystal orientations at time [time]. The area percentage; The formula for calculating the percentage increase of the target crystal orientation is as follows:

[0091] In the formula, This indicates the percentage increase in the proportion of the target crystal orientation; These represent the target crystal orientation at time [time]. The area percentage.

[0092] The generated set of target crystal orientation dominance enhancement constraint conditions is sent to the adjustable execution component of the single crystal growth system. At the same time, the execution window parameter set is set and determined. This parameter set includes three core parameters: total constraint application time, set value update cycle, and allowable disturbance bandwidth. These parameters are used to limit the rhythm and magnitude of constraint application, so as to avoid the problem of crystal orientation control failure caused by excessive constraint application leading to sudden changes in interface morphology.

[0093] Based on the execution window parameter set, the candidate set of growth front crystal directions is extracted in real time during the constraint execution period, and the advancement difference and lamination difference of the target crystal direction relative to each competing crystal direction are calculated. The former reflects the relative advantage of the target crystal direction in the interface advancement speed, and the latter characterizes the advantage difference of its spatial lamination growth. At the same time, the two differences of all competing crystal directions are comprehensively weighted to calculate the comprehensive advantage index of the target crystal direction, transforming the multi-dimensional advantages into a single criterion, avoiding misjudgment of advantages caused by occasional fluctuations of a single competing crystal direction.

[0094] Based on the progress difference, comprehensive advantage indicators, and execution window parameters, the constraint execution magnitude is dynamically adjusted. If the comprehensive advantage indicators do not meet expectations, the constraint bias magnitude is increased to strengthen the target crystal orientation advantage. If the indicators meet the target, the magnitude is maintained or gradually reduced to achieve precise constraint adaptation. Simultaneously, the decreasing rate of the competing crystal orientation proportion and the increasing rate of the target crystal orientation proportion are calculated to quantify the weakening degree of the competing crystal orientation and the enhancement degree of the target crystal orientation's growth advantage, respectively. In engineering practice, this stage requires that the target crystal orientation proportion shows an increasing trend, while the proportions of most competing crystal orientations show a decreasing trend.

[0095] Based on preset quantitative criteria, it is determined whether the target crystal orientation has formed a unique and dominant stable state. The determination requires meeting several core conditions, namely, the area ratio of the target crystal orientation reaches a preset threshold, the maximum area ratio of the competing crystal orientation is lower than the limit threshold, and the duration of continuous positive comprehensive advantage indicators meets the specified requirements. All three conditions must be met simultaneously to ensure that the locking of the main crystal orientation is not an instantaneous and accidental state, but rather a stable growth advantage.

[0096] The determined stable locking state is systematically parameterized, integrating the unique dominant marker of the target crystal orientation, the locking duration, and the upper limit of residual competition ratio. Simultaneously, the crystal orientation reference parameters of the target crystal orientation under the locked state are extracted, collectively forming the master crystal orientation locked state. This locked state fully characterizes the growth state where the target crystal orientation becomes the unique master crystal orientation. The crystal orientation reference parameters it contains will serve as the core reference for subsequent single master crystal orientation growth stages and the constraint control of subtle crystal orientation shifts.

[0097] It should be noted that the index weight constant (q: 0.2~2) is used to balance the weights of the propulsion difference and the lamination difference. For high-precision applications (such as optical crystals), a value of 1.2~2 is used, emphasizing the lamination difference to ensure crystal orientation consistency; for scenarios requiring growth efficiency, a value of 0.2~0.8 is used, emphasizing the propulsion difference to accelerate the expansion of the target crystal orientation; for general scenarios, a value of 0.8~1.2 is used to ensure that the comprehensive advantage index matches the actual control needs.

