Method and system for controlling thermal field based on size self-adapting single crystal silicon rod

Abstract

The present application belongs to the technical field of single crystal silicon rod manufacturing, and particularly relates to a heat field control method and system based on size self-adaptive single crystal silicon rod, which comprises the following steps: arranging a thermocouple array to collect temperature and construct a three-dimensional temperature field data set; calculating axial and radial temperature gradients through a finite difference operator with direction correction weight, and performing non-uniform resampling on the space step when the cosine of the included angle is lower than the lower limit; taking the axial radial temperature gradient ratio as an interface shape characteristic quantity, calculating the gradient fluctuation rate through a sliding time window; combining the diameter deviation, the pulling speed deviation and the gradient fluctuation rate to construct a feedback deviation quantity, generating a control command through an adjuster when the threshold value is exceeded, and decoupling and regulating the heater power and the height of the heat preservation screen; maintaining the radial temperature gradient in a preset interval and linearly translating and adjusting with the growth length in the constant diameter stage. The present application can improve the resolution accuracy and suppress the size fluctuation.

Description

Technical Field

[0001] This invention relates to the field of single-crystal silicon rod manufacturing technology. More specifically, this invention relates to a method and system for thermal field control of size-adaptive single-crystal silicon rods. Background Technology

[0002] In the Czochralski (CZ) single-crystal silicon growth process, the spatial distribution of the thermal field within the single-crystal furnace and the dynamic changes in the solid-liquid interface directly affect the growth rate, crystal diameter uniformity, and internal micro-defect level of the single-crystal silicon rod. Especially in the fabrication of large-size single-crystal silicon rods, due to the large heat capacity of the furnace, strong melt convection, and complex heat transfer paths, the solid-liquid interface is highly susceptible to strong thermal disturbances, leading to interface warping and temperature gradient distortion. If overheating or undercooling occurs in localized areas of the solid-liquid interface, the release of latent heat of crystallization will become unstable, causing abrupt changes in the crystal growth rate and drastic fluctuations in the diameter of the single-crystal silicon rod. In severe cases, this can even induce quality accidents such as polycrystalline formation, increased dislocation defects, or rod breakage.

[0003] Regarding quality control during the growth of single-crystal silicon rods, Chinese patent application CN121204810A discloses a method for preparing single-crystal silicon rods and a silicon wafer. In the constant-diameter stage, this application controls the crystal pulling rate within a first pulling speed range (0.5 mm / min - 1.1 mm / min) and the solid-liquid interface temperature gradient within a first gradient range (3℃ / cm - 5℃ / cm). By reducing the solid-liquid interface temperature gradient and lowering the crystal pulling rate, thermal field stability is enhanced, thereby extending the residence time of the single-crystal silicon rod in the high-temperature region. This provides sufficient conditions for the recombination reaction of interstitial atoms and vacancies in silicon, aiming to reduce the internal defect density of the single-crystal silicon rod and remove internal impurities.

[0004] However, in the calculation of temperature field and temperature gradient, existing technologies mostly use fixed grid space step size and fixed weight allocation to extract temperature gradients. This cannot adapt to the complex spatial state of solid-liquid interface bending, tilting, and local morphological abrupt warping under high-intensity convection. As a result, traditional orthogonal differential grids produce large truncation errors at abrupt surface changes, and the feature extraction accuracy of axial and radial temperature gradients is severely insufficient. Secondly, traditional control strategies mostly use fixed window widths to smooth the acquired data, failing to correlate the actual diameter of the single-crystal silicon rod, the change in crystal pulling speed, and the microscopic temperature gradient fluctuation state of the solid-liquid interface in modeling. This results in low sensitivity of the control system to dynamic thermal field disturbances, easily leading to control lag, regulation overshoot, or system oscillation.

[0005] Furthermore, existing crystal pulling equipment and control systems lack a cross-coupling and decoupling control mechanism for multiple actuators such as heater power and insulation screen height. When heater power adjustment and insulation screen height adjustment have cross-thermal effects on the thermodynamic temperature field, single feedback adjustment is prone to mutual interference, making it difficult to achieve coordinated and precise control of multiple actuators. Especially in the long-term constant diameter growth stage of the entire process cycle, as the crystal length continues to increase and the single-crystal silicon melt in the crucible gradually decreases, the continuous upward movement of the crucible causes the boundary heat dissipation conditions and long-term thermodynamic conditions of the thermal field in the single crystal furnace to drift slowly. If the control system still uses a fixed temperature gradient target range in the middle and later stages of the constant diameter stage without directional range translation adjustment and thermal field drift compensation, it will be unable to maintain the full-cycle stability of the radial temperature gradient, resulting in a significant decrease in the dimensional control accuracy of the single-crystal silicon rod in the middle and later stages, making it difficult to meet the requirements of high-precision diameter control throughout the entire life cycle. Summary of the Invention

[0006] To address the problems of insufficient accuracy in analyzing the solid-liquid interface temperature gradient, fixed feedback control parameters, weak coupling and adjustment capabilities of multiple execution variables, and insufficient compensation for thermal field drift during the constant diameter stage in existing technologies, which lead to diameter fluctuations and reduced crystallization quality in large-size single-crystal silicon rods, this invention provides solutions in the following aspects.

