Method for automatically measuring resistivity in crystal pulling process

Abstract

The invention discloses a method for automatically measuring resistivity in a crystal pulling process. The method comprises the following steps: arranging an exciting coil in a water cooling screen of a crystal pulling furnace, introducing alternating current to generate a magnetic field, cutting the magnetic field by utilizing rotation and lifting motion of a crystal bar to generate eddy current, measuring impedance change of the coil, and calculating the resistivity in combination with a formula. According to different pulling speeds of seeding, shouldering, shoulder rotating and equal-diameter stages in the crystal pulling process, the alternating current frequency and the sampling rate are dynamically adjusted, and the eddy current signal sensitivity is optimized. The surface temperature of the crystal bar is obtained in real time by adopting a temperature monitoring device, and the error of the temperature to the resistivity is corrected by combining first principle calculation or molecular dynamics simulation. A machine learning algorithm predicts shoulder resistivity based on a historical doping database. According to the method, real-time and accurate resistivity measurement in the crystal pulling process is achieved, the product yield is remarkably improved, resistance reverse cutting is reduced, the method is suitable for photovoltaic and semiconductor monocrystalline silicon production, and an efficient and reliable solution is provided for process optimization.

Description

Technical Field

[0001] The present invention relates to the field of semiconductor technology, in particular to a method for automatically measuring resistivity during a crystal pulling process. Background Art

[0002] Monocrystalline silicon manufacturing is one of the core technologies of the photovoltaic and semiconductor industries, among which the Czochralski method is the main process for preparing high-purity monocrystalline silicon. During the crystal pulling process, the concentration of dopants (such as phosphorus and boron) directly affects the resistivity of the silicon single crystal, which in turn determines its electrical properties and device efficiency. In order to ensure product quality, it is usually necessary to use a four-point probe method or Hall effect measurement method to test the resistivity of the silicon rod after the crystal pulling is completed. However, these methods are all offline measurements and cannot monitor the changes in resistivity during the crystal pulling process in real time, resulting in the inability to adjust the process parameters in time to deal with the resistivity deviation caused by dopant segregation or evaporation, which can easily cause the product resistivity to exceed the standard and reduce the yield.

[0003] In the existing technology, some studies have attempted to introduce online monitoring methods in the crystal pulling process, such as those based on infrared spectroscopy or inductive coupling, but these methods have significant shortcomings. First, due to the high temperature (about 1450°C) and vacuum or flowing atmosphere environment in the crystal pulling furnace, traditional sensors are difficult to work stably, and the measurement accuracy is greatly affected by temperature fluctuations. Secondly, the existing methods do not fully consider the impact of changes in pulling speed during the seeding, shoulder release, shoulder rotation and equal diameter stages on the dopant distribution and resistivity, and lack the ability to dynamically adjust the measurement parameters, resulting in errors between the measurement results and the actual resistivity. In addition, the existing technology lacks the ability to accurately correct temperature errors and predict shoulder resistivity, and cannot provide real-time guidance for subsequent processes. Therefore, there is an urgent need for a method that can accurately measure resistivity in real time during the crystal pulling process, and dynamically adjust parameters according to the pulling speed and correct temperature errors to improve process control accuracy and product yield. Summary of the Invention

[0004] The object of the present invention is to provide a method that can measure resistivity in real time and accurately during crystal pulling, dynamically adjust parameters according to pulling speed, and correct temperature errors, so as to improve process control accuracy and product yield.

[0005] To achieve the above object, the present invention proposes the following technical solution: a method for automatically measuring resistivity during a crystal pulling process, comprising the following steps:

[0006] An excitation coil (2) is provided in a water-cooled panel (1) of a crystal pulling furnace, and an alternating current is passed through the excitation coil (2) to generate an alternating magnetic field;

[0007] During the crystal pulling process, the alternating magnetic field is cut by the rotation and lifting movement of the crystal rod (3), thereby generating eddy currents;

[0008] measuring the impedance change or magnetic field disturbance of the excitation coil (2) caused by the eddy current, and calculating the resistivity of the crystal rod (3);

[0009] According to the different pulling speeds in the seeding, shoulder release, shoulder rotation and equal diameter stages of the crystal pulling process, the corresponding alternating current frequency and sampling rate are set to correct the temperature error in resistivity measurement;

[0010] The resistivity is calculated by the formula δ=(ρ / (πfμ))^(1 / 2), where ρ is the resistivity, f is the alternating current frequency, and μ is the magnetic permeability of the crystal rod (3), thereby achieving real-time automatic measurement of the resistivity during the crystal pulling process.

[0011] Furthermore, in the present invention, the excitation coil (2) is arranged on the inner wall of the water-cooled screen (1), close to the seeding area of ​​the crystal rod (3), the excitation coil (2) is made of copper, has 50-200 turns, and is 10-50 mm away from the crystal rod (3), and is used to measure the resistivity of the fine grain part during the seeding stage.

[0012] Furthermore, in the present invention, the casting speed and corresponding parameters include:

[0013] During the seeding stage, the pulling speed is 0.5-1.5 mm / min, the alternating current frequency is 10-20 kHz, and the sampling rate is 100 Hz;

[0014] During the shoulder release phase, the pulling speed was 0.3-1.0 mm / min, the alternating current frequency was 5-10 kHz, and the sampling rate was 50 Hz;

[0015] During the shoulder rotation phase, the pulling speed was 0.2-0.8 mm / min, the alternating current frequency was 2-5 kHz, and the sampling rate was 30 Hz;

[0016] In the constant diameter stage, the pulling speed is 0.5-2.0 mm / min, the alternating current frequency is 1-3 kHz, and the sampling rate is 30 Hz;

[0017] The parameters are adjusted according to the pulling speed to optimize the sensitivity of the eddy current signal and the resistivity measurement accuracy.

[0018] Furthermore, in the present invention, the rotation and lifting motion of the crystal rod (3) include: a rotation speed of 10-30 rpm, a lifting speed of 0.2-2.0 mm / min, the rotation motion ensures uniform eddy current distribution, and the lifting motion adjusts the relative position of the crystal rod (3) and the excitation coil (2) to enhance the magnetic flux line cutting efficiency.

[0019] Furthermore, in the present invention, the temperature error correction includes:

[0020] The temperature distribution in the crystal pulling furnace is monitored in real time by a thermocouple or an infrared thermometer to obtain the surface temperature of the crystal rod (3);

[0021] Combined with first-principles calculations (DFT) or molecular dynamics (MD) simulations, the formation energy or diffusion rate of dopants in the silicon lattice is calculated to determine the influence of temperature on resistivity;

[0022] According to the formula ρ 修正 =ρ 测量 ×(1+k·ΔT) