A method and related apparatus for controlling crystal rise speed

Abstract

This application discloses a crystal rise rate control method and related apparatus. It acquires target shoulder morphology data and growth state data at the current control moment. For multiple candidate crystal rise rate compensation amounts, it predicts the predicted diameter data for each candidate compensation amount at the future control moment, and then determines the corresponding predicted shoulder morphology data based on the predicted diameter data. This allows for the advance determination of the impact of different candidate crystal rise rate compensation amounts on the subsequent outer contour morphology of the crystal shoulder. Based on the difference between the predicted shoulder morphology data and the target shoulder morphology data, a target crystal rise rate compensation amount is determined from the multiple candidate compensation amounts. The crystal rise rate during the shoulder formation process is then adjusted according to the target compensation amount, enabling the adjustment to be made in advance in conjunction with changes in the subsequent outer contour morphology of the crystal shoulder, thereby improving the timeliness of crystal rise rate adjustment during the Czochralski single-crystal silicon shoulder formation process.

Description

Technical Field

[0001] This invention relates to the field of Czochralski single-crystal silicon technology, and in particular to a method and related apparatus for controlling crystal growth rate. Background Technology

[0002] In the fabrication of Czochralski single-crystal silicon, after the seed crystal comes into contact with the molten silicon and is guided by the crystal, shoulder growth is required to gradually increase the crystal diameter from the small size formed by the seed crystal to the target diameter required for constant-diameter growth. During the shoulder growth process, the crystal shoulder gradually expands outward as the crystal growth position changes. The crystal rise rate affects the crystal growth state and thus the outer contour morphology of the crystal shoulder. Therefore, it is necessary to control the crystal rise rate during the shoulder growth process to ensure that the crystal can stably complete the transition from the smaller diameter to the target diameter.

[0003] In related technologies, crystal growth rate curves are usually preset based on human experience, and crystal growth is controlled according to the preset crystal growth rate curve during the shoulder formation process; or, based on the current diameter or current diameter deviation measured during the shoulder formation process, the crystal growth rate is adjusted by feedback so that the crystal diameter gradually changes towards the target diameter.

[0004] However, when using the above method to control the crystal growth rate, it is difficult to adjust the crystal growth rate in a timely manner according to the actual growth state of the crystal shoulder, which can easily cause the outer contour of the crystal shoulder to deviate from the reasonable shoulder formation shape and affect the stability of the shoulder growth. Summary of the Invention

[0005] To address the aforementioned issues, this application provides a crystal rise rate control method and related apparatus to improve the timeliness of crystal rise rate adjustment during the shoulder formation process of Czochralski single crystal silicon.

[0006] Based on this, the following technical solution is disclosed in this application:

[0007] In a first aspect, embodiments of this application provide a crystal rise rate control method, the method comprising:

[0008] Acquire target shoulder morphology data, which is used to characterize the target outer contour morphology of the crystal shoulder as the crystal growth position changes during the shoulder formation process of Czochralski single crystal silicon.

[0009] Obtain the growth state data of the Czochralski single crystal silicon at the current control moment;

[0010] Determine multiple candidate crystal rise rate compensation values;

[0011] For each of the multiple candidate crystal rise rate compensation amounts, based on the growth state data and the candidate crystal rise rate compensation amount, predict the predicted diameter data of the Czochralski single crystal silicon at a future control moment;

[0012] Based on the predicted diameter data corresponding to each candidate crystal rise rate compensation amount, the predicted shoulder morphology data corresponding to each candidate crystal rise rate compensation amount is determined;

[0013] Based on the difference between the predicted shoulder shape data corresponding to each of the candidate crystal rise rate compensation amounts and the target shoulder shape data, the target crystal rise rate compensation amount is determined from the multiple candidate crystal rise rate compensation amounts;

[0014] The crystal rise rate of the Czochralski single crystal silicon during the shoulder formation process is adjusted according to the target crystal rise rate compensation amount.

[0015] Secondly, embodiments of this application provide a crystal rise speed control device, the device comprising:

[0016] The acquisition unit is used to acquire target shoulder morphology data, which is used to characterize the target outer contour morphology of the crystal shoulder as the crystal growth position changes during the shoulder formation process of Czochralski single crystal silicon.

[0017] The acquisition unit is also used to acquire the growth state data of the Czochralski single crystal silicon at the current control moment;

[0018] A determination unit is used to determine the compensation amount for multiple candidate crystal rise rates;

[0019] The prediction unit is used to predict the predicted diameter data of the Czochralski single crystal silicon at a future control moment, based on the growth state data and the candidate crystal rise rate compensation amount, for each of the multiple candidate crystal rise rate compensation amounts.

[0020] The determining unit is further configured to determine the predicted shoulder morphology data corresponding to each candidate crystal rise rate compensation amount based on the predicted diameter data corresponding to each candidate crystal rise rate compensation amount.

[0021] The determining unit is further configured to determine the target crystal rise rate compensation amount from the plurality of candidate crystal rise rate compensation amounts based on the difference between the predicted shoulder shape data corresponding to each candidate crystal rise rate compensation amount and the target shoulder shape data.

[0022] An adjustment unit is used to adjust the crystal rise rate of the Czochralski single crystal silicon during the shoulder formation process according to the target crystal rise rate compensation amount.

[0023] Thirdly, embodiments of this application provide a computer device, the computer device including a processor and a memory:

[0024] The memory is used to store computer programs and to transfer the computer programs to the processor;

[0025] The processor is configured to execute the method described in the first aspect above according to the computer program.

[0026] Fourthly, embodiments of this application provide a computer-readable storage medium for storing a computer program for performing the method described in the first aspect above.

[0027] Fifthly, embodiments of this application provide a computer program product including a computer program, which, when run on a computer device, causes the computer device to perform the method described in the first aspect above.

[0028] As can be seen from the above technical solutions, this application has at least the following beneficial effects:

[0029] The process involves acquiring target shoulder morphology data. This data characterizes the outer contour of the crystal shoulder as it changes with the crystal growth position during the shoulder formation process in Czochralski single-crystal silicon. This allows subsequent crystal rise rate control to move beyond solely focusing on a single target diameter and instead use the outer contour of the target shoulder that should form at different crystal growth positions as the control basis. Furthermore, the process acquires growth state data at the current control moment and predicts the diameter data for each candidate crystal rise rate compensation value at the next control moment. Based on these predicted diameter data, the corresponding predicted shoulder morphology data is then determined. Thus, the impact of different candidate crystal rise rate compensation values ​​on the subsequent outer contour of the crystal shoulder can be obtained beforehand, without waiting for a significant deviation in the crystal shoulder before adjustment. Based on this, according to the difference between the predicted shoulder morphology data and the target shoulder morphology data, the target crystal rise rate compensation amount is determined from multiple candidate crystal rise rate compensation amounts. The crystal rise rate during the shoulder formation process is adjusted according to the target crystal rise rate compensation amount, so that the crystal rise rate adjustment can be carried out in advance in combination with the subsequent changes in the outer contour morphology of the crystal shoulder. This improves the timeliness of crystal rise rate adjustment during the shoulder formation process of Czochralski single crystal silicon, reduces the risk of significant deviation in the outer contour morphology of the crystal shoulder and the resulting breakage, and improves the stability and diameter consistency of the shoulder growth. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1A schematic flowchart illustrating a crystal rise rate control method provided in an embodiment of this application;

[0032] Figure 2 This is a schematic diagram of the structure of a crystal rise speed control device provided in an embodiment of this application;

[0033] Figure 3 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0034] Embodiments of this application will now be described in more detail with reference to the accompanying drawings. While some embodiments of this application are shown in the drawings, it should be understood that this application can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this application. It should be understood that the drawings and embodiments of this application are for illustrative purposes only and are not intended to limit the scope of protection of this application.

[0035] The shoulder formation process differs from a constant-diameter growth process where the crystal diameter remains relatively stable. During shoulder formation, the crystal diameter itself is in a dynamic state of continuous increase, and the outer contour shape of the shoulder should vary depending on the location of the crystal growth. Therefore, even if a pre-set crystal growth rate curve is applicable to some shoulder formation processes, it is difficult to adapt to scenarios where the thermal state, solidification state, and crystal growth changes differ across different furnace runs. When the actual growth state deviates from the preset conditions, continuing to control crystal growth according to the preset crystal growth rate curve can easily cause the crystal shoulder to expand too quickly or too insufficiently at certain growth locations.

[0036] The feedback adjustment method based on the current diameter reflects the growth result of the crystal shoulder at the current moment, rather than the subsequent outer contour shape of the crystal shoulder under different crystal rise rate adjustment methods. Since the growth state of Czochralski single-crystal silicon is affected by factors such as molten silicon temperature, solidification process, and thermal state changes, the effect of adjusting the crystal rise rate usually requires a certain growth process before it is reflected in the diameter change. Therefore, when adjusting the crystal rise rate based on the existing diameter deviation, the outer contour shape of the crystal shoulder may have already deviated, causing the adjustment to lag behind the actual growth change. This can easily lead to increased deviation of the crystal shoulder shape during the shoulder formation process, increased risk of breakage, and decreased diameter consistency between different shoulder formation processes.

[0037] Therefore, improving the timeliness of crystal rise speed adjustment during the Czochralski single-crystal silicon shoulder formation process to reduce the risk of significant deviation in the outer contour of the crystal shoulder has become a technical problem that needs to be solved.

[0038] Based on this, embodiments of this application provide a crystal rise rate control method and related apparatus. Based on target shoulder morphology data, the method predicts the future shoulder morphology corresponding to multiple candidate crystal rise rate compensation amounts, and determines the target crystal rise rate compensation amount based on the difference between the predicted shoulder morphology data and the target shoulder morphology data. Therefore, it is possible to select a crystal rise rate compensation amount suitable for the current growth state in advance before the outer contour morphology of the crystal shoulder deviates significantly, avoiding delayed adjustments based solely on the already formed diameter deviation. This improves the timeliness of crystal rise rate adjustment during shoulder formation, reduces the risk of breakage, and enhances the stability and diameter consistency of shoulder growth.

[0039] The crystal speed control method provided in this application can be applied to computer devices with data processing capabilities, such as terminal devices and servers. Specifically, terminal devices can be desktop computers, laptops, mobile phones, and tablets; servers can be independent physical servers, server clusters composed of multiple physical servers, or distributed systems. Terminal devices and servers can be directly or indirectly connected via wired or wireless communication, and this application does not impose any restrictions.

[0040] See Figure 1 This figure is a schematic flowchart of the crystal rise speed control method provided in an embodiment of this application. For ease of description, the following embodiments use a server as the executing entity of the crystal rise speed control method. Figure 1 As shown, the crystal rise rate control method includes S101-S107.

[0041] In this embodiment, the Czochralski-grown single-crystal silicon is single-crystal silicon grown using the Czochralski method. Specifically, during the growth of Czochralski-grown single-crystal silicon, a seed crystal can be brought into contact with molten silicon, and the seed crystal can be lifted upwards to allow the molten silicon to solidify along the crystal orientation of the seed crystal to form a crystal. Shoulder formation is the growth process after the crystal is successfully pulled, where the crystal diameter gradually increases from the smaller size formed by the pulling process to the size required for constant-diameter growth. During shoulder formation, as the crystal gradually extends along the growth direction, the outer contour of the crystal shoulder gradually expands outwards, thus forming a shoulder shape that transitions from a smaller diameter to a larger diameter.

[0042] The crystal rise rate is the speed at which Czochralski-grown single-crystal silicon moves along the lifting direction during growth. During the shoulder formation process, changes in the crystal rise rate affect the crystal's growth state, thus influencing the subsequent outer contour morphology of the crystal shoulder. For example, if other growth conditions change, and the original crystal rise rate is still used, the crystal shoulder may expand too quickly or not at all. Therefore, in this application, embodiments select a target crystal rise rate compensation amount for actual crystal rise rate adjustment based on the future shoulder morphology corresponding to different candidate crystal rise rate compensation amounts, so that crystal rise rate adjustment can be performed in advance in conjunction with the possible subsequent outer contour morphology of the crystal shoulder.