[0007] In a first aspect, the present invention provides a thermal field control method based on size-adaptive single-crystal silicon rods, comprising: S1, constructing a three-dimensional temperature field dataset and extracting the normal to the melting point isothermal surface, determining a direction correction weight based on the cosine and sine of the angle between the normal and the direction of gravity, calculating the axial and radial temperature gradients using a finite difference operator with the weights, and when the cosine of the angle is lower than a set lower limit, reducing the radial and axial spatial step sizes in the corresponding isothermal surface warping region, inserting densified grid nodes to perform non-uniform resampling, and recalculating the temperature gradients based on the densified grid; S2. Using the ratio of the temperature gradients as the interface shape feature quantity, the gradient fluctuation rate of the interface shape feature quantity is calculated through a sliding time window whose window width is adjusted with the cosine of the included angle. S3. Perform dimensionless calculations on the silicon rod diameter deviation, pulling speed deviation, and gradient volatility to construct a feedback deviation. When the feedback deviation exceeds a threshold, a proportional-integral-derivative controller generates a control command. Combined with the actuator transformation matrix, the heater power and the insulation screen height are decoupled and controlled. The proportional coefficient of the controller is configured to increase non-linearly with the increase of the absolute value of the silicon rod diameter deviation, and the integral time constant is configured to increase with the increase of the gradient volatility. S4. After entering the constant diameter stage, maintain the radial temperature gradient within the preset range, and perform translation adjustment on the preset range according to the slope of the average gradient fluctuation rate of the previous process stage as the growth length increases.

[0008] This invention improves the accuracy of temperature gradient calculation and analytical accuracy of isothermal surface warping regions by constructing a three-dimensional temperature field dataset and combining it with a finite difference operator with orientation correction weights and non-uniform resampling. It also enhances the system's response speed to complex thermal field changes by constructing feedback deviations using parameters such as gradient volatility and performing decoupled control, effectively suppressing dimensional fluctuations during crystal pulling. Furthermore, it compensates for thermal field drift by translating a preset interval during the constant diameter stage, ensuring the stability of the thermal field throughout the entire cycle, thereby improving the diameter uniformity and crystal formation quality of single-crystal silicon rods.

[0009] Preferably, the step of constructing a three-dimensional temperature field dataset and extracting the normal of the melting point isothermal surface includes: obtaining the coordinate parameters of all measuring points relative to the growth center to establish a spatial coordinate mapping matrix, synchronously acquiring discrete temperature signals, combining the spatial coordinate mapping matrix to interpolate and fit the discrete temperature signals into a three-dimensional temperature field spatial distribution model, and adding a timestamp identifier to the three-dimensional temperature field spatial distribution model to construct the three-dimensional temperature field dataset.

[0010] This invention combines spatial coordinate mapping matrix to interpolate and fit discrete temperature data, thereby constructing a high-resolution and smooth three-dimensional temperature field spatial distribution model, providing an accurate reference data pool for subsequent finite difference calculation of microscopic temperature gradients and thermodynamic feature tracing.

[0011] Preferably, the step of determining the direction correction weight includes: calculating the dot product of the normal of the melting point isothermal surface and the direction of gravity to construct the cosine of the included angle; using the value 1 as a reference term, calculating the difference between the value 1 and the cosine of the included angle and adding the difference to the reference term to construct the axial direction correction weight; and adding the sine of the included angle to the reference term to construct the radial direction correction weight.

[0012] This invention incorporates the angle between the melting point isothermal surface and the direction of gravity into the construction of the orientation correction weight, and uses the normal tilt of the geometric interface as a correction factor, which effectively reduces the truncation error generated by the traditional orthogonal differential mesh at the abrupt change of the surface, and improves the calculation stability of the temperature gradient characteristic quantity in the warped region.

[0013] Preferably, the step of performing non-uniform resampling on the spatial step size of the finite difference operator includes: extracting the isothermal surface warping region where the included angle cosine is lower than the set lower limit, reducing the radial and axial spatial step sizes and inserting densified mesh nodes within the isothermal surface warping region, and recalculating the axial and radial temperature gradients based on the densified mesh nodes and spline interpolation algorithm.