[0098] The method of determining the crystal orientation reference and allowable offset zone based on the principal crystal orientation locked state, and dynamically pulling back the fine offsets during the single principal crystal orientation growth process, specifically includes: The unit normal component of the target crystal direction is extracted based on the principal crystal direction locked state and used as the crystal direction reference. A crystal direction offset angle threshold is set to form an offset allowable band. Based on the crystal orientation reference, the offset allowable band and the real-time interface unit normal component, the crystal orientation offset angle is calculated, and the offset trend term is extracted by the change of offset angle within a short time window. Compare the crystal orientation offset angle, offset trend term, and offset allowable zone to determine whether dynamic pullback constraint needs to be applied. Based on the constraint trigger determination result, the pullback strength and constraint execution duration in the interval from 0 to 1 are calculated to form dynamic pullback constraint parameters; Based on the dynamic pullback constraint parameters, a dynamic pullback constraint instruction set that can be sent to the growth system is encapsulated to achieve reverse fine-tuning of crystal orientation shift.

[0099] The formula for calculating the crystal orientation offset angle is as follows:

[0100] In the formula, The unit normal component representing the crystal orientation reference; The formula for calculating the offset trend term is as follows:

[0101] In the formula, V represents the offset trend term; Indicates time Crystal orientation offset angle; The formula for calculating pullback strength is as follows:

[0102] In the formula, Y represents the pullback strength; This represents the pullback ratio constant; Indicates the threshold of crystal orientation offset angle. The value is set to 0.05°~1.5°. For high-precision scenarios (such as single crystals used in semiconductor chips), the value is set to 0.05°~0.6° to strictly control minute offsets. For general scenarios, the value is set to 0.6°~1.5° to be compatible with normal micro-perturbations, so as to match the stability of the material's crystal orientation with the control precision of the growth system, and avoid frequent pullback caused by an overly strict threshold, or crystal orientation loss of control caused by an overly wide threshold.

[0103] In practical applications, the unit normal component of the target crystal orientation is extracted from the already formed principal crystal orientation locked state as the sole crystal orientation reference for subsequent growth of micron-sized single crystals. This reference is the core reference for determining crystal orientation shift. At the same time, according to the accuracy requirements of single crystal growth, a crystal orientation shift angle threshold is set to construct the shift allowable band. The threshold selection takes into account both engineering control tolerance and crystal orientation accuracy requirements, avoiding the judgment of normal interface perturbations as crystal orientation drift.

[0104] Based on the solidified crystal orientation reference, and combined with the real-time acquired unit normal component of the growth interface, the crystal orientation offset angle is obtained by calculating the normal angle, which accurately represents the degree of deviation of the current crystal orientation from the reference. Then, a short time window is selected to continuously and dynamically monitor the offset angle, calculate the rate of change of the offset angle within the window and extract the offset trend term, so as to effectively distinguish between instantaneous interface perturbation and continuous crystal orientation drift, and avoid constraint false triggering caused by single-point offset data.

[0105] The real-time crystal orientation offset angle, offset trend term, and preset offset allowable band are comprehensively compared and judged to form a multi-dimensional judgment logic: if the offset angle does not exceed the allowable band and the offset trend term is in a convergent state, it is judged as an acceptable normal perturbation and no pull-back constraint is required; if the offset angle exceeds the allowable band, or the offset trend term continues to expand, even if the offset angle has not exceeded the limit, it is judged as having a drift risk and the dynamic pull-back constraint mechanism is immediately triggered.

[0106] Based on the determination result of constraint triggering, the appropriate dynamic pullback constraint parameters are calculated, with the core being the pullback strength and constraint execution duration in the range of 0 to 1. The pullback strength comprehensively considers the degree of exceeding the limit of the offset angle and the expansion range of the offset trend. The larger the values ​​of both, the higher the pullback strength. Moreover, the strength value is strictly limited within the engineering executable range to avoid over-adjustment that may cause sudden changes in the interface morphology. The execution duration is set adaptively according to the degree of drift to ensure the effectiveness and controllability of pullback regulation.

[0107] Pull-back proportional constant ( : 0.2~5; (0.05~2) Follow the principle of precise suppression and avoidance of disturbance. High-precision scenarios (such as semiconductor single crystals) Take 3~5. Choose 1~2 to strengthen the pullback of offset and drift trend; general scenario Take 0.2~1 The value should be between 0.05 and 0.5, and the material's crystal orientation stability should be matched to ensure that the pull-back strength is controllable and does not cause interface abrupt changes.