[0043] This application does not specifically limit the data transmission method between the server and the single crystal furnace. The server can be a computer device connected to the single crystal furnace, or it can be a server in the single crystal furnace big data control system. The server can acquire relevant data during the Czochralski single crystal silicon shoulder formation process and send control commands to the control equipment of the single crystal furnace according to the determined target crystal rise speed compensation amount.

[0044] S101: Obtain target shoulder shape data.

[0045] Among them, the target shoulder morphology data is used to characterize the target outer contour morphology of the crystal shoulder as the crystal growth position changes during the shoulder formation process of Czochralski single crystal silicon.

[0046] The crystal growth position refers to the location of the crystal along the growth direction during the shoulder formation process. Because the crystal diameter needs to gradually increase from a smaller size to the size required for constant-diameter growth during shoulder formation, the outer contour shape of the crystal shoulder differs at different crystal growth positions. For example, the outer contour of the crystal shoulder is narrower near the beginning of shoulder formation, and gradually expands outward as the crystal growth position changes along the growth direction, eventually transitioning to the outer contour shape corresponding to constant-diameter growth.

[0047] Target shoulder morphology data describes the desired outer contour shape of the crystal shoulder during the shoulder-growing process. This data represents the target outer contour state that the crystal shoulder should have at different growth positions. Therefore, target shoulder morphology data does not only characterize the final diameter the crystal needs to reach at the end of shoulder growth, but also characterizes the target morphology of the crystal shoulder as the crystal grows throughout the entire shoulder-growing process.

[0048] By acquiring target shoulder morphology data, we can provide a comparative basis for judging the impact of different crystal rise rate adjustment methods on the subsequent growth morphology of the crystal shoulder, enabling crystal rise rate control around the target outer contour morphology of the crystal shoulder during the shoulder formation process.

[0049] S102: Obtain the growth status data of Czochralski single crystal silicon at the current control moment.

[0050] The current control time is the control time corresponding to the determination of the crystal growth rate compensation amount. The growth state data is used to reflect the growth state of Czochralski single crystal silicon at the current control time.

[0051] During the shoulder formation process, the subsequent growth of the crystal shoulder depends not only on the proposed crystal rise rate adjustment method but also on the current growth state of the crystal. For example, if the crystal shoulder is already showing a rapid expansion trend, the future shoulder morphology after applying a certain crystal rise rate compensation may differ from the future shoulder morphology after applying the same compensation when the crystal shoulder is currently showing a slower expansion trend. Therefore, before predicting and evaluating candidate crystal rise rate compensation values, it is necessary to obtain the growth state data at the current control moment.

[0052] One implementation method is to obtain growth state data corresponding to the current control moment from the single crystal furnace control system or data acquisition system. This growth state data can provide input for predicting diameter changes at future control moments. This application does not specifically limit the specific data types and data acquisition methods included in the growth state data; the specific content of the growth state data can be further described in subsequent embodiments.

[0053] S103: Determine the compensation amount for multiple candidate crystal rise rates.

[0054] The crystal rise speed compensation amount is used to adjust the crystal rise speed during the shoulder release process. The candidate crystal rise speed compensation amounts are the alternative crystal rise speed compensation amounts that can be selected during this control process. The target crystal rise speed compensation amount is the final crystal rise speed compensation amount used to adjust the crystal rise speed from among the multiple candidate crystal rise speed compensation amounts.

[0055] In other words, instead of directly determining and immediately implementing a crystal rise rate compensation amount, multiple candidate crystal rise rate compensation amounts are first determined to assess the impact of different candidate compensation amounts on the subsequent outer contour morphology of the crystal shoulder. For example, multiple candidate compensation amounts can be used to adjust the current crystal rise rate to different degrees, thus forming multiple crystal rise rate adjustment schemes to be evaluated.

[0056] This application does not specifically limit the number, value range, or determination method of multiple candidate crystal rise rate compensation amounts. Multiple candidate crystal rise rate compensation amounts can be determined according to preset candidate compensation amount determination rules, or they can be determined based on the crystal rise rate adjustment range available in the current control process.

[0057] By determining multiple candidate crystal rise rate compensation amounts, the potential future growth results of different alternative adjustment schemes can be compared before the actual crystal rise rate adjustment is implemented, avoiding the need to make a single adjustment based on the current state and then observe the adjustment effect.

[0058] S104: For each candidate crystal rise rate compensation amount among multiple candidate crystal rise rate compensation amounts, predict the predicted diameter data of Czochralski single crystal silicon at future control moments based on growth state data and candidate crystal rise rate compensation amounts.

[0059] The future control time is a later control time used to evaluate the impact of candidate crystal rise rate compensation on subsequent crystal growth. The predicted diameter data is the diameter-related data of Czochralski single-crystal silicon expected to have at the future control time when the corresponding candidate crystal rise rate compensation is adopted.

[0060] For any candidate crystal rise rate compensation value among multiple candidate crystal rise rate compensation values, this candidate crystal rise rate compensation value can be used as a crystal rise rate adjustment scheme to be evaluated. Combined with the growth state data at the current control moment, the predicted diameter data corresponding to the crystal growth at a future control moment after adopting this candidate crystal rise rate compensation value is predicted. Therefore, different candidate crystal rise rate compensation values ​​each correspond to a set of predicted diameter data.

[0061] It should be noted that the predictions in this step are not intended to replace measurements during the actual growth process, but rather to pre-evaluate the potential consequences of different candidate crystal rise rate compensation amounts before actually adjusting the crystal rise rate.

[0062] S105: Based on the predicted diameter data corresponding to the rising speed compensation amount of each candidate crystal, determine the predicted shoulder morphology data corresponding to the rising speed compensation amount of each candidate crystal.

[0063] Among them, the predicted shoulder morphology data is used to characterize the expected outer contour morphology of the crystal shoulder of Czochralski single-crystal silicon at future control moments, under the condition of adopting the corresponding candidate crystal rise rate compensation amount.

[0064] Since the control objective during the shoulder formation process is not only to make the crystal reach a certain large diameter, but also to make the crystal shoulder form a reasonable outer contour shape as the diameter gradually increases, it is necessary to further determine the predicted shoulder shape data corresponding to the predicted diameter data in addition to obtaining the predicted diameter data at the future control time.

[0065] In this embodiment, for each candidate crystal rise rate compensation amount, the predicted shoulder morphology data corresponding to that candidate crystal rise rate compensation amount can be determined based on the predicted diameter data. Therefore, each candidate crystal rise rate compensation amount corresponds to predicted diameter data and predicted shoulder morphology data determined based on that predicted diameter data.

[0066] S106: Based on the difference between the predicted shoulder shape data and the target shoulder shape data corresponding to each candidate crystal rise rate compensation amount, determine the target crystal rise rate compensation amount from multiple candidate crystal rise rate compensation amounts.

[0067] After obtaining the predicted shoulder shape data corresponding to each candidate crystal rise rate compensation amount, each predicted shoulder shape data can be compared with the target shoulder shape data to determine the difference between the outer contour shape of the crystal shoulder expected to be formed at the future control time after adopting each candidate crystal rise rate compensation amount and the target outer contour shape.

[0068] The smaller the difference between the predicted shoulder morphology data and the target shoulder morphology data, the closer the expected outer contour of the crystal shoulder will be to the target outer contour after applying the corresponding candidate crystal rise rate compensation. Conversely, the greater the difference between the predicted and target shoulder morphology data, the higher the probability of morphological deviation of the crystal shoulder at future control times after applying the corresponding candidate crystal rise rate compensation.

[0069] This application does not specifically limit the specific calculation method of the difference, the specific form of the evaluation result, or the specific content of the preset selection conditions. As one implementation, the evaluation result corresponding to each candidate crystal rise rate compensation amount can be determined based on the difference between the predicted shoulder morphology data and the target shoulder morphology data corresponding to each candidate crystal rise rate compensation amount. The candidate crystal rise rate compensation amount whose evaluation result satisfies the preset selection conditions is then determined as the target crystal rise rate compensation amount.

[0070] Therefore, before actually implementing crystal rise rate adjustment, it is possible to compare the future shoulder outer contour shape corresponding to multiple candidate crystal rise rate compensation amounts in advance, thereby selecting the crystal rise rate compensation amount that is more suitable for the current growth state.

[0071] S107: Adjust the crystal rise rate of Czochralski single crystal silicon during the shoulder formation process according to the target crystal rise rate compensation amount.

[0072] After determining the target crystal rise rate compensation amount, a crystal rise rate adjustment command can be generated based on the target crystal rise rate compensation amount, and the crystal rise rate adjustment command can be sent to the control equipment of the single crystal furnace so that the single crystal furnace can adjust the crystal rise rate of Czochralski single crystal silicon during the shoulder formation process according to the target crystal rise rate compensation amount.

[0073] Since the target crystal rise rate compensation amount is determined based on the future shoulder shape corresponding to multiple candidate crystal rise rate compensation amounts, adjusting the crystal rise rate according to the target crystal rise rate compensation amount can make the current crystal rise rate adjustment combined with the possible outer contour shape of the crystal shoulder in advance, rather than making feedback adjustment after the crystal shoulder has already deviated significantly.

[0074] As can be seen from the above technical solution, acquiring target shoulder morphology data, which characterizes the target outer contour morphology of the crystal shoulder as it changes with the crystal growth position during the shoulder formation process of Czochralski single-crystal silicon, allows subsequent crystal rise rate control to no longer revolve solely around a specific target diameter, but rather to use the target shoulder outer contour morphology that should form at different crystal growth positions during the shoulder formation process as the control basis. Furthermore, acquiring growth state data at the current control moment, and predicting the predicted diameter data for each candidate crystal rise rate compensation amount at the future control moment, and then determining the corresponding predicted shoulder morphology data based on each predicted diameter data. Thus, before actually adopting a certain crystal rise rate compensation amount, the influence of different candidate crystal rise rate compensation amounts on the subsequent outer contour morphology of the crystal shoulder can be obtained in advance, without having to wait until the crystal shoulder has already deviated significantly before making adjustments. Based on this, according to the difference between the predicted shoulder morphology data and the target shoulder morphology data, the target crystal rise rate compensation amount is determined from multiple candidate crystal rise rate compensation amounts. The crystal rise rate during the shoulder formation process is adjusted according to the target crystal rise rate compensation amount, so that the crystal rise rate adjustment can be carried out in advance in combination with the subsequent changes in the outer contour morphology of the crystal shoulder. This improves the timeliness of crystal rise rate adjustment during the shoulder formation process of Czochralski single crystal silicon, reduces the risk of significant deviation in the outer contour morphology of the crystal shoulder and the resulting breakage, and improves the stability and diameter consistency of the shoulder growth.

[0075] In one possible implementation, the target shoulder morphology data includes the target absolute angle curve, the target relative angle curve, the allowable absolute angle range, and the allowable relative angle range. The target absolute angle curve characterizes the degree of unfolding of the target outer contour at different crystal growth positions, while the target relative angle curve characterizes the degree of change in the target's local outer contour at different crystal growth positions. The allowable absolute angle range characterizes the allowable range of variation corresponding to the overall unfolding of the crystal shoulder's outer contour, and the allowable relative angle range characterizes the allowable range of variation corresponding to the degree of change in the local outer contour of the crystal shoulder.