[0014] This invention reduces the spatial step size, inserts denser grid nodes, and recalculates the gradient within the warped region of the isothermal surface. This eliminates numerical instability caused by abrupt changes in the surface and further improves the analytical accuracy of the spatial distribution characteristics of the warped region of the isothermal surface.

[0015] Preferably, the step of calculating the gradient volatility using a sliding time window whose window width is adjusted according to the cosine of the included angle includes: updating the current window width of the sliding time window to the larger of the product of a preset reference window width and the cosine of the included angle and a preset minimum window width threshold; calculating the differential rate of change of the interface shape feature quantity between adjacent sampling points within the sliding time window; and obtaining the root mean square value of all the differential rates of change to constitute the gradient volatility.

[0016] This invention dynamically adjusts the width of the sliding time window. When the interface is stable, it maintains a large window width to provide a smoothing effect for low-frequency data. When the liquid surface is churning, it tightens the window width to improve the response speed to short-term thermal field fluctuations, thereby ensuring the statistical validity of the root mean square calculation and the anti-interference capability of the system.

[0017] Preferably, the step of constructing the feedback deviation includes: performing a division operator operation on the silicon rod diameter deviation, the pulling speed deviation, and the gradient volatility to output dimensionless parameters, and performing a weighted summation operation on all the dimensionless parameters according to a preset weight constant to construct the feedback deviation used to determine the threshold triggering condition.

[0018] This invention constructs a comprehensive feedback deviation by integrating multi-dimensional parameters, which can reduce the control lag caused by the macroscopic thermal inertia of the system, reduce the impact of thermal stress imbalance in the edge cooling zone on solid-liquid interface warping, and effectively suppress micro-oscillations at the crystallization front.

[0019] Preferably, the step of decoupling the control commands by combining the actuator conversion matrix to adjust the heater power and the insulation screen height separately includes: independently applying step control signals to the heater power and the insulation screen height, measuring and recording the steady-state response changes of the temperature gradient and interface characteristics, and obtaining the actuator conversion matrix offline based on the steady-state response changes; expanding the control commands into a two-dimensional control demand vector, multiplying the two-dimensional control demand vector by the actuator conversion matrix to perform signal decoupling operations, and outputting independent target heater power adjustment and target insulation screen height adjustment.

[0020] This invention utilizes inverse matrices for signal decoupling operations, which can effectively counteract the cross-influence of heating power and insulation screen displacement on the thermodynamic temperature field, thereby achieving cross-free coordinated control of multiple execution variables.

[0021] Preferably, the step of performing linear translation adjustment based on the slope calibrated by the average gradient volatility of the previous stage includes: calculating the arithmetic mean of all historical gradient volatility in the previous growth process stage, multiplying the arithmetic mean by a preset reference value by a calibrated slope benchmark constant to generate the interval translation adjustment slope.

[0022] This invention generates an interval translation adjustment slope based on the average historical gradient volatility, which can more accurately determine the direction and magnitude of the temperature gradient target interval shift with growth length, and improve the scientific nature of thermal field drift compensation in the constant diameter stage.

[0023] Preferably, the step of maintaining the radial temperature gradient within a preset range includes: when it is determined that the measured radial temperature gradient value exceeds the preset range after translation adjustment, compensating for the drift of heat dissipation conditions at the furnace boundary by adjusting the heater power and / or the height of the insulation screen, and controlling the measured radial temperature gradient to fall back into the preset range.

[0024] This invention can effectively compensate for the long-term slow drift of the thermal field caused by the drop in the melt level in the crucible and the change in the heat dissipation conditions of the side wall, thus ensuring the stability of the thermal field throughout the entire cycle.

[0025] Secondly, the present invention provides a thermal field control system based on size-adaptive single-crystal silicon rods, including a processor and a memory, wherein the memory stores computer program instructions, and when the computer program instructions are executed by the processor, the above-mentioned thermal field control method based on size-adaptive single-crystal silicon rods is implemented.

[0026] By adopting the above technical solution, the above-mentioned thermal field control method based on size adaptive single crystal silicon rod is generated into a computer program and stored in a memory so that it can be loaded and executed by a processor. In this way, a terminal device can be made based on the memory and the processor for convenient use.

[0027] The beneficial effects of this invention are as follows: This invention constructs a three-dimensional temperature field dataset by arranging a thermocouple array inside a single-crystal silicon growth furnace. By combining a finite difference operator with directional correction weights and a spatial step size to perform non-uniform resampling technology, it can improve the calculation accuracy of axial and radial temperature gradients, enhance the analytical accuracy of the warped region of the isothermal surface, and improve the monitoring accuracy of the solid-liquid interface morphology. By using gradient fluctuation rate, silicon rod diameter deviation, and pulling speed deviation to construct feedback deviation, and decoupling the output through a proportional-integral-derivative controller, it achieves coordinated control of heater power and insulation screen height.