[0108] The calculated core constraint parameters, such as pullback strength and execution duration, are systematically integrated and encapsulated into a dynamic pullback constraint instruction set that can be directly issued to the single crystal growth system. This instruction set can directly interface with the system's execution components. Based on this instruction set, the growth system performs reverse fine-tuning of the growth conditions, such as the thermal field and morphology, corresponding to the locked state of the principal crystal direction according to the set parameters. Through the synergistic effect of each constraint channel, the crystal direction offset angle gradually falls back into the offset allowable band, achieving precise dynamic pullback constraint for minute offsets during the growth of a single principal crystal direction, ensuring stable crystal direction extension.

[0109] Through the above embodiments, this invention utilizes a dynamic constraint control method for crystal orientation in micron-scale single crystal growth. By identifying and characterizing the orientations of each crystal plane simultaneously exposed at the growth interface during the initial stage of micron-scale single crystal growth, a multi-orientation growth front crystal orientation candidate set is formed, encompassing the interface normal characteristics, growth extension trend characteristics, and spatial distribution range of each candidate crystal orientation. Based on this multi-orientation growth front crystal orientation candidate set, the dominant potential of each candidate crystal orientation is calculated, and the target crystal orientation, competing crystal orientation sequence, and competition intensity index are obtained by prioritizing the dominant potential. Based on the target crystal orientation, competing crystal orientation sequence, and competition intensity index, combined with engineering applications… The system establishes a constraint channel to generate a set of targeted crystal orientation dominance reinforcement constraints. By applying this set, it quantifies whether the target crystal orientation has formed a uniquely dominant master crystal orientation locked state. Based on the master crystal orientation locked state, it determines the crystal orientation reference and allowable offset band, and dynamically pulls back the constraints on minor offsets during the growth process of a single master crystal orientation. This allows for precise screening and locking of the target crystal orientation, hierarchical control of constraint strength to avoid interface disturbances, and dynamic pull-back to suppress minor crystal orientation offsets. This achieves crystal orientation stability throughout the entire growth cycle of a single crystal, significantly improves crystal orientation consistency, and solves the problem of crystal orientation constraint failure under multi-orientation competition.

[0110] This invention designs a dynamic constraint control method for crystal orientation in multi-orientation competition scenarios. First, it constructs a candidate set of crystal orientations and evaluates their dominance potential to accurately screen target crystal orientations. Then, it generates dynamic dominance strengthening constraints based on the competition intensity, achieving stable locking of the target crystal orientation and completely solving the core problem of constraint failure in traditional methods. Furthermore, the constraint strength is adjusted in stages according to the degree of competition, avoiding excessive bias leading to interface disturbances or insufficient bias causing crystal orientation loss of control, thus improving the adaptability and accuracy of the control. After the main crystal orientation is locked, dynamic pull-back constraints suppress minor deviations, ensuring crystal orientation stability throughout the entire growth cycle of the single crystal, effectively weakening the influence of competing crystal orientations, and significantly improving the growth quality and crystal orientation consistency of micron-scale single crystals, adapting to the engineering application needs of high-precision single crystal materials.

[0111] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for dynamically constraining and controlling the crystal orientation of micron-scale single crystal growth, characterized in that, The method includes: The orientations of each crystal plane simultaneously exposed at the growth interface during the initial stage of micron-scale single crystal growth are identified and characterized, forming a multi-orientation growth front crystal direction candidate set that includes the interface normal characteristics, growth extension trend characteristics, and spatial distribution range of each candidate crystal direction. Based on the candidate set of crystal orientations at the growth front of multiple orientations, the dominant potential of each candidate crystal orientation is calculated, and the target crystal orientation, the sequence of competing crystal orientations and the competition intensity index are obtained by sorting them according to the priority of the dominant potential. Based on the target crystal orientation, competing crystal orientation sequences and competition intensity indicators, combined with engineering-feasible constraint channels, a set of directional target crystal orientation dominance enhancement constraint conditions is generated. Apply a set of constraints to strengthen the dominance of the target crystal orientation, and quantitatively determine whether the target crystal orientation forms a unique dominant master crystal orientation locked state. Based on the principal crystal direction locked state, the crystal direction reference and offset allowable zone are determined, and the subtle offsets in the single principal crystal direction growth process are dynamically pulled back to constrain them.