[0076] In this embodiment, the crystal growth position can be characterized by the position per unit length of the crystal during the shoulder formation process. As the position per unit length changes, the diameter of the crystal shoulder gradually increases, and the outer contour of the crystal shoulder changes accordingly. Therefore, the target shoulder morphology data for controlling the current shoulder formation process can be determined based on the diameter changes corresponding to different positions per unit length during historical shoulder formation processes. See A1-A6 for details.

[0077] A1: Obtain the historical diameter curves corresponding to multiple historical shoulder-raising processes.

[0078] The historical diameter curve is used to characterize how the crystal diameter changes with the crystal growth position during a corresponding historical shoulder formation process. For a single historical shoulder formation process, the crystal growth position can be used as the abscissa, and the crystal diameter measured at the corresponding crystal growth position can be used as the ordinate to form the historical diameter curve corresponding to that historical shoulder formation process.

[0079] In one implementation, the multiple historical diameter curves can be the original diameter curves corresponding to multiple historical shoulder-expansion processes, or they can be reference diameter curves selected from the original diameter curves corresponding to multiple historical shoulder-expansion processes, which can be used to characterize a reasonable shoulder-expansion shape. For a detailed implementation of selecting multiple historical diameter curves, please refer to the following embodiments.

[0080] A2: Based on multiple historical diameter curves, determine the target diameter curve, the upper diameter boundary curve, and the lower diameter boundary curve.

[0081] The target diameter curve is used to characterize the trend of target diameter change of the crystal shoulder as the crystal growth position changes during the shoulder formation process. The upper and lower diameter boundary curves are used to characterize the allowable fluctuation boundaries corresponding to this target diameter change trend.

[0082] One approach is to determine the measured diameter corresponding to multiple historical diameter curves at each crystal growth location, and then calculate the average value of these measured diameters. Connecting the average measured diameters at each crystal growth location sequentially yields the mean diameter curve. Furthermore, a univariate spline smoothing algorithm can be used to smooth the mean diameter curve, and this smoothed mean diameter curve is then used as the target diameter curve. Thus, the target diameter curve can characterize a relatively stable trend in shoulder diameter variation across multiple historical shoulder formation processes.

[0083] As one approach, for each crystal growth location, the maximum and minimum values ​​of the measured diameters corresponding to multiple historical diameter curves at that location can be statistically analyzed. Connecting the maximum values ​​at each crystal growth location sequentially yields the upper boundary curve of the initial diameter; connecting the minimum values ​​at each crystal growth location sequentially yields the lower boundary curve of the initial diameter.

[0084] Since directly connecting the maximum or minimum values ​​corresponding to each crystal growth position may cause local unevenness in the boundary curves, fitting processing can be performed on the initial diameter upper and lower boundary curves. In one specific implementation, a fifth-order polynomial can be used, and the initial diameter upper and lower boundary curves can be fitted respectively based on the least squares method. The fitted initial diameter upper boundary curve is determined as the diameter upper boundary curve, and the fitted initial diameter lower boundary curve is determined as the diameter lower boundary curve.

[0085] In one possible implementation, to facilitate the subsequent determination of angle data at the same crystal growth location, linear interpolation can be performed on the target diameter curve, the upper diameter boundary curve, and the lower diameter boundary curve respectively, mapping the target diameter curve, the upper diameter boundary curve, and the lower diameter boundary curve to a unified set of integer unit lengths, so that each curve has corresponding diameter data at the same integer unit length position.

[0086] A3: Determine the target absolute angle curve based on the relationship between the radius corresponding to each crystal growth position in the target diameter curve and the crystal growth position.

[0087] Among them, the target absolute angle curve is used to characterize the degree of expansion of the target outer contour of the crystal shoulder at the corresponding crystal growth position.

[0088] Specifically, for any crystal growth position on the target diameter curve, the target diameter corresponding to that crystal growth position can be obtained and converted into a target radius. Then, the ratio between this target radius and the unit length corresponding to that crystal growth position can be calculated. This ratio characterizes the degree to which the crystal shoulder extends outwards at that crystal growth position. Further, this ratio can be converted into an angle value using an arctangent method to obtain the target absolute angle corresponding to that crystal growth position.

[0089] By performing the above processing on each crystal growth position in the target diameter curve, we can obtain the target absolute angles corresponding to multiple crystal growth positions. Arranging these multiple target absolute angles according to their corresponding crystal growth positions forms a target absolute angle curve.

[0090] A4: Determine the target relative angle curve based on the relationship between the radius change and the crystal growth position change at different crystal growth positions in the target diameter curve.

[0091] Among them, the target relative angle curve is used to characterize the degree of change of the target local outer contour of the crystal shoulder at the corresponding crystal growth position.

[0092] Specifically, the unit length span can be preset. For any crystal growth position in the target diameter curve, the target diameter corresponding to that crystal growth position and the target diameter corresponding to another crystal growth position separated from that crystal growth position by a unit length span can be obtained, and the two target diameters can be converted into target radii respectively. Then, the radius change between the two target radii and the unit length change between the two crystal growth positions can be determined, and the ratio between the radius change and the unit length change can be calculated. Further, this ratio can be converted into an angle value using the arctangent method to obtain the corresponding target relative angle.

[0093] In one specific implementation, the unit length span can be set to 1. In this case, the corresponding target relative angle can be determined based on the change in the target radius between two adjacent crystal growth positions. By performing the above processing on each crystal growth position in the target diameter curve that allows for local change calculations, a target relative angle curve can be generated.

[0094] A5: For each diameter boundary curve in the upper and lower diameter boundary curves, determine the corresponding absolute angle boundary curve and relative angle boundary curve.

[0095] For the upper boundary curve of the diameter, the same absolute angle determination method as the target diameter curve can be used. For each crystal growth position, the upper boundary data of the diameter corresponding to the upper boundary curve is converted into upper boundary radius data, and the corresponding absolute angle upper boundary curve is determined according to the relationship between the upper boundary radius data and the corresponding crystal growth position.

[0096] For the lower boundary curve of the diameter, the same absolute angle determination method as the target diameter curve can be used. For each crystal growth position, the lower boundary data of the diameter corresponding to the lower boundary curve is converted into lower boundary radius data, and the corresponding absolute angle lower boundary curve is determined according to the relationship between the lower boundary radius data and the corresponding crystal growth position.

[0097] Accordingly, for the upper boundary curve of the diameter, the same relative angle determination method as the target diameter curve can be adopted. The relative angle upper boundary curve is determined based on the radius change between the upper boundary radii corresponding to different crystal growth positions and the unit length change between the corresponding crystal growth positions.

[0098] For the lower boundary curve of the diameter, the same relative angle determination method as the target diameter curve can be used. The relative angle lower boundary curve is determined based on the radius change between the lower boundary radii corresponding to different crystal growth positions and the unit length change between the corresponding crystal growth positions.

[0099] A6: Determine the allowable range of absolute angles based on the absolute angle boundary curve, and determine the allowable range of relative angles based on the relative angle boundary curve.

[0100] Specifically, for any crystal growth location, the allowable range of absolute angles at that location can be determined based on the angle values ​​corresponding to the upper and lower absolute angle boundary curves at that location. The allowable range of absolute angles characterizes the degree of overall outer contour expansion that the crystal shoulder is allowed to exhibit at that crystal growth location.

[0101] For any given crystal growth location, the allowable range of relative angles at that location can be determined based on the angle values ​​corresponding to the upper and lower boundary curves of the relative angle at that location. The allowable range of relative angles characterizes the degree of local outer contour variation that is permitted to occur at that crystal growth location.

[0102] Therefore, the target absolute angle curve and the target relative angle curve can be used to characterize the degree of overall outer contour expansion and local outer contour change that the crystal shoulder is expected to form during the shoulder formation process. The allowable range of absolute angle and the allowable range of relative angle can be used to characterize the range of fluctuations allowed for the corresponding target shape. By converting the target curve and upper and lower boundaries in the diameter dimension into target curves and allowable ranges in the angle dimension, a control basis can be provided for selecting the target crystal lifting speed compensation amount based on the predicted shoulder shape data.

[0103] In one possible implementation, historical data may contain local anomalies or overall curve shifts due to measurement noise and other issues. Therefore, a multi-stage, multi-index fusion diameter curve preprocessing method can be used to filter multiple historical diameter curves and determine the target diameter curve, upper diameter boundary curve, and lower diameter boundary curve based on the retained diameter curves after filtering. See B1-B5 for details.

[0104] B1: Select multiple diameter curves from multiple historical diameter curves that meet the preset length conditions for equal diameter length.

[0105] The constant diameter length is used to characterize the growth length of the corresponding historical shoulder-expanding process after it enters the constant diameter growth stage. A small constant diameter length corresponding to a historical shoulder-expanding process indicates that the shoulder-expanding effect of that process was not ideal and is difficult to use as a reference for target shoulder morphology data.

[0106] Specifically, the data files corresponding to multiple historical shoulder-expansion processes can first be filtered for validity, deleting empty files and files with abnormally large sizes. Furthermore, a threshold of 1000 for the equal diameter length can be set, and historical shoulder-expansion processes with equal diameter lengths less than 1000 are considered to have unsatisfactory shoulder-expansion effects and cannot be used as reference data for the target shoulder shape. Therefore, historical diameter curves with equal diameter lengths less than 1000 can be deleted, and historical diameter curves with equal diameter lengths greater than or equal to 1000 are identified as the diameter curves to be processed.

[0107] B2: Perform sampling position alignment processing on multiple diameter curves to be processed to obtain multiple diameter curves to be screened.

[0108] Since the number of length sampling points of the measured diameter curve in each valid file may not be consistent, in order to achieve curve family statistics, multiple diameter curves to be processed need to be processed into diameter curves with consistent dimensions.

[0109] For example, the original unit length array corresponding to the diameter curve to be processed can be used as the horizontal axis, and the measured diameter can be used as the vertical axis. Linear interpolation can be performed on each diameter curve to be processed, and a unified sampling point sequence with a length of 160 sampling points can be set so that each diameter curve to be processed has a corresponding measured diameter at the same sampling position, thereby giving each diameter curve to be processed a consistent dimension.

[0110] Furthermore, to reduce the impact of spike noise from individual sensors, median filtering can be used to smooth the interpolated diameter curve. In one specific implementation, the number of kernels for median filtering can be set to 5. That is, for the sampling position to be processed in the diameter curve, the median can be determined based on the measured diameters corresponding to 5 consecutive sampling positions, including the sampling position to be processed. The measured diameters corresponding to the sampling position to be processed are then smoothed based on this median to reduce the impact of local outliers on the entire diameter curve.

[0111] After linear interpolation and median filtering, multiple diameter curves to be screened can be obtained with consistent scale and suppressed local spike noise.

[0112] B3: Determine the median diameter curve based on the median diameter at each sampling position of multiple diameter curves to be screened.

[0113] After initial screening and sampling location alignment, several diameter curves to be screened may still exhibit different overall trends, excessive amplitude, average value deviation, or poor correlation with the mainstream curve. Therefore, it is advisable to first determine the median diameter curve that can characterize the mainstream trend of the multiple diameter curves to be screened, so as to identify and remove diameter curves that are far from the mainstream trend in the subsequent process.

[0114] For example, for any sampling position in a unified sampling point sequence, multiple diameter curves to be screened can be obtained, corresponding to the measured diameters at that sampling position. The median of these measured diameters is then calculated and used as the diameter data for the median diameter curve at that sampling position. Following this method, the median diameters for all sampling positions are calculated, and the curve formed by the median diameters at each sampling position is determined as the median diameter curve.

[0115] B4: For each diameter curve to be screened, determine the deviation score corresponding to the diameter curve to be screened based on the mean square error, correlation difference, amplitude deviation, and mean deviation between the diameter curve to be screened and the median diameter curve.

[0116] For example, for any diameter curve to be screened, the mean square error (MSE), correlation difference (1-corr), amplitude deviation, and mean deviation between the diameter curve to be screened and the median diameter curve can be calculated respectively.