[0028] Furthermore, by selectively adjusting the time window width and regulator parameters according to actual operating conditions, the system's response speed and control accuracy to complex thermal field changes are enhanced, dimensional fluctuations during crystal pulling are suppressed, the radial temperature gradient is maintained near the target range during the constant diameter stage, and the temperature range is shifted and adjusted according to the growth length and previous fluctuation data, ensuring the stability of the thermal field throughout the entire cycle and improving the diameter uniformity and crystal formation quality of the single crystal silicon rod. Attached Figure Description

[0029] Figure 1 This is a flowchart of a thermal field control method based on size-adaptive single-crystal silicon rods; Figure 2 This is a schematic diagram of the feedback error variables; Figure 3 This is a schematic diagram comparing ablation experiments. Detailed Implementation

[0030] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0031] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0032] This invention discloses a thermal field control method based on a size-adaptive single-crystal silicon rod, referring to... Figure 1 This includes steps S1-S4: S1. Construct a three-dimensional temperature field and perform differential resampling.

[0033] First, a three-dimensional temperature field dataset is constructed, and the normal to the melting point isothermal surface is extracted. A multi-layer thermocouple array is uniformly arranged in a ring inside the heater, insulation cylinder, and flow guide cylinder of the single-crystal silicon growth furnace. Specifically, 5 to 8 layers are arranged axially, with 8 to 16 measuring points evenly distributed radially outward from each layer. The axial, radial, and circumferential coordinates of all measuring points relative to the single-crystal silicon growth center are obtained, and a spatial coordinate mapping matrix is ​​established. The control system uses a data acquisition card to synchronously acquire the temperature signals output by the thermocouple array at a fixed sampling period of 1 to 2 seconds, and uses a Kalman filter algorithm to filter out noise interference caused by the alternating magnetic field. Based on the spatial coordinate mapping matrix, the spatial boundary conditions of each measuring point are established. A three-dimensional kriging interpolation algorithm or a multi-dimensional spline interpolation algorithm is used to interpolate and fit the spatially discrete temperature data into a smooth three-dimensional temperature field spatial distribution model with a spatial resolution of 1 mm. A unified timestamp is added to the three-dimensional temperature field spatial distribution model, which is then encapsulated and constructed as a three-dimensional temperature field dataset containing a time dimension. This dataset is written to a time-series database in real time through a streaming data pipeline, forming a thermodynamic feature data pool.

[0034] Next, a three-dimensional isosurface extraction algorithm is used to locate the surface boundary with a temperature equal to the silicon melting point (1414℃) from the three-dimensional temperature field spatial distribution model in the time-series database, thereby extracting the solid-liquid melting point isothermal surface from the previous sampling period. When the control system is initially started, resulting in the loss of data from the previous sampling period, the solid-liquid melting point isothermal surface of the current sampling period is extracted as a substitute reference. After locating the solid-liquid melting point isothermal surface, the outward unit normal vector of each spatial grid point on the surface is calculated. The arithmetic mean three-dimensional vector of the normal vectors of all vertices in the central region centered on the silicon rod growth axis and with radial coordinates less than or equal to 50mm is obtained as the overall melting point isothermal surface normal.

[0035] Calculate the dot product of the normal to the isothermal surface at the melting point and the unit vector of the vertically downward gravitational direction to construct the cosine of the included angle, and then calculate the corresponding sine of the included angle based on the cosine. Using value 1 as the reference term, calculate the difference between value 1 and the cosine of the included angle, and then multiply the difference by a preset axial correction factor. This is then added to the baseline term to construct the axial direction correction weight. Multiply the sine of the included angle by a preset radial correction factor. The obtained result is added to the baseline term to construct the radial direction correction weight. The formula for calculating the axial direction correction weight is:

[0036] The formula for calculating the radial direction correction weight is:

[0037] in, Represents the cosine of the included angle. Represents the sine of the included angle, and the radial correction factor. and axial correction factor All of these are dimensionless correction coefficients, and their values ​​are determined in conjunction with the specific thermal field size of the single-crystal silicon growth furnace. In this embodiment, the value range is set to 0.3 to 0.8 to avoid absolute fixation of the values.

[0038] After determining the orientation correction weights, the axial and radial temperature gradients are calculated using a finite difference operator with orientation correction weights. The axial base distance of the spatial mesh is set to... The radial foundation distance is The axial temperature gradient along the crystal growth axis is weighted by adjusting the axial direction. The initial axial temperature gradient, obtained by multiplying by the derivative of the central finite difference operator, is corrected and calculated. The radial temperature gradient perpendicular to the growth axis is calculated by adjusting the radial direction weight. The initial radial temperature gradient obtained by multiplying by the derivative of the central finite difference operator is then corrected and calculated.