2. The method for dynamic constraint control of crystal orientation in micron-scale single crystal growth according to claim 1, characterized in that, The process involves identifying and characterizing the orientations of various crystal planes simultaneously exposed at the growth interface during the initial stage of micron-scale single crystal growth, forming a multi-orientation growth front crystal orientation candidate set that includes the interface normal characteristics, growth extension trend characteristics, and spatial distribution range of each candidate crystal orientation. Specifically, this includes: The growth interface measurement results and system calibration parameters of the initial stage of micron-scale single crystal growth are converted into the interface height field in the device coordinate system. After resampling and local smoothing, unusable areas are removed to generate an effective area mask. Based on the interface height field and the effective region mask, the three-directional gradient components and the unit normal component of the interface are calculated. After filtering out invalid points, the interface normal characteristics are obtained, including the interface normal component field and the interface normal stability index. Based on the interface normal component field and interface normal stability index, after screening out strong fluctuation regions, crystal plane plate set is divided, plate statistics are calculated, and candidate crystal directions are formed by clustering according to normal similarity. The corresponding growth extension trend characteristics are calculated based on the changes in the area ratio of each candidate crystal orientation within a short time window. By integrating the interface normal characteristics, growth extension trend characteristics, and spatial distribution range of each candidate crystal orientation, a multi-orientation growth front crystal orientation candidate set is obtained.

3. The method for dynamic constraint control of crystal orientation in micron-scale single crystal growth according to claim 2, characterized in that, The formulas for calculating the three-directional gradient components of the interface are as follows: In the formula, Represents the three-directional gradient components of the interface; This represents the height value of the interface height field at coordinates (x, y, z); Indicates the sampling step size in the x and y directions; The formula for calculating the unit normal component of the interface is as follows: In the formula, The normal component represents the unit normal component of the interface; den represents the normalized denominator. The formula for calculating the area ratio of a district is as follows: In the formula, This represents the area percentage of the i-th candidate crystal orientation; This represents the total area of ​​the region corresponding to the i-th candidate crystal orientation; Indicates the total area of ​​the effective region; A constant that prevents division by zero; The formula for calculating the growth extension trend characteristics is as follows: In the formula, This represents the growth and extension trend characteristics of the i-th candidate crystal orientation. Indicates orientation expansion, Indicates oriented contraction; These represent the i-th candidate crystal orientation at time t. The total area of ​​the district.

4. The method for dynamic constraint control of crystal orientation in micron-scale single crystal growth according to claim 1, characterized in that, The process involves calculating the dominant potential of each candidate crystal orientation based on a multi-orientation growth front crystal orientation candidate set, and ranking them according to the priority of the dominant potential to obtain the target crystal orientation, the sequence of competing crystal orientations, and the competition intensity index. Specifically, this includes: Based on the candidate set of crystal orientations at the growth front of multiple orientations, the growth extension trend characteristics of each candidate crystal orientation are extracted. Combined with the corresponding area ratio, the spatial continuity coefficient is calculated to form a set of basic characterization quantities. Based on the set of basic characterization quantities, dimensionless proportion terms, expansion terms, and contiguous terms are constructed and normalized to obtain the set of dominant potential component terms. Dominant potential is generated by weighting the set of dominant potential components, and a competition intensity index is calculated to identify near-equipotential competition scenarios. Based on the dominant potential, all candidate crystal directions are sorted from largest to smallest to obtain a preliminary sorting sequence of candidate crystal directions. Based on the preliminary sorting sequence of candidate crystal directions and the competition intensity index, the competition mode is marked, and the sorting results of the target crystal direction, the competing crystal direction sequence, and the competition intensity index are obtained by encapsulation.