[0117] The mean square error (MSE) characterizes the degree to which the diameter curve to be screened deviates from the median diameter curve. The correlation difference (1-corr) characterizes the difference between the diameter curve to be screened and the median diameter curve in terms of diameter variation trends, where corr is the correlation coefficient between the two curves. The amplitude deviation characterizes the difference in diameter variation amplitude of the diameter curve to be screened relative to the median diameter curve. The mean deviation characterizes the degree of deviation of the diameter curve to be screened relative to the median diameter curve in terms of overall diameter level.

[0118] Since the dimensions of mean square error, correlation difference, amplitude deviation, and mean deviation may differ, these four indicators can be standardized to ensure consistency in their dimensions. Furthermore, the standardized four indicators can be weighted and summed, and the weighted sum can be used as the deviation score for the corresponding diameter curve to be screened. A larger deviation score indicates that the corresponding diameter curve deviates more from the mainstream trend formed by multiple diameter curves to be screened.

[0119] B5: Based on the deviation scores corresponding to each diameter curve to be screened, iteratively screen multiple diameter curves to be screened, and determine the target diameter curve, the upper boundary curve of the diameter, and the lower boundary curve of the diameter based on the multiple diameter curves to be screened that are retained after screening.

[0120] Specifically, the screening threshold for the current round can be determined based on the deviation scores corresponding to multiple diameter curves to be screened. In one specific implementation, the mean and coefficient of multiple deviation scores can be multiplied by the sum of the standard deviations of the multiple deviation scores to determine the screening threshold. Then, only diameter curves to be screened with deviation scores lower than the screening threshold are retained, while diameter curves to be screened with deviation scores greater than or equal to the screening threshold are removed.

[0121] After each round of eliminating abnormal diameter curves, the median diameter curve can be re-determined based on the multiple diameter curves retained after the current round of screening. The mean squared error (MSE), correlation difference (1-corr), amplitude deviation, mean deviation, and deviation score for each diameter curve to be screened are then recalculated based on the updated median diameter curve to continue eliminating diameter curves that deviate significantly from the current mainstream trend. In one specific implementation, the above iterative screening process can be repeated 3 to 6 times until the set of retained diameter curves reaches a stable state.

[0122] After the iterative screening is completed, the multiple diameter curves to be screened that are retained after screening can be used as a reference diameter curve set, and the target diameter curve, the upper boundary curve of the diameter, and the lower boundary curve of the diameter can be determined based on the reference diameter curve set.

[0123] Specifically, the target diameter curve can be set as the smoothed mean curve corresponding to the reference diameter curve set. For each unit length position, the average measured diameter of each reference diameter curve in the reference diameter curve set at that unit length position can be calculated, and the mean diameter curve is obtained from the average measured diameter at each unit length position. Then, a univariate spline smoothing algorithm can be used to smooth the mean diameter curve, and the smoothed mean diameter curve is determined as the target diameter curve.

[0124] For the upper and lower boundary curves of the diameter, at each unit length position, the maximum and minimum measured diameter values ​​corresponding to each reference diameter curve in the reference diameter curve set at that unit length position can be statistically analyzed. Connecting the maximum measured diameter values ​​corresponding to each unit length position yields the initial upper boundary curve of the diameter; connecting the minimum measured diameter values ​​corresponding to each unit length position yields the initial lower boundary curve of the diameter. Furthermore, polynomial fitting can be performed on the initial upper and lower boundary curves of the diameter. In one specific implementation, a 5th-order polynomial can be used to fit the initial upper and lower boundary curves of the diameter using the least squares method, and the fitted curves are determined as the upper and lower boundary curves of the diameter, respectively.

[0125] Therefore, by first screening diameter curves from multiple historical diameter curves that meet the preset length condition, historical shoulder-forming data that have not formed a stable constant-diameter growth state can be excluded, avoiding the participation of data with unsatisfactory shoulder-forming effects in the determination of target diameter curves and boundary curves. Furthermore, by aligning the sampling positions of multiple diameter curves to be processed, diameter data from different historical shoulder-forming processes at the same crystal growth position can be compared accordingly. Based on this, the median diameter curve is determined according to the median diameter at each sampling position, and deviation scores are determined according to the mean square error, correlation difference, amplitude deviation, and mean deviation between each diameter curve to be screened and the median diameter curve. This allows for the identification of abnormal curves with large overall deviations, inconsistent trends, excessive diameter fluctuations, and overall diameter shifts. By iteratively screening multiple diameter curves to be screened based on the deviation scores, historical diameter curves that deviate from the mainstream shoulder-forming morphology can be gradually eliminated, making the retained diameter curves more representative of a stable and consistent shoulder-forming growth process. Therefore, determining the target diameter curve, upper diameter boundary curve, and lower diameter boundary curve based on the multiple diameter curves retained after screening can improve the data reliability of the target shoulder morphology data, making the subsequent selection of crystal rise speed compensation based on the target shoulder morphology data more consistent with the reasonable shoulder shape.

[0126] In one possible implementation, the growth state data includes the current diameter data corresponding to the current control moment, and the predicted shoulder morphology data includes the predicted absolute angle and the predicted relative angle. The predicted absolute angle characterizes the overall outer contour expansion of the crystal shoulder at a future control moment when the corresponding candidate crystal rise rate compensation is applied; the predicted relative angle characterizes the degree of local outer contour change of the crystal shoulder from the current control moment to a future control moment when the corresponding candidate crystal rise rate compensation is applied.

[0127] In this embodiment, model predictive control can be used to evaluate multiple candidate crystal rise rate compensation amounts. Specifically, based on the predicted absolute and relative angles corresponding to each candidate crystal rise rate compensation amount, the difference between the outer contour shape of the crystal shoulder at future control moments and the target shoulder shape after adopting each candidate crystal rise rate compensation amount can be evaluated. Simultaneously, the magnitude of the candidate crystal rise rate compensation amounts and the changes in crystal rise rate compensation amounts between adjacent control moments can be considered to select a target crystal rise rate compensation amount that both makes the future shoulder shape close to the target shoulder shape and avoids excessively large or abrupt crystal rise rate compensation amounts. See C1-C8 for details.

[0128] C1: Determine the current radius data based on the current diameter data.

[0129] The current diameter data is the crystal diameter data measured at the current control moment, and the current radius data is the data determined based on the current diameter data, used to characterize the lateral dimension of the crystal shoulder at the current control moment.

[0130] Specifically, the current diameter data corresponding to the current control time can be obtained and converted into current radius data. The current radius data is used to compare with the predicted radius data corresponding to the future control time when determining the predicted relative angle, so as to reflect the local outer contour change of the crystal shoulder between the current control time and the future control time.

[0131] C2: For each candidate crystal rise rate compensation amount, determine the prediction radius data based on the corresponding prediction diameter data.

[0132] The predicted diameter data refers to the diameter of the Czochralski-grown single-crystal silicon at a future control moment, calculated using the corresponding candidate crystal rise rate compensation. The predicted radius data is the radius obtained by converting the predicted diameter data.

[0133] Specifically, for any candidate crystal rise rate compensation amount among multiple candidate crystal rise rate compensation amounts, the predicted diameter data corresponding to that candidate crystal rise rate compensation amount can be obtained, and the predicted diameter data can be converted into predicted radius data. Since each candidate crystal rise rate compensation amount corresponds to a predicted diameter data, each candidate crystal rise rate compensation amount also corresponds to a predicted radius data.

[0134] C3: Based on the relationship between the predicted radius data and the crystal growth position corresponding to the future control time, determine the predicted absolute angle corresponding to the candidate crystal rise rate compensation amount.

[0135] Among them, the predicted absolute angle is used to characterize the degree to which the crystal shoulder will expand outward as a whole at future control moments after adopting the corresponding candidate crystal rise rate compensation amount.

[0136] Specifically, for any candidate crystal rise rate compensation amount, the predicted radius data corresponding to the candidate crystal rise rate compensation amount and the crystal growth position corresponding to the future control time can be obtained. Then, the ratio between the predicted radius data and the crystal growth position corresponding to the future control time can be determined, and the ratio can be converted into an angle value according to the arctangent method to obtain the predicted absolute angle corresponding to the candidate crystal rise rate compensation amount.

[0137] C4: Based on the radius change between the predicted radius data and the current radius data, and the position change between the crystal growth position at the future control time and the crystal growth position at the current control time, determine the predicted relative angle corresponding to the candidate crystal rise rate compensation amount.

[0138] Among them, the predicted relative angle is used to characterize the degree of change in the local outer contour of the crystal shoulder between the current control time and the future control time after adopting the corresponding candidate crystal rise rate compensation amount.

[0139] Specifically, for any candidate crystal growth rate compensation amount, the radius change between the predicted radius data and the current radius data corresponding to the candidate crystal growth rate compensation amount can be determined, as well as the position change between the crystal growth position at the future control time and the crystal growth position at the current control time. Then, the ratio between the radius change and the position change can be determined, and this ratio can be converted into an angle value using the arctangent method to obtain the predicted relative angle corresponding to the candidate crystal growth rate compensation amount.

[0140] C5: For each candidate crystal rise rate compensation amount, determine the angle deviation cost based on the difference between the predicted absolute angle and the corresponding target absolute angle, as well as the difference between the predicted relative angle and the corresponding target relative angle.

[0141] In this embodiment, the target absolute angle curve and the target relative angle curve respectively include the target absolute angle and the target relative angle corresponding to different crystal growth positions. Therefore, for any candidate crystal growth rate compensation amount, the corresponding target absolute angle can be determined from the target absolute angle curve and the corresponding target relative angle can be determined from the target relative angle curve based on the crystal growth position corresponding to the future control time.

[0142] Specifically, the difference between the predicted absolute angle and the target absolute angle can be determined, as well as the difference between the predicted relative angle and the target relative angle. As a specific implementation, the squares of the differences between the predicted absolute angle and the target absolute angle, and the squares of the differences between the predicted relative angle and the target relative angle, can be weighted separately, and the sum of the weighted results can be determined as the angle deviation cost.

[0143] The smaller the cost of the angle deviation, the closer the overall outer contour development and local outer contour change of the crystal shoulder will be to the target shoulder shape at future control moments after the corresponding candidate crystal rise rate compensation amount is adopted; the larger the cost of the angle deviation, the more likely the corresponding candidate crystal rise rate compensation amount may cause a large deviation in the future shoulder shape.

[0144] C6: Determine the compensation range value based on the compensation amount of the candidate crystal rise rate.

[0145] The compensation range is used to limit the overshoot that may occur during the growth process due to excessive compensation for a single crystal rise rate.

[0146] Specifically, for any candidate crystal rise rate compensation amount, the compensation range cost can be determined based on the magnitude of the candidate crystal rise rate compensation amount. In one specific implementation, the squares of the absolute values ​​of the candidate crystal rise rate compensation amounts can be weighted, and the weighted result can be determined as the compensation range cost. The corresponding weights can be used to adjust the sensitivity to changes in crystal rise rate.

[0147] For example, when the predicted shoulder shape corresponding to the two candidate crystal rise rate compensation amounts is relatively close to the target shoulder shape, the compensation magnitude cost can make the control process tend to select the candidate crystal rise rate compensation amount with a smaller crystal rise rate change, so as to prevent the crystal rise rate from changing too much at once and causing excessive changes in the crystal growth state.

[0148] C7: Determine the compensation smoothing value based on the difference between the candidate crystal rise rate compensation amount and the target crystal rise rate compensation amount corresponding to the previous control time.

[0149] The compensation smoothing cost is used to limit abrupt changes in the crystal rise rate compensation between continuous control moments, thereby ensuring a smooth process of crystal shoulder morphology change.