[0039] Axial temperature gradient The corrected calculation formula is as follows:

[0040] radial temperature gradient The corrected calculation formula is as follows:

[0041] in, This represents the temperature difference between spatial nodes located one axial foundation distance on either side of the current node along the axial direction. This represents the temperature difference between spatial nodes that are a radial base distance apart on both sides of the current node. By using the normal inclination of the geometric interface as a correction factor for the temperature gradient, the quotient of the temperature difference between adjacent nodes and the spatial distance is corrected, reducing the truncation error at abrupt changes in the surface and improving control stability.

[0042] Finally, non-uniform resampling is performed on the spatial step size of the finite difference operator when the cosine of the angle falls below a set lower limit. The preset lower limit threshold for the cosine of the angle is 0.866. During each computational polling, the control system scans the cosine data of the angles of all spatial nodes on the melting point isothermal surface in real time. Once a local region is detected where the cosine of the angle of the edge chilling zone with radial coordinates greater than or equal to 135 mm and less than or equal to 150 mm in the epitaxial region of a 300 mm diameter single crystal silicon rod is lower than the set lower limit of 0.866, the edge chilling zone is determined to be a warped region of the melting point isothermal surface caused by melt convection shear and edge thermal stress imbalance. Within the defined isothermal surface warped region, the spatial mesh nodes of the original finite difference operator are reconstructed with a locally high-density mesh. By introducing a set reduction factor, the local radial spatial step size is adjusted. With axial spatial step size The spatial step size is reduced from the original 1mm to 0.25mm or 0.2mm, thereby reducing the spatial step size and inserting denser mesh nodes within the warped region of the isothermal surface. A higher-order spline interpolation algorithm is used to fill in the temperature data at the denser mesh nodes, and the finite difference operator is reloaded based on the denser mesh nodes to recalculate and output the axial temperature gradient within the warped region of the isothermal surface. With radial temperature gradient This eliminates numerical instability caused by abrupt changes in the surface and improves the analytical accuracy of the spatial distribution characteristics of the warped region of the isothermal surface.

[0043] S2. Calculate the interface shape characteristics and gradient volatility.

[0044] After obtaining the temperature gradient and the cosine of the included angle, the ratio of the axial to the radial temperature gradient is used as the interface shape feature. The control system divides the axial temperature gradient values ​​calculated in the previous steps by the corresponding radial temperature gradient values, extracting the spatial arithmetic mean to form the interface shape feature, which is used to macroscopically characterize the transient morphological changes of the solid-liquid interface. A variable-length one-dimensional first-in-first-out data structure is constructed within the control system as a sliding time window to store the interface shape feature under historical time series.

[0045] Furthermore, the gradient volatility is calculated using a sliding time window whose window width is adjusted according to the cosine of the included angle. A dimensionless preset baseline window width is set at 30 sampling periods, and a minimum window width threshold to ensure a filtering baseline is set at 10 sampling periods. The control system extracts the cosine of the included angle calculated in the previous period and multiplies the preset baseline window width by the cosine of the included angle to obtain the product. Subsequently, the product is compared with the preset minimum window width threshold, and the larger of the two is taken, rounded down, and updated as the current window width of the sliding time window. The technical significance of introducing the larger-value comparison operation is to set a physically enforced boundary, preventing excessive window width reduction that could lead to sample depletion when the cosine of the included angle approaches zero due to extreme warping of the isothermal surface. This ensures the statistical validity of the root mean square calculation and the anti-interference capability of the control system. This adjustment mechanism allows the sliding time window to maintain a large window width when the interface is stable, providing a smoothing effect for low-frequency data; when the isothermal surface tumbles violently, causing the cosine of the included angle to drop to 0.8, the current window width is compressed to 24 sampling periods, improving the response speed of the control system to short-term thermal field fluctuations.

[0046] After each reset and update of the current window width, the time series of interface shape features within the current time window is extracted, and the differential rate of change of interface shape features between adjacent sampling points within the sliding time window is calculated. Specifically, the difference between the interface shape features at two adjacent sampling times is calculated and divided by a fixed sampling time interval to obtain discrete differential rate of change values. Then, the sum of the squares of all differential rates of change within the sliding time window is calculated, divided by the total number of terms, and the square root is taken to obtain the root mean square value of all differential rates of change. The final calculated root mean square value constitutes the gradient volatility, which is output as a scalar parameter characterizing the thermal field stability state and transmitted to the downstream control stage. The gradient volatility value typically falls within the range of 0.01 / s to 0.4 / s.

[0047] S3. Construct feedback deviation and perform decoupling control.