5. The method for dynamic constraint control of crystal orientation in micron-scale single crystal growth according to claim 4, characterized in that, The formula for calculating the spatial continuity coefficient is as follows: In the formula, Let represent the spatial continuity coefficient of the i-th candidate crystal orientation, and The larger the value, the stronger the directional continuity. Let represent the perimeter of the outer boundary of the region union of the i-th candidate crystal orientation; The formula for calculating the expansion term is as follows: In the formula, This represents the expansion term for the i-th candidate crystal orientation; The saturation scale constant represents the expansion term; The formula for calculating contiguous items is as follows: In the formula, This represents the lamination term for the i-th candidate crystal orientation; Represents the maximum spatial continuity coefficient for all candidate crystal orientations; Represents the minimum spatial continuity coefficient for all candidate crystal orientations; The formula for calculating dominant potential is as follows: In the formula, This represents the dominant potential of the i-th candidate crystal orientation; These represent the weights of the percentage item, the expansion item, and the contiguous item, respectively. This represents the proportion of the i-th candidate crystal orientation; The formula for calculating the competition intensity index is as follows: In the formula, Let represent the competition intensity index of the i-th candidate crystal orientation, and The closer the value is to 1, the stronger the competition is; This indicates the greatest potential for dominance; This indicates the second largest potential dominant force; This represents the difference scale constant.

6. The method for dynamic constraint control of crystal orientation in micron-scale single crystal growth according to claim 1, characterized in that, Based on the target crystal orientation, competing crystal orientation sequences, and competition intensity indices, and combined with engineering-feasible constraint channels, a set of dominance enhancement constraint conditions for the target crystal orientation is generated, specifically including: Based on the ranking results of the target crystal orientation, competing crystal orientation sequence and competition intensity index, the dominance enhancement target amount is calculated, and the dominance enhancement target amount is mapped to the dominance enhancement level in the range of 0 to 1 to characterize the constraint bias strength requirement. Based on the target amount and level of dominance enhancement, the directional growth bias is calculated, and the directional growth bias is allocated to three types of engineering constraint channels: thermal field, interface morphology, and solute transport, and the corresponding allocation coefficients are determined. Based on the directional growth bias and the thermal field channel allocation coefficient, the thermal field bias amplitude is calculated, and thermal field orientation constraint conditions containing temperature gradient range and thermal asymmetry limit are generated. Based on the directional growth bias and the morphology channel allocation coefficient, the morphology bias amplitude is calculated, and interface morphology orientation constraints containing curvature intervals and step density limits are generated. By integrating thermal field orientation constraints, interface morphology orientation constraints, and solute transport orientation constraints, a set of dominance enhancement constraints for the target crystal orientation is encapsulated.

7. The method for dynamic constraint control of crystal orientation in micron-scale single crystal growth according to claim 6, characterized in that, The formula for calculating the dominant power reinforcement target quantity is as follows: In the formula, This indicates that the dominance of the target crystal orientation strengthens the target quantity; This indicates the dominant potential of the target crystal orientation; This indicates the dominant potential of the secondary competitive crystal orientation; An index representing the intensity of competition for a target crystal orientation; Indicates the strong competition threshold; 'a' represents the target quantity proportionality coefficient. The formula for calculating the dominance enhancement level is as follows: In the formula, Indicates the level of dominance enhancement in the target crystal orientation. The closer to 1, the stronger the required constraint bias; exp represents an exponential function with the natural constant e as the base; b represents the level slope constant; The formula for calculating the directional growth bias is as follows: In the formula, Indicates the directional growth bias of the target crystal orientation; This represents the bias gain constant; The formula for calculating the thermal field offset amplitude is as follows: In the formula, Indicates the magnitude of thermal field offset; Indicates the thermal field reference offset; This represents the proportionality constant of the thermal field channels; Indicates the thermal field channel distribution coefficient; The formula for calculating the topographic offset magnitude is as follows: In the formula, Indicates the magnitude of topographic offset; Indicates the topographic reference offset; This represents the scaling constant of the morphology channel; This represents the morphology channel allocation coefficient.