[0150] Specifically, for any candidate crystal rise rate compensation amount, the difference between the candidate crystal rise rate compensation amount and the target crystal rise rate compensation amount determined at the previous control moment can be determined. In one specific implementation, the square of this difference can be weighted, and the weighted result can be determined as the compensation smoothing cost. The corresponding weights can be used to adjust the limiting strength of the degree of change in the crystal rise rate compensation amount between two consecutive control moments.

[0151] For example, if the target crystal rise rate compensation amount corresponding to the previous control time is small, and the current candidate crystal rise rate compensation amount changes significantly relative to the target crystal rise rate compensation amount, then the compensation smoothing cost corresponding to the candidate crystal rise rate compensation amount is large, thereby reducing the possibility of the candidate crystal rise rate compensation amount being selected and avoiding the sudden impact of the crystal rise rate compensation amount change on the crystal shoulder morphology.

[0152] C8: Based on the value of the angle deviation, the value of the compensation amplitude, and the value of the compensation smoothing, determine the total value corresponding to the candidate crystal rise speed compensation amount, and determine the candidate crystal rise speed compensation amount with the smallest total value as the target crystal rise speed compensation amount.

[0153] Specifically, for each candidate crystal rise rate compensation amount, the value of the angle deviation, the value of the compensation amplitude, and the value of the compensation smoothing corresponding to the candidate crystal rise rate compensation amount can be summed to obtain the total value corresponding to the candidate crystal rise rate compensation amount.

[0154] Among them, the angle deviation cost is used to evaluate the degree of deviation between the future shoulder shape and the target shoulder shape after adopting the candidate crystal rise speed compensation amount; the compensation amplitude cost is used to limit the crystal rise speed change at the current control moment to be too large; and the compensation smoothing cost is used to limit the candidate crystal rise speed compensation amount at the current control moment from abruptly changing relative to the target crystal rise speed compensation amount at the previous control moment.

[0155] After determining the total substitution value corresponding to multiple candidate crystal rise rate compensation amounts, the predicted diameter data, predicted absolute angle, predicted relative angle, and total substitution value corresponding to each candidate crystal rise rate compensation amount can be recorded, and the total substitution values ​​corresponding to each candidate crystal rise rate compensation amount can be compared. The candidate crystal rise rate compensation amount with the smallest total substitution value is determined as the target crystal rise rate compensation amount. This target crystal rise rate compensation amount is used to characterize the compensation amount that, within the currently selectable crystal rise rate adjustment range, makes the crystal shoulder morphology at future control moments closer to the target shoulder morphology, while taking into account the crystal rise rate adjustment amplitude and smoothness.

[0156] Therefore, based on the predicted diameter data corresponding to each candidate crystal rise rate compensation amount, the corresponding predicted absolute angle and predicted relative angle are determined. This allows for the prior acquisition of the impact of different candidate crystal rise rate compensation amounts on the overall outer contour development and local outer contour changes of the crystal shoulder before actual crystal rise rate compensation is performed. The angle deviation cost is determined based on the difference between the predicted absolute angle, predicted relative angle, and the corresponding target angle. Furthermore, the total cost is determined by combining the compensation amplitude cost and compensation smoothing cost. This approach ensures that the future shoulder shape closely approximates the target shoulder shape while limiting excessive single crystal rise rate adjustments and abrupt changes in continuous crystal rise rate compensation amounts. Thus, by determining the candidate crystal rise rate compensation amount with the minimum total cost as the target crystal rise rate compensation amount, the timeliness and stability of crystal rise rate adjustment can be improved, reducing the risk of the crystal shoulder outer contour deviating from the target shape.

[0157] In one possible implementation, the growth state data includes the current absolute angle and the current relative angle. The current absolute angle characterizes the overall outer contour unfolding of the crystal shoulder at the crystal growth position corresponding to the current control moment, while the current relative angle characterizes the degree of local outer contour change of the crystal shoulder near the current control moment.

[0158] In this embodiment, the control mode corresponding to the current shoulder-forming process can be determined based on whether the current absolute angle is within the allowable range and whether the current relative angle is within the allowable range. If both the current absolute and relative angles are within their respective allowable ranges, it indicates that the overall outer contour expansion and local outer contour changes of the crystal shoulder have not deviated significantly, and a small range of crystal rise speed compensation can be used for fine-tuning. If either the current absolute or relative angle exceeds its respective allowable range, it indicates that the overall outer contour expansion or local outer contour changes of the crystal shoulder have deviated, and the selection range of the crystal rise speed compensation can be expanded, and the correction degree for out-of-bounds angles can be increased to quickly restore the crystal shoulder shape to its respective allowable range. See D1-D4 for details.

[0159] D1: Determine the current absolute angle and the current relative angle based on the current diameter data and the historical diameter data before the current control time.

[0160] Specifically, the current diameter data corresponding to the current control moment can be obtained and converted into current radius data. Then, the current absolute angle can be determined based on the relationship between the current radius data and the crystal growth position corresponding to the current control moment.

[0161] For example, the ratio between the current radius data and the unit length corresponding to the current control time can be determined, and this ratio can be converted into an angle value using the arctangent method to obtain the current absolute angle. The current absolute angle can be used to reflect the degree to which the crystal shoulder has expanded outward at the crystal growth position corresponding to the current control time.

[0162] Furthermore, historical diameter data prior to the current control moment can be obtained and converted into historical radius data. Then, the current relative angle can be determined based on the radius change between the current radius data and the historical radius data, as well as the positional change between the corresponding crystal growth positions.

[0163] In one specific implementation, a position one unit length away from the crystal growth position corresponding to the current control moment can be selected, and the historical radius data corresponding to that position can be obtained. Then, the radius change between the current radius data and the historical radius data can be determined, and the current relative angle can be obtained by converting the radius change to one unit length using the arctangent method. The current relative angle can be used to reflect the degree of change in the local outer contour of the crystal shoulder near the current control moment.

[0164] D2: In response to the current absolute angle being within the allowable range of absolute angle and the current relative angle being within the allowable range of relative angle, determine multiple candidate crystal rise rate compensation amounts based on the first compensation amount range.

[0165] If the current absolute angle is within the allowable range for both absolute and relative angles, it can be determined that the current shoulder-forming process is in normal mode. Normal mode refers to the control mode used when both the overall outer contour expansion and the degree of local outer contour change of the crystal shoulder are within the allowable range.

[0166] In normal mode, there is no significant deviation in the shape of the crystal shoulder. Therefore, there is no need to make a large adjustment to the crystal rise rate. Instead, the subsequent shoulder shape can be fine-tuned by a small range of crystal rise rate compensation, so that the predicted absolute angle and the predicted relative angle are closer to the target absolute angle and the target relative angle.

[0167] In one specific implementation, the first compensation range can be set to [-1, 1]. That is, in normal mode, multiple candidate crystal rise rate compensation values ​​can be generated within the crystal rise rate compensation range corresponding to [-1, 1], and the predicted diameter data at future control moments can be predicted for each candidate crystal rise rate compensation value, thereby determining the corresponding predicted absolute angle, predicted relative angle, and total substitution value.

[0168] D3: In response to the current absolute angle exceeding the allowable range of absolute angle, or the current relative angle exceeding the allowable range of relative angle, determine multiple candidate crystal rise rate compensation amounts based on the second compensation amount range.

[0169] If the current absolute angle exceeds the allowable range for absolute angles, or the current relative angle exceeds the allowable range for relative angles, it can be determined that the current shoulder formation process is in an abnormal mode. An abnormal mode is a control mode employed when the overall or local outer contour development of the crystal shoulder exceeds the allowable range.

[0170] For example, if the current absolute angle exceeds the allowable range, it indicates that the overall outer contour development of the crystal shoulder has deviated from the reasonable range; if the current relative angle exceeds the allowable range, it indicates that the stability of the local diameter change of the crystal shoulder has deviated from the reasonable range. When either the current absolute angle or the current relative angle exceeds the limit, the candidate range of crystal rise rate compensation can be expanded to improve the ability to correct for deviations in the current shoulder shape.

[0171] In one specific implementation, the second compensation range can be set to [-5, 5]. That is, in abnormal mode, multiple candidate crystal rise rate compensation amounts can be generated within the crystal rise rate compensation range corresponding to [-5, 5]. The second compensation range is larger than the first compensation range, which allows for a larger crystal rise rate adjustment scheme when the crystal shoulder shape has already deviated, so that a target crystal rise rate compensation amount that can restore the future shoulder shape to the allowable range can be selected from multiple adjustment schemes.

[0172] D4: Determine the evaluation weight in the angle deviation cost based on whether the current absolute angle and the current relative angle exceed the corresponding allowable range.

[0173] In this embodiment, the angle deviation cost is used to evaluate the degree of deviation between the predicted absolute angle and predicted relative angle corresponding to the candidate crystal rise rate compensation amount and the target absolute angle and target relative angle. To adapt the control strategy under different growth states to the degree of deviation of the current shoulder morphology, the evaluation weight in the angle deviation cost can be adjusted according to whether the current absolute angle and current relative angle exceed the corresponding allowable range.

[0174] When both the current absolute angle and relative angle are within their allowable ranges, the current shoulder formation process is in normal mode. In this case, a smaller evaluation weight can be used to assess the difference between the predicted absolute angle and the target absolute angle, as well as the difference between the predicted relative angle and the target relative angle. This allows for a gradual adjustment of the crystal rise rate to bring the crystal shoulder shape closer to the target shoulder shape. In one specific implementation, the small weight parameter win for normal mode can be set to 0.1.

[0175] If either the absolute angle or the relative angle exceeds the allowable range, the current shoulder-laying process is in an abnormal mode. If only one of the current absolute or relative angles exceeds the corresponding allowable range, a higher evaluation weight can be applied to the out-of-range angle, and a lower evaluation weight can be applied to the non-out-of-range angle. Specifically, a higher evaluation weight can be applied to the square of the difference between the out-of-range angle and the corresponding target angle, and a lower evaluation weight can be applied to the square of the difference between the non-out-of-range angle and the corresponding target angle, in order to prioritize restoring the out-of-range angle to the corresponding allowable range.

[0176] When both the current absolute angle and the current relative angle exceed their respective allowable ranges, a larger evaluation weight can be applied to both the current absolute angle and the current relative angle to simultaneously improve the correction effect on the deviation of the overall outer contour development degree of the crystal shoulder and the deviation of the local outer contour change degree. In one specific implementation, the larger weight parameter wout corresponding to the abnormal mode can be set to 0.5.

[0177] In other words, in normal mode, a smaller weight corresponding to win=0.1 can be used to evaluate the difference between the predicted angle and the target angle, allowing the crystal rise rate to be fine-tuned within a small compensation range. In abnormal mode, a larger weight corresponding to wout=0.5 can be used to evaluate angles that exceed the corresponding allowable range, and when both angles exceed the limit, a larger weight corresponding to wout=0.5 can be used for both angles, so that the evaluation result of the candidate crystal rise rate compensation amount focuses more on restoring the out-of-limit angles to the corresponding allowable range.

[0178] Therefore, based on whether the current absolute angle and the current relative angle are within the corresponding allowable range, different candidate crystal rise rate compensation ranges and evaluation weights for angle deviation costs are determined. When the crystal shoulder shape is within a reasonable range, smooth fine-tuning can be performed based on a smaller range of candidate crystal rise rate compensation amounts. When the overall outer contour expansion or local outer contour change of the crystal shoulder has exceeded the allowable range, the range of candidate crystal rise rate compensation amounts can be expanded, and the evaluation weight corresponding to the out-of-bounds angle can be increased. This makes the target crystal rise rate compensation amount more inclined to correct the already occurred shoulder shape deviation, thereby taking into account both the stability of crystal rise rate adjustment under normal shoulder release conditions and the correction capability of crystal rise rate adjustment under abnormal shoulder release conditions, reducing the risk of crystal shoulder shape deviation being further aggravated and leading to breakage.