[0048] During the constant diameter growth process, a vision diameter gauge is used to obtain the real-time measured diameter of the silicon rod. The diameter deviation is calculated by subtracting the target diameter from the real-time measured diameter. Simultaneously, a servo absolute encoder transmits the measured crystal pulling speed, and the pulling speed deviation is calculated by subtracting the target pulling speed from the measured pulling speed. Subsequently, dimensionless calculations are performed on the silicon rod diameter deviation, pulling speed deviation, and gradient fluctuation rate to construct the feedback deviation. Specifically, the silicon rod diameter deviation, pulling speed deviation, and gradient fluctuation rate are divided by their respective preset reference bases using a division operator to output dimensionless parameters. The preset reference bases for diameter deviation are 5 mm, pulling speed deviation is 0.1 mm / min, and gradient fluctuation rate is 0.5 s.

[0049] Next, a weighted summation operation is performed on all dimensionless parameters according to preset weight constants to construct the feedback deviation used to determine the threshold triggering condition, and the weight constants of the dimensionless diameter parameter are set. The weighting constant for the dimensionless parameter of pulling speed is 0.5. The weighting constant for the dimensionless parameter of gradient volatility is 0.3. The value is 0.2. This is the magnitude of the overall feedback deviation used to determine the threshold trigger condition. The calculation formula is as follows:

[0050] Simultaneously, a weighted summation is performed on the dimensionless parameters of diameter and tension speed (with ± signs) to generate a control deviation signal for input to the control terminal. The corresponding calculation formula is:

[0051] like Figure 2 As shown, where, This represents the dimensionless diameter deviation. This represents the dimensionless deviation in pulling speed. This represents the dimensionless gradient volatility. Figure 2 The total error corresponds to the aforementioned comprehensive feedback deviation amplitude. .

[0052] The trigger threshold for feedback deviation is set to 0.15. The system will trigger when the feedback deviation exceeds this threshold. When the deviation is greater than 0.15, a control command is generated via a proportional-integral-derivative (PID) controller. Specifically, the control deviation signal is input to the PID controller, whose proportional gain and integral time constant are determined by the absolute value of the diameter deviation and the gradient fluctuation rate, respectively. Explicitly, the proportional gain is set to a nonlinearly increasing function output value that increases with the absolute value of the deviation between the actual and target diameters, and the integral time constant is set to an increasing function output value that increases with the gradient fluctuation rate, thus avoiding control overshoot.

[0053] Finally, the heater power and insulation screen height are adjusted separately by combining the actuator transformation matrix with the decoupled control commands. In specific implementation, the control commands output by the proportional-integral-derivative controller are extended into a two-dimensional control demand vector. The calibration method of the actuator transformation matrix, i.e., the two-dimensional inverse matrix, is obtained offline. The specific steps include independently applying step control signals to the heater power and insulation screen height, measuring and recording the steady-state response changes of the temperature gradient and interface characteristics to construct a two-dimensional sensitivity matrix, then inverting the two-dimensional sensitivity matrix to obtain the two-dimensional inverse matrix, left-multiplying the two-dimensional control demand vector by the calibrated two-dimensional inverse matrix to perform signal decoupling operations, and outputting the decoupled target heater power adjustment and target insulation screen height adjustment after the execution signal decoupling operations, which are then sent to the heater actuator power regulator and the insulation screen lifting motor driver, respectively, to achieve multi-parameter non-overlapping coordinated control of heater power and insulation screen height.

[0054] S4, temperature gradient interval translation adjustment during constant diameter stage.

[0055] After the monocrystalline silicon growth enters the constant diameter stage, the control system maintains the radial temperature gradient within a preset range, and performs linear translation adjustment of the preset range according to the slope calibrated by the average gradient fluctuation rate of the previous stage as the growth length increases.

[0056] In the specific implementation phase, after analyzing the mass change data from the weighing sensor to confirm the end of the single-crystal silicon shoulder-forming stage and the entry into the constant-diameter stage, the initial upper and lower limits of the radial temperature gradient of the melting point isothermal surface are extracted from the database, and the initial growth length of the single-crystal silicon rod at the time of entering the constant-diameter stage is recorded as the length reference value. The absolute encoder of the crystal lifting servo motor is used to read the current position count and calculate the current axial growth length of the single-crystal silicon rod. The relative growth length is obtained by subtracting the current axial growth length of the single-crystal silicon rod from the length reference value.