8. The method for dynamic constraint control of crystal orientation in micron-scale single crystal growth according to claim 1, characterized in that, The set of constraint conditions for strengthening the dominance of the target crystal orientation is applied to quantitatively determine whether the target crystal orientation forms a uniquely dominant master crystal orientation locked state, specifically including: The set of target crystal orientation dominance enhancement constraint conditions is sent to the execution component of the growth system to determine the set of execution window parameters for constraint application duration, constraint update cycle and constraint perturbation bandwidth; Based on the execution window parameter set and the real-time extracted multi-orientation growth front crystal direction candidate set, the advance difference, bridging difference and comprehensive advantage index between the target crystal direction and the competing crystal direction are calculated. Based on the difference in advancement, comprehensive advantage indicators, and execution window parameter set, the constraint execution amplitude is adjusted, and the percentage decrease rate of the competing crystal orientation and the percentage increase rate of the target crystal orientation are calculated. Based on the decreasing rate of the proportion of competing crystal orientations, the increasing rate of the proportion of the target crystal orientation, and comprehensive advantage indicators, a stable main crystal orientation locked state is determined according to preset criteria. By encapsulating the unique dominant marker of the target crystal orientation, the locking duration, the upper limit of the residual competition ratio, and the crystal orientation reference parameters, the main crystal orientation locked state is obtained.

9. The method for dynamic constraint control of crystal orientation in micron-scale single crystal growth according to claim 8, characterized in that, The formula for calculating the propulsion difference is as follows: In the formula, This represents the difference in advancement of the target crystal orientation relative to the competing crystal orientation; This indicates the growth and extension trend characteristics of the target crystal orientation; The formula for calculating the difference between consecutive pieces is as follows: In the formula, This indicates the lamination difference between the target crystal orientation and the competing crystal orientation; Indicates the spatial continuity coefficient of the target crystal orientation; The formula for calculating the comprehensive advantage index is as follows: In the formula, The index represents the overall advantage of the target crystal orientation; n represents the number of competing crystal orientations; q represents the index weighting constant. The formula for calculating the percentage decrease rate of competing crystal orientations is as follows: In the formula, This indicates the rate of decrease in the proportion of competing crystal orientations; These represent the competing crystal orientations at time [time]. The area percentage; The formula for calculating the percentage increase of the target crystal orientation is as follows: In the formula, This indicates the percentage increase in the proportion of the target crystal orientation; These represent the target crystal orientation at time [time]. The area percentage.

10. The method for dynamic constraint control of crystal orientation in micron-scale single crystal growth according to claim 1, characterized in that, The method of determining the crystal orientation reference and allowable offset zone based on the principal crystal orientation locked state, and dynamically pulling back the fine offsets during the single principal crystal orientation growth process, specifically includes: The unit normal component of the target crystal direction is extracted based on the principal crystal direction locked state and used as the crystal direction reference. A crystal direction offset angle threshold is set to form an offset allowable band. Based on the crystal orientation reference, the offset allowable band and the real-time interface unit normal component, the crystal orientation offset angle is calculated, and the offset trend term is extracted by the change of offset angle within a short time window. Compare the crystal orientation offset angle, offset trend term, and offset allowable zone to determine whether dynamic pullback constraint needs to be applied. Based on the constraint trigger determination result, the pullback strength and constraint execution duration in the interval from 0 to 1 are calculated to form dynamic pullback constraint parameters; Based on the dynamic pullback constraint parameters, a dynamic pullback constraint instruction set that can be sent to the growth system is encapsulated to achieve reverse fine-tuning of crystal orientation offset; The formula for calculating the crystal orientation offset angle is as follows: In the formula, The unit normal component representing the crystal orientation reference; The formula for calculating the offset trend term is as follows: In the formula, V represents the offset trend term; Indicates time Crystal orientation offset angle; The formula for calculating pullback strength is as follows: In the formula, Y represents the pullback strength; This represents the pullback ratio constant; This indicates the threshold for the crystal orientation offset angle.

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