[0179] In one possible implementation, the growth state data includes process state data at the current control moment and historical diameter sequences prior to the current control moment. The process state data characterizes the process control and measurement states of the Czochralski-grown single-crystal silicon during the shoulder formation process, while the historical diameter sequence characterizes the changes in crystal diameter over time or crystal growth position prior to the current control moment.

[0180] In this embodiment, a diameter prediction model can be constructed, and this model can be used to predict the diameter data of Czochralski-grown monocrystalline silicon at future control moments when different candidate crystal rise rate compensation amounts are adopted. The diameter prediction model can be a time-series neural network model based on a nonlinear autoregressive input structure. This nonlinear autoregressive input structure combines the process state data from the historical shoulder-growing process with the corresponding historical diameter sequence as the model input, and uses the future diameter data following the historical diameter sequence as the model output target. Therefore, the diameter prediction model can not only predict the future diameter based on the current process state, but also predict the possible future diameter changes corresponding to different candidate crystal rise rate compensation amounts by combining the crystal diameter change trend before the current control moment. See E1-E5 for details.

[0181] E1: Obtain historical shoulder data used to build the diameter prediction model.

[0182] Specifically, key parameters and measurement data from multiple historical shoulder-laying processes can be collected. These key parameters and measurement data may include the crystal pulling power ratio, crystal rise setting, crucible rise setting, measurement diameter, and charge-coupled device (CCD) temperature measurement data.

[0183] Among them, the crystal pulling power ratio is used to characterize the power control state before or related to the shoulder formation process; the crystal lift setting is used to characterize the control setting for the crystal movement along the lifting direction; the crucible lift setting is used to characterize the control setting for the crucible movement; the measured diameter is used to characterize the actual diameter of the crystal at the corresponding time or at the corresponding crystal growth position; and the CCD temperature measurement data is used to characterize the temperature measurement state related to crystal growth during the shoulder formation process.

[0184] In this embodiment, the crystal pulling power ratio, crystal rise setting, crucible rise setting, and CCD temperature measurement data can be used as process status data during the historical shoulder formation process. The measured diameters are arranged according to the corresponding time or the corresponding crystal growth position to form historical diameter data. The above-mentioned process status data and historical diameter data can be used as training samples to construct a diameter prediction model.

[0185] E2: Preprocess the historical data to obtain preprocessed data for constructing training samples.

[0186] Since the unit length data and other time series data in different historical shoulder-lifting processes may not correspond directly, and there may be missing or outlier values ​​in the original measurement data, the historical shoulder-lifting data can be uniformly processed before constructing training samples.

[0187] Specifically, unit length and other time series data can be interpolated to integer unit lengths, so that each integer unit length has corresponding crystal-driving power ratio, crystal rise setting, crucible rise setting, measurement diameter, and CCD temperature measurement data. Thus, data from different historical shoulder-forming processes can be organized and compared according to the same crystal growth position.

[0188] Furthermore, since the diameter prediction model targets the diameter data corresponding to the next future moment, so as to determine the predicted shoulder morphology data based on the future diameter data, the measured diameter can be time-shifted. In one specific implementation, the future control moment can be the moment corresponding to one minute after the current moment. The measured diameter can be shifted forward by one minute, using the process status data and historical diameter data corresponding to the current moment as input data, and the measured diameter corresponding to one minute after the current moment as the future diameter prediction target.

[0189] For example, for a specific historical control moment, the crystal-driving power ratio, crystal rise setting, crucible rise setting, CCD temperature measurement data, and the measured diameter sequence before that historical control moment can be used as model inputs, and the measured diameter one minute after that historical control moment can be used as the model output target. Multiple samples can be generated using the inputs and outputs corresponding to multiple historical control moments to train the diameter prediction model.

[0190] Furthermore, all input features and the future diameter data used as the model output target can be normalized to map data of different dimensions to a unified data interval, thereby reducing the impact of different data dimensions on the model training process. For missing or outlier values ​​in historical data, interpolation or removal can be performed to ensure the continuity and effectiveness of the training data.

[0191] E3: Construct training samples corresponding to the nonlinear autoregressive input structure based on preprocessed data.

[0192] The nonlinear autoregressive input structure, also known as the NARX input structure, is used to predict future diameter data by combining external process status data and historical diameter sequences. In this embodiment, the external process status data may include the crystal pulling power ratio, crystal rise setting, crucible rise setting, and CCD temperature measurement data, while the historical diameter sequence may include the measured diameters corresponding to several times prior to the current time.

[0193] Specifically, for each historical data sample, the process status data at the corresponding historical moment can be combined with the measured diameter at several moments prior to that historical moment to form a nonlinear autoregressive input vector. The historical diameter sequence reflects the growth and change characteristics of the crystal diameter before that historical moment, while the process status data reflects the control and measurement states affecting crystal growth. Therefore, by concatenating the historical diameter sequence with the process status data to form a multidimensional input vector, the model can simultaneously utilize the existing diameter change trend of the crystal and the corresponding process control states to predict future diameter data.

[0194] Furthermore, to improve the diameter prediction model's ability to capture time dependencies, the dataset formed by multiple nonlinear autoregressive input vectors can be further packaged. Specifically, the nonlinear autoregressive input vectors corresponding to multiple consecutive historical moments can be combined into a time series segment, and the future diameter data following this time series segment can be used as the corresponding model output target, thereby forming supervised learning samples suitable for recurrent neural networks.

[0195] Therefore, the diameter prediction model can not only obtain process state data and historical diameter data at a single moment, but also obtain state changes at multiple consecutive moments to identify the relationship between crystal rise setting, temperature state and measured diameter changes over time, thereby improving the stability and accuracy of future diameter predictions.

[0196] E4: Construct and train a diameter prediction model based on training samples.

[0197] In one specific implementation, the core of the diameter prediction model can be a bidirectional long short-term memory network, also known as a BiLSTM network. The bidirectional long short-term memory network is used to perform sequence modeling of time segments corresponding to multiple consecutive time points in order to capture the complex nonlinear characteristics of the crystal diameter changing over time.

[0198] Furthermore, a multi-head attention mechanism can be introduced into the output of the bidirectional long short-term memory network. This mechanism is used to identify moments and data features in historical time series that have a significant impact on future diameter prediction. For example, changes in crystal rise settings, CCD temperature measurement data, or measured diameter at certain moments in a historical time series may have a significant impact on future diameter data. The multi-head attention mechanism can improve the model's focus on these key moments and data features.

[0199] In one possible implementation, residual connections and layer normalization can be introduced into the diameter prediction model. Residual connections and layer normalization are used to improve the stability of the model training process and reduce the risk of gradient vanishing during training. The output layer of the diameter prediction model can be a fully connected layer, which outputs the predicted diameter data corresponding to future control moments.

[0200] In the process of training the diameter prediction model, multiple training samples constructed based on historical shoulder data can be divided into training set and test set. The diameter prediction model is trained using the training set, and the prediction ability of the diameter prediction model on data that was not involved in the training is evaluated using the test set, thereby verifying the generalization ability of the model.

[0201] In one specific implementation, mean squared error can be used as the loss function of the diameter prediction model to evaluate the difference between the predicted diameter data output by the model and the future diameter data that serves as the model's output target. An early stopping strategy can also be introduced, with the number of early stops set to 5. If the validation error no longer decreases during 5 consecutive validation iterations, model training can be terminated to reduce the risk of the model overfitting the training data.

[0202] Furthermore, a dynamic learning rate adjustment method can be used. In one specific implementation, if the loss function value does not decrease after three consecutive iterations, the learning rate can be reduced by 0.05 to adjust the magnitude of parameter updates during model training.

[0203] Using the above method, a diameter prediction model can be obtained to predict the predicted diameter data for future control moments based on the process state data corresponding to the current control moment, the historical diameter sequence before the current control moment, and the candidate crystal rise rate compensation amount.

[0204] E5: For each candidate crystal rise rate compensation amount, the corresponding predicted diameter data is determined using the diameter prediction model.

[0205] During the actual shoulder formation process of Czochralski single-crystal silicon, process status data corresponding to the current control moment and historical diameter sequences prior to the current control moment can be obtained. The process status data corresponding to the current control moment may include the crystal pulling power ratio, crystal rise setting, crucible rise setting, and CCD temperature measurement data at the current control moment. The historical diameter sequence may include the measured diameters at several moments prior to the current control moment.

[0206] For any candidate crystal rise rate compensation value among multiple candidate crystal rise rate compensation values, this candidate value can be used as the crystal rise rate adjustment input to be evaluated in the current control process. The candidate value, the process state data corresponding to the current control moment, and the historical diameter sequence prior to the current control moment are input into the diameter prediction model. Based on the input process state data, historical diameter variation characteristics, and the candidate value, the diameter prediction model outputs the predicted diameter data for future control moments when the candidate value is used.

[0207] In one specific implementation, the future control time can be the control time one minute after the current control time. In this case, for each candidate crystal rise rate compensation amount, the predicted diameter data one minute after adopting that candidate crystal rise rate compensation amount can be predicted using a diameter prediction model. Then, based on the predicted diameter data corresponding to each candidate crystal rise rate compensation amount, the corresponding predicted absolute angle and predicted relative angle can be determined, and the corresponding total substitution value can be further calculated.

[0208] For example, after determining multiple candidate crystal rise rate compensation values ​​in the current control process, each candidate crystal rise rate compensation value can be input into the diameter prediction model to obtain the predicted diameter data for the next time step corresponding to each candidate crystal rise rate compensation value. For each predicted diameter data for the next time step, the predicted shoulder morphology data corresponding to the candidate crystal rise rate compensation value can be further determined, and the suitability of the candidate crystal rise rate compensation value for crystal rise rate adjustment in the current shoulder placement process can be evaluated based on the difference between the predicted shoulder morphology data and the target shoulder morphology data.

[0209] Therefore, a nonlinear autoregressive input structure is constructed based on the process status data and historical diameter sequence during the historical shoulder formation process. A time-series neural network model is then used to learn the future diameter change relationship under different process states and historical diameter variations. This enables the diameter prediction model to predict the diameter data at future control moments by combining the existing diameter change trend of the crystal. Multiple candidate crystal rise rate compensation values ​​are used as inputs for crystal rise rate adjustment to be evaluated. The diameter prediction model is then used to determine the predicted diameter data corresponding to each candidate crystal rise rate compensation value. This allows for the prediction of the impact of different crystal rise rate compensation values ​​on the future shoulder morphology before actual crystal rise rate adjustment. This provides a predictive basis for subsequently selecting the target crystal rise rate compensation value that makes the predicted shoulder morphology close to the target shoulder morphology, improving the timeliness of crystal rise rate adjustment.

[0210] In one possible implementation, a dual-loop control architecture combining a proportional-integral-derivative (PID) controller and a model predictive controller can be used to control the crystal rise rate during the shoulder formation process of Czochralski-grown monocrystalline silicon. The PID controller, acting as the outer loop controller, determines the base crystal rise rate based on the diameter deviation at the current control moment to ensure macroscopic tracking of the crystal diameter during the shoulder formation process. The model predictive controller determines the target crystal rise rate compensation amount based on predicted shoulder morphology data corresponding to different candidate crystal rise rate compensation amounts, thus pre-compensating for the base crystal rise rate. See F1-F3 for details.

[0211] F1: Based on the diameter deviation of the Czochralski single crystal silicon at the current control moment, the basic crystal rise rate is determined by a proportional-integral-derivative controller.

[0212] Here, diameter deviation is data used to characterize the difference between the current diameter and the corresponding target diameter of the Czochralski single crystal silicon at the current control moment. The base crystal rise rate is the crystal rise rate determined by the proportional-integral-derivative controller based on the diameter deviation, used to control the shoulder growth of the Czochralski single crystal silicon.