[0057] Subsequently, a linear translation adjustment is performed based on the slope calibrated by the average gradient volatility of the previous stage. All historical gradient volatility time-series data from the previous growth process stage are extracted, and the arithmetic mean of all historical gradient volatility within the previous growth process stage is calculated. The arithmetic mean is divided by a preset reference value and then multiplied by a preset calibration slope benchmark constant to generate the interval translation adjustment slope. The unit of the calibration slope benchmark constant is set to Kelvin per square millimeter, used to determine the direction and magnitude of the temperature gradient target interval shift with the growth length. The interval translation adjustment slope is multiplied by the relative growth length to obtain the temperature gradient adjustment offset. The temperature gradient adjustment offset is synchronously superimposed onto the initial upper and lower limits of the radial temperature gradient at the melting point isothermal surface to generate the preset interval after translation adjustment, achieving linear translation of the interval as the crystal growth length changes.

[0058] Finally, the radial temperature gradient is maintained within a preset range. The control system cyclically executes logical judgments according to a set control cycle. When the measured radial temperature gradient value exceeds the preset range after translation adjustment, the proportional-integral-derivative controller issues an adjustment amount to compensate for the drift of the heat dissipation conditions at the furnace boundary. By adjusting the heater power and the height of the insulation screen, the measured radial temperature gradient is controlled to fall back into the preset range. Through this logical judgment and feedback mechanism, the long-term slow drift of the thermal field caused by the drop in the melt level in the crucible and the change in the heat dissipation conditions of the side wall is compensated, ensuring the stability of the thermal field throughout the entire cycle.

[0059] The aforementioned thermal field control method based on size-adaptive monocrystalline silicon rods was adopted and compared through control system testing. Experimental conditions were set as follows: three identical 300mm monocrystalline silicon growth furnaces, all using the same batch of high-purity polycrystalline silicon raw materials, maintaining an ambient temperature of 25℃ for continuous crystal pulling for 50 hours, with a temperature data synchronous sampling period of 1 second. Three comparative test groups were set up: the control group used traditional constant grid orthogonal difference and conventional single-parameter proportional-integral-derivative control; the ablation group, based on the control group, input directional weighted finite difference and grid refinement but lacking gradient volatility feedback; and the experimental group used a complete scheme including sliding time window gradient volatility and multi-parameter feedback weighted fusion.

[0060] The control group had an average truncation error of 1.5 K / mm in temperature gradient calculation, a diameter fluctuation amplitude of ±2.5 mm on the isothermal surface of the crystal pulling process, and a microdislocation defect rate as high as 8.5% in the finished product. The ablation group, due to the optimized spatial mesh algorithm, reduced the truncation error to 0.08 K / mm, narrowed the diameter fluctuation to ±1.2 mm, and reduced the defect rate to 4.2%. The experimental group using the complete scheme maintained a stable temperature truncation error within 0.07 K / mm, compressed the diameter control fluctuation to an extremely narrow range of ±0.4 mm, and achieved a microdislocation defect rate as low as 1.1% in the single-crystal silicon rod. Figure 3As shown, by introducing a finite difference operator with directional correction weights and a non-uniform resampling technique, and by integrating gradient volatility to construct a feedback deviation, the control lag caused by macroscopic thermal inertia is reduced, the influence of thermal stress imbalance in the edge cooling zone on solid-liquid interface warping is suppressed, and the dimensional uniformity and final yield of the single crystal silicon rod are improved.

[0061] This invention also discloses a thermal field control system based on a size-adaptive single-crystal silicon rod, including a processor and a memory. The memory stores computer program instructions, and when the computer program instructions are executed by the processor, the thermal field control method based on a size-adaptive single-crystal silicon rod according to the present invention is implemented.

[0062] The aforementioned thermal field control system based on size-adaptive single-crystal silicon rods also includes other components well-known to those skilled in the art, such as communication buses and communication interfaces. Their configurations and functions are known in the art and will not be described in detail here.

[0063] In the description of this specification, "multiple" or "several" means at least two, such as two, three or more, unless otherwise expressly and specifically defined.

Claims

1. A thermal field control method based on size-adaptive single-crystal silicon rods, characterized in that, include: S1. Construct a three-dimensional temperature field dataset and extract the normal to the melting point isothermal surface. Determine the direction correction weight based on the cosine and sine of the angle between the normal and the gravity direction. Calculate the axial and radial temperature gradients using a finite difference operator with the weights. When the cosine of the angle is lower than a set lower limit, reduce the radial and axial spatial step sizes in the corresponding isothermal surface warping region and insert densified mesh nodes to perform non-uniform resampling. Recalculate the temperature gradient based on the densified mesh. S2. Using the ratio of the temperature gradients as the interface shape feature quantity, the gradient fluctuation rate of the interface shape feature quantity is calculated through a sliding time window whose window width is adjusted with the cosine of the included angle. S3. Perform dimensionless calculations on the silicon rod diameter deviation, pulling speed deviation, and gradient volatility to construct a feedback deviation. When the feedback deviation exceeds a threshold, a proportional-integral-derivative controller generates a control command. Combined with the actuator transformation matrix, the heater power and the insulation screen height are decoupled and controlled. The proportional coefficient of the controller is configured to increase non-linearly with the increase of the absolute value of the silicon rod diameter deviation, and the integral time constant is configured to increase with the increase of the gradient volatility. S4. After entering the constant diameter stage, maintain the radial temperature gradient within the preset range, and perform translation adjustment on the preset range according to the slope of the average gradient fluctuation rate of the previous process stage as the growth length increases.