[0213] In one implementation, the current diameter data corresponding to the current control moment and the target diameter data at the crystal growth position corresponding to the current control moment can be obtained. Then, based on the difference between the current diameter data and the target diameter data, the diameter deviation corresponding to the current control moment can be determined, and this diameter deviation can be input into a proportional-integral-derivative (PID) controller to determine the basic crystal growth rate.

[0214] In this embodiment, a proportional-integral-derivative (PID) controller is used to provide feedback control over the overall deviation between the crystal diameter and the target diameter during the shoulder formation process, ensuring that the crystal diameter grows according to the target diameter's changing trend. It should be noted that the base crystal rise rate determined by the PID controller is primarily used to ensure macroscopic tracking during the shoulder formation process, while advance adjustments for future changes in the outer contour of the crystal shoulder can be achieved through compensation from the target crystal rise rate.

[0215] F2: The target crystal rise rate compensation is added to the base crystal rise rate to obtain the target crystal rise rate.

[0216] The target crystal rise rate compensation is determined based on the differences between the predicted shoulder morphology data and the target shoulder morphology data corresponding to multiple candidate crystal rise rate compensations, and is used to correct the base crystal rise rate. The target crystal rise rate is the crystal rise rate used to actually control the shoulder growth of Czochralski single crystal silicon at the current control moment.

[0217] Specifically, the base crystal rise rate can be used as the basic output for crystal rise rate control during the shoulder placement process, and the target crystal rise rate compensation can be used as the compensation output superimposed on this basic output. The target crystal rise rate compensation determined by the model predictive controller can be added to the base crystal rise rate determined by the proportional-integral-derivative controller, and the resulting crystal rise rate can be determined as the target crystal rise rate.

[0218] In this embodiment, the proportional-integral-derivative (PID) controller determines the base crystal rise rate based on the diameter deviation at the current control moment, and the model predictive controller determines the target crystal rise rate compensation amount based on the future shoulder shape corresponding to each candidate crystal rise rate compensation amount. Therefore, by superimposing the target crystal rise rate compensation amount with the base crystal rise rate, it is possible to further correct the future outer contour change trend of the crystal shoulder in advance, while ensuring macroscopic tracking of the crystal diameter with the base crystal rise rate.

[0219] For example, if the difference between the current diameter and the corresponding target diameter is small, but predictions indicate that continuing growth at the base crystal rise rate may cause the future shoulder shape to deviate from the target shoulder shape, the base crystal rise rate can be corrected by superimposing a compensation amount based on the target crystal rise rate. Therefore, the crystal rise rate can be adjusted based on the predicted future shoulder shape without waiting for the crystal shoulder to actually form a significant diameter deviation.

[0220] F3: Adjust the crystal rise rate of the Czochralski single crystal silicon during the shoulder formation process according to the target crystal rise rate.

[0221] After determining the target crystal rise rate, a corresponding crystal rise rate control command can be generated based on the target crystal rise rate, and the crystal rise rate of the Czochralski single crystal silicon during the shoulder formation process can be adjusted according to the crystal rise rate control command.

[0222] One implementation approach involves acquiring the current diameter data and determining the corresponding diameter deviation at each control moment. A proportional-integral-derivative (PID) controller is then used to determine the base crystal growth rate for that control moment. Simultaneously, based on the growth state data at the current control moment, multiple candidate crystal growth rate compensation amounts are evaluated for future diameter prediction and predicted shoulder morphology to determine the target crystal growth rate compensation amount for that control moment. This target crystal growth rate compensation amount is then superimposed on the base crystal growth rate to obtain the target crystal growth rate for that control moment. The crystal is then controlled to continue shoulder growth according to this target crystal growth rate.

[0223] In one possible implementation, to improve the reliability of the crystal rise speed control process, an anomaly handling mechanism can be set up for the determination of the target crystal rise speed compensation amount. When the diameter prediction model lacks sufficient data, fails to predict, fails to determine a valid candidate crystal rise speed compensation amount, or encounters an unknown anomaly in the program, the target crystal rise speed compensation amount corresponding to the previous control moment can be used. When the angle data determined based on the predicted diameter data is less than 0, the current crystal rise speed adjustment based on the target crystal rise speed compensation amount can be skipped. When the crystal rise speed obtained after superimposing the candidate crystal rise speed compensation amount onto the base crystal rise speed is less than a preset lower limit or greater than a preset upper limit, control based on that candidate crystal rise speed compensation amount can be skipped. This avoids unreasonable changes in the crystal rise speed caused by abnormal prediction data, compensation amounts, or program operation, improving the safety and stability of the chip release control process.

[0224] Therefore, by determining the basic crystal rise rate using a proportional-integral-derivative (PID) controller based on the diameter deviation at the current control moment, the crystal rise rate control can take into account the overall deviation between the crystal diameter and the target diameter change trend. The target crystal rise rate is obtained by superimposing the target crystal rise rate compensation amount determined based on predicted shoulder morphology data with the basic crystal rise rate. This allows for advance correction of the crystal rise rate based on the future outer contour morphology of the crystal shoulder, while ensuring macroscopic tracking during the shoulder formation process. This reduces the adjustment lag caused by relying solely on feedback adjustment based on the current diameter deviation, improves the timeliness and stability of crystal rise rate adjustment during the shoulder formation process, and reduces the risk of breakage.

[0225] See Figure 2 , Figure 2 This is a schematic diagram of a crystal rise rate control device provided in an embodiment of this application. The device 200 includes:

[0226] The acquisition unit 201 is used to acquire target shoulder morphology data, which is used to characterize the target outer contour morphology of the crystal shoulder as the crystal growth position changes during the shoulder formation process of Czochralski single crystal silicon.

[0227] The acquisition unit 201 is also used to acquire the growth state data of the Czochralski single crystal silicon at the current control moment;

[0228] Determining unit 202 is used to determine multiple candidate crystal rise rate compensation amounts;

[0229] Prediction unit 203 is used to predict the predicted diameter data of the Czochralski single crystal silicon at a future control moment, based on the growth state data and the candidate crystal rise rate compensation amount, for each of the multiple candidate crystal rise rate compensation amounts.

[0230] The determining unit 202 is further configured to determine the predicted shoulder morphology data corresponding to each candidate crystal rise rate compensation amount based on the predicted diameter data corresponding to each candidate crystal rise rate compensation amount.

[0231] The determining unit 202 is further configured to determine the target crystal rise speed compensation amount from the multiple candidate crystal rise speed compensation amounts based on the difference between the predicted shoulder shape data corresponding to each candidate crystal rise speed compensation amount and the target shoulder shape data.

[0232] The adjustment unit 204 is used to adjust the crystal rise rate of the Czochralski single crystal silicon during the shoulder formation process according to the target crystal rise rate compensation amount.

[0233] Optionally, the target shoulder morphology data includes the target absolute angle curve, the target relative angle curve, the absolute angle allowable range, and the relative angle allowable range. The acquisition unit 201 is specifically used for:

[0234] Obtain the historical diameter curves corresponding to multiple historical shoulder-raising processes;

[0235] Based on multiple historical diameter curves, determine the target diameter curve, the upper diameter boundary curve, and the lower diameter boundary curve;

[0236] Based on the relationship between the radius corresponding to each crystal growth position in the target diameter curve and the crystal growth position, the target absolute angle curve is determined. The target absolute angle curve is used to characterize the degree of expansion of the target outer contour of the crystal shoulder at the corresponding crystal growth position.

[0237] Based on the relationship between the radius change and the crystal growth position change at different crystal growth positions in the target diameter curve, the target relative angle curve is determined. The target relative angle curve is used to characterize the degree of change of the target local outer contour of the crystal shoulder at the corresponding crystal growth position.

[0238] For each diameter boundary curve in the upper and lower diameter boundary curves, the corresponding absolute angle boundary curve is determined based on the relationship between the radius corresponding to each crystal growth position and the crystal growth position in the diameter boundary curve. The corresponding relative angle boundary curve is determined based on the relationship between the radius change corresponding to different crystal growth positions and the crystal growth position change in the diameter boundary curve.

[0239] The absolute angle allowable range is determined based on the absolute angle boundary curves corresponding to the upper and lower diameter boundary curves, respectively, and the relative angle allowable range is determined based on the relative angle boundary curves corresponding to the upper and lower diameter boundary curves, respectively.

[0240] Optionally, the acquisition unit 201 is specifically used for:

[0241] From the multiple historical diameter curves, select multiple diameter curves to be processed whose equal diameter lengths meet the preset length conditions;

[0242] The sampling positions of the multiple diameter curves to be processed are aligned to obtain multiple diameter curves to be screened.

[0243] The median diameter curve is determined based on the median diameter at each sampling position of the multiple diameter curves to be screened.

[0244] For each diameter curve to be screened, the deviation score corresponding to the diameter curve to be screened is determined based on the mean square error, correlation difference, amplitude deviation and mean deviation between the diameter curve to be screened and the median diameter curve.

[0245] Based on the deviation scores corresponding to each of the diameter curves to be screened, the multiple diameter curves to be screened are iteratively screened, and based on the multiple diameter curves to be screened retained after screening, the target diameter curve, the upper boundary curve of the diameter, and the lower boundary curve of the diameter are determined.

[0246] Optionally, the growth state data includes the current diameter data corresponding to the current control moment, the predicted shoulder morphology data includes the predicted absolute angle and the predicted relative angle, and the determining unit 202 is specifically used for:

[0247] Based on the current diameter data, determine the current radius data;

[0248] For each candidate crystal rise rate compensation amount, the predicted radius data is determined based on the corresponding predicted diameter data;

[0249] Based on the relationship between the predicted radius data and the crystal growth position corresponding to the future control time, the predicted absolute angle corresponding to the candidate crystal rise rate compensation amount is determined;

[0250] Based on the radius change between the predicted radius data and the current radius data, and the position change between the crystal growth position corresponding to the future control time and the crystal growth position corresponding to the current control time, the predicted relative angle corresponding to the candidate crystal rise rate compensation is determined.

[0251] For each candidate crystal growth rate compensation amount, the angle deviation cost is determined based on the difference between the predicted absolute angle and the target absolute angle curve corresponding to the crystal growth position at the future control time, and the difference between the predicted relative angle and the target relative angle curve corresponding to the crystal growth position at the future control time.

[0252] The compensation magnitude cost is determined based on the candidate crystal rise rate compensation amount, and the compensation smoothing cost is determined based on the difference between the candidate crystal rise rate compensation amount and the target crystal rise rate compensation amount corresponding to the previous control moment.

[0253] The total compensation value corresponding to the candidate crystal rise rate compensation amount is determined based on the angle deviation compensation value, the compensation amplitude compensation value, and the compensation smoothing compensation value.

[0254] The candidate crystal rise rate compensation amount with the lowest total value is determined as the target crystal rise rate compensation amount.

[0255] Optionally, the growth state data includes the current absolute angle and the current relative angle. The current absolute angle is determined based on the relationship between the current radius data and the crystal growth position corresponding to the current control time. The current relative angle is determined based on the radius change between the current radius data and historical radius data before the current control time, and the position change between corresponding crystal growth positions. The determining unit 202 is specifically used for:

[0256] In response to the current absolute angle being within the allowable range of the absolute angle and the current relative angle being within the allowable range of the relative angle, a plurality of candidate crystal rise rate compensation amounts are determined according to a first compensation amount range;

[0257] In response to the current absolute angle exceeding the allowable range of the absolute angle, or the current relative angle exceeding the allowable range of the relative angle, a plurality of candidate crystal rise rate compensation amounts are determined according to a second compensation amount range, wherein the second compensation amount range is greater than the first compensation amount range;

[0258] Wherein, when the current absolute angle or the current relative angle exceeds the corresponding allowable range, the evaluation weight of the angle deviation value corresponding to the angle exceeding the corresponding allowable range is greater than the evaluation weight when the angle does not exceed the corresponding allowable range.