2. The thermal field control method based on size-adaptive single-crystal silicon rod according to claim 1, characterized in that, The construction of the three-dimensional temperature field dataset and extraction of the normal to the melting point isothermal surface includes: A spatial coordinate mapping matrix is ​​established by acquiring the coordinate parameters of all measuring points relative to the growth center. Discrete temperature signals are collected synchronously, and the discrete temperature signals are interpolated and fitted into a three-dimensional temperature field spatial distribution model by combining the spatial coordinate mapping matrix. A timestamp is added to the three-dimensional temperature field spatial distribution model to construct the three-dimensional temperature field dataset.

3. The thermal field control method based on size-adaptive single-crystal silicon rod according to claim 1, characterized in that, The determination of the direction correction weight includes: Calculate the cosine of the angle between the normal and the direction of gravity. Using the value 1 as the reference term, calculate the difference between the value 1 and the cosine of the angle and add the difference to the reference term to construct the axial direction correction weight. Add the sine of the angle to the reference term to construct the radial direction correction weight.

4. The thermal field control method based on size-adaptive single-crystal silicon rod according to claim 1, characterized in that, The step of performing non-uniform resampling on the spatial step size and recalculating the temperature gradient includes: Extract the isothermal surface warping region where the cosine of the included angle is lower than the set lower limit, reduce the radial and axial spatial step size and insert densified mesh nodes within the isothermal surface warping region, and recalculate the axial and radial temperature gradients based on the densified mesh nodes and spline interpolation algorithm.

5. The thermal field control method based on size-adaptive single-crystal silicon rod according to claim 1, characterized in that, The calculation of gradient volatility using a sliding time window whose window width is adjusted according to the cosine of the included angle includes: The larger of the product of the preset baseline window width and the cosine of the included angle and the preset minimum window width threshold is updated as the current window width of the sliding time window. The differential change rate of the interface shape feature between adjacent sampling points within the sliding time window is calculated, and the root mean square value of all the differential change rates is obtained to form the gradient volatility.

6. The thermal field control method based on size-adaptive single-crystal silicon rod according to claim 1, characterized in that, The constructed feedback deviation includes: The division operator is used to perform division operations on the silicon rod diameter deviation, the pulling speed deviation, and the gradient volatility to output dimensionless parameters. A weighted summation operation is then performed on all the dimensionless parameters according to a preset weight constant to construct the feedback deviation amount used to determine the threshold triggering condition.

7. The thermal field control method based on size-adaptive single-crystal silicon rod according to claim 1, characterized in that, The decoupling and control of heater power and insulation screen height by combining actuator conversion matrix includes: Step control signals are applied independently to the heater power and the insulation screen height, and the steady-state response changes of the temperature gradient and interface characteristics are measured and recorded. The actuator transformation matrix is ​​obtained offline based on the steady-state response changes. The control command is extended into a two-dimensional control demand vector. The two-dimensional control demand vector is multiplied by the actuator transformation matrix to perform a decoupling operation on the execution signal, and the independent target heater power adjustment amount and target insulation screen height adjustment amount are output.

8. The thermal field control method based on size-adaptive single-crystal silicon rod according to claim 1, characterized in that, The process of shifting and adjusting the preset interval according to the slope of the average gradient fluctuation rate of the previous process stage as the growth length increases includes: Calculate the arithmetic mean of all historical gradient volatility rates in the previous process stage, and multiply the arithmetic mean by a preset reference value and the result by a calibration slope benchmark constant to generate an interval translation adjustment slope.

9. The thermal field control method based on size-adaptive single-crystal silicon rod according to claim 1, characterized in that, Maintaining the radial temperature gradient within a preset range includes: When it is determined that the measured radial temperature gradient exceeds the preset range after translation adjustment, the drift of heat dissipation conditions at the furnace boundary is compensated by adjusting the heater power and / or the height of the insulation screen, thereby controlling the measured radial temperature gradient to fall back into the preset range.

10. A thermal field control system based on a size-adaptive single-crystal silicon rod, characterized in that, include: A processor and a memory, wherein the memory stores computer program instructions that, when executed by the processor, implement the thermal field control method based on a size-adaptive single-crystal silicon rod according to any one of claims 1-9.

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