[0259] Optionally, the growth status data includes the process status data at the current control moment and the historical diameter sequence before the current control moment. The prediction unit 203 is specifically used for:

[0260] For each candidate crystal rise rate compensation amount, the candidate crystal rise rate compensation amount, the process status data, and the historical diameter sequence are input into the diameter prediction model to obtain the predicted diameter data corresponding to the candidate crystal rise rate compensation amount;

[0261] The diameter prediction model is a time-series neural network model based on a nonlinear autoregressive input structure. The nonlinear autoregressive input structure is used to combine the process status data of the historical shoulder-laying process and the corresponding historical diameter sequence as the model input, and to take the future diameter data located after the historical diameter sequence as the model output target.

[0262] Optionally, the device 200 further includes a base speed acquisition unit 201, used for:

[0263] The basic crystal rise rate is determined by a proportional-integral-derivative controller based on the diameter deviation of the Czochralski single crystal silicon at the current control moment.

[0264] The adjustment unit 204 is specifically used for:

[0265] The target crystal rise rate compensation amount is added to the base crystal rise rate to obtain the target crystal rise rate;

[0266] Adjust the crystal rise rate of the Czochralski single crystal silicon during the shoulder formation process according to the target crystal rise rate.

[0267] See Figure 3 This application also provides a computer device, which includes a memory 301 and a processor 302.

[0268] The memory is used to store computer programs and to transfer the computer programs to the processor;

[0269] The processor is used to execute the method of the above method embodiment according to the computer program.

[0270] This application also provides a computer-readable storage medium, characterized in that the computer-readable storage medium is used to store a computer program, the computer program being used to execute the method of the above-described method embodiments.

[0271] This application also provides a computer program product including a computer program, which, when run on a computer device, causes the computer device to perform the method described in the above method embodiments.

[0272] It should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems or apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and relevant parts can be referred to the method section.

[0273] The term "comprising" and its variations as used herein are open-ended inclusions, meaning "including but not limited to". The term "based on" means "at least partially based on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments". Definitions of other terms will be given in the description below.

[0274] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0275] It should also be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0276] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0277] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for controlling crystal rise speed, characterized in that, The method includes: Acquire target shoulder morphology data, which is used to characterize the target outer contour morphology of the crystal shoulder as the crystal growth position changes during the shoulder formation process of Czochralski single crystal silicon. Obtain the growth state data of the Czochralski single crystal silicon at the current control moment; Determine multiple candidate crystal rise rate compensation values; For each of the multiple candidate crystal rise rate compensation amounts, based on the growth state data and the candidate crystal rise rate compensation amount, predict the predicted diameter data of the Czochralski single crystal silicon at a future control moment; Based on the predicted diameter data corresponding to each candidate crystal rise rate compensation amount, the predicted shoulder morphology data corresponding to each candidate crystal rise rate compensation amount is determined; Based on the difference between the predicted shoulder shape data corresponding to each of the candidate crystal rise rate compensation amounts and the target shoulder shape data, the target crystal rise rate compensation amount is determined from the multiple candidate crystal rise rate compensation amounts; The crystal rise rate of the Czochralski single crystal silicon during the shoulder formation process is adjusted according to the target crystal rise rate compensation amount.

2. The method according to claim 1, characterized in that, The target shoulder morphology data includes the target absolute angle curve, the target relative angle curve, the allowable absolute angle range, and the allowable relative angle range. Acquiring the target shoulder morphology data includes: Obtain the historical diameter curves corresponding to multiple historical shoulder-raising processes; Based on multiple historical diameter curves, determine the target diameter curve, the upper diameter boundary curve, and the lower diameter boundary curve; Based on the relationship between the radius corresponding to each crystal growth position in the target diameter curve and the crystal growth position, the target absolute angle curve is determined. The target absolute angle curve is used to characterize the degree of expansion of the target outer contour of the crystal shoulder at the corresponding crystal growth position. Based on the relationship between the radius change and the crystal growth position change at different crystal growth positions in the target diameter curve, the target relative angle curve is determined. The target relative angle curve is used to characterize the degree of change of the target local outer contour of the crystal shoulder at the corresponding crystal growth position. For each diameter boundary curve in the upper and lower diameter boundary curves, the corresponding absolute angle boundary curve is determined based on the relationship between the radius corresponding to each crystal growth position and the crystal growth position in the diameter boundary curve. The corresponding relative angle boundary curve is determined based on the relationship between the radius change corresponding to different crystal growth positions and the crystal growth position change in the diameter boundary curve. The absolute angle allowable range is determined based on the absolute angle boundary curves corresponding to the upper and lower diameter boundary curves, respectively, and the relative angle allowable range is determined based on the relative angle boundary curves corresponding to the upper and lower diameter boundary curves, respectively.

3. The method according to claim 2, characterized in that, The step of determining the target diameter curve, the upper diameter boundary curve, and the lower diameter boundary curve based on multiple historical diameter curves includes: From the multiple historical diameter curves, select multiple diameter curves to be processed whose equal diameter lengths meet the preset length conditions; The sampling positions of the multiple diameter curves to be processed are aligned to obtain multiple diameter curves to be screened. The median diameter curve is determined based on the median diameter at each sampling position of the multiple diameter curves to be screened. For each diameter curve to be screened, the deviation score corresponding to the diameter curve to be screened is determined based on the mean square error, correlation difference, amplitude deviation and mean deviation between the diameter curve to be screened and the median diameter curve. Based on the deviation scores corresponding to each of the diameter curves to be screened, the multiple diameter curves to be screened are iteratively screened, and based on the multiple diameter curves to be screened retained after screening, the target diameter curve, the upper boundary curve of the diameter, and the lower boundary curve of the diameter are determined.

4. The method according to claim 2, characterized in that, The growth state data includes the current diameter data corresponding to the current control moment, and the predicted shoulder morphology data includes the predicted absolute angle and the predicted relative angle. Determining the predicted shoulder morphology data corresponding to each candidate crystal rise rate compensation amount based on the predicted diameter data corresponding to each candidate crystal rise rate compensation amount includes: Based on the current diameter data, determine the current radius data; For each candidate crystal rise rate compensation amount, the predicted radius data is determined based on the corresponding predicted diameter data; Based on the relationship between the predicted radius data and the crystal growth position corresponding to the future control time, the predicted absolute angle corresponding to the candidate crystal rise rate compensation amount is determined; Based on the radius change between the predicted radius data and the current radius data, and the position change between the crystal growth position corresponding to the future control time and the crystal growth position corresponding to the current control time, the predicted relative angle corresponding to the candidate crystal rise rate compensation is determined. The step of determining the target crystal rise rate compensation amount from multiple candidate crystal rise rate compensation amounts based on the difference between the predicted shoulder shape data corresponding to each of the candidate crystal rise rate compensation amounts and the target shoulder shape data includes: For each candidate crystal growth rate compensation amount, the angle deviation cost is determined based on the difference between the predicted absolute angle and the target absolute angle curve corresponding to the crystal growth position at the future control time, and the difference between the predicted relative angle and the target relative angle curve corresponding to the crystal growth position at the future control time. The compensation magnitude cost is determined based on the candidate crystal rise rate compensation amount, and the compensation smoothing cost is determined based on the difference between the candidate crystal rise rate compensation amount and the target crystal rise rate compensation amount corresponding to the previous control moment. The total compensation value corresponding to the candidate crystal rise rate compensation amount is determined based on the angle deviation compensation value, the compensation amplitude compensation value, and the compensation smoothing compensation value. The candidate crystal rise rate compensation amount with the lowest total value is determined as the target crystal rise rate compensation amount.

5. The method according to claim 4, characterized in that, The growth state data includes the current absolute angle and the current relative angle. The current absolute angle is determined based on the relationship between the current radius data and the crystal growth position corresponding to the current control time. The current relative angle is determined based on the radius change between the current radius data and historical radius data before the current control time, and the position change between corresponding crystal growth positions. Determining multiple candidate crystal rise rate compensation amounts includes: In response to the current absolute angle being within the allowable range of the absolute angle and the current relative angle being within the allowable range of the relative angle, a plurality of candidate crystal rise rate compensation amounts are determined according to a first compensation amount range; In response to the current absolute angle exceeding the allowable range of the absolute angle, or the current relative angle exceeding the allowable range of the relative angle, a plurality of candidate crystal rise rate compensation amounts are determined according to a second compensation amount range, wherein the second compensation amount range is greater than the first compensation amount range; Wherein, when the current absolute angle or the current relative angle exceeds the corresponding allowable range, the evaluation weight of the angle deviation value corresponding to the angle exceeding the corresponding allowable range is greater than the evaluation weight when the angle does not exceed the corresponding allowable range.

6. The method according to claim 4, characterized in that, The growth state data includes the process state data at the current control moment and the historical diameter sequence before the current control moment. The prediction of the predicted diameter data of the Czochralski-grown monocrystalline silicon at future control moments, based on the growth state data and the candidate crystal rise rate compensation amounts, for each of the multiple candidate crystal rise rate compensation amounts, includes: For each candidate crystal rise rate compensation amount, the candidate crystal rise rate compensation amount, the process status data, and the historical diameter sequence are input into the diameter prediction model to obtain the predicted diameter data corresponding to the candidate crystal rise rate compensation amount; The diameter prediction model is a time-series neural network model based on a nonlinear autoregressive input structure. The nonlinear autoregressive input structure is used to combine the process status data of the historical shoulder-laying process and the corresponding historical diameter sequence as the model input, and to take the future diameter data located after the historical diameter sequence as the model output target.

7. The method according to any one of claims 1-6, characterized in that, The method further includes: The basic crystal rise rate is determined by a proportional-integral-derivative controller based on the diameter deviation of the Czochralski single crystal silicon at the current control moment. The step of adjusting the crystal rise rate of the Czochralski single crystal silicon during the shoulder formation process according to the target crystal rise rate compensation amount includes: The target crystal rise rate compensation amount is added to the base crystal rise rate to obtain the target crystal rise rate; Adjust the crystal rise rate of the Czochralski single crystal silicon during the shoulder formation process according to the target crystal rise rate.

8. A crystal riser speed control device, characterized in that, The device includes: The acquisition unit is used to acquire target shoulder morphology data, which is used to characterize the target outer contour morphology of the crystal shoulder as the crystal growth position changes during the shoulder formation process of Czochralski single crystal silicon. The acquisition unit is also used to acquire the growth state data of the Czochralski single crystal silicon at the current control moment; A determination unit is used to determine the compensation amount for multiple candidate crystal rise rates; The prediction unit is used to predict the predicted diameter data of the Czochralski single crystal silicon at a future control moment, based on the growth state data and the candidate crystal rise rate compensation amount, for each of the multiple candidate crystal rise rate compensation amounts. The determining unit is further configured to determine the predicted shoulder morphology data corresponding to each candidate crystal rise rate compensation amount based on the predicted diameter data corresponding to each candidate crystal rise rate compensation amount. The determining unit is further configured to determine the target crystal rise rate compensation amount from the plurality of candidate crystal rise rate compensation amounts based on the difference between the predicted shoulder shape data corresponding to each candidate crystal rise rate compensation amount and the target shoulder shape data. An adjustment unit is used to adjust the crystal rise rate of the Czochralski single crystal silicon during the shoulder formation process according to the target crystal rise rate compensation amount.

9. A computer device, characterized in that, The computer device includes a processor and memory: The memory is used to store computer programs and to transfer the computer programs to the processor; The processor is configured to perform the method according to any one of claims 1-7 according to the computer program.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store a computer program for performing the method according to any one of claims 1-7.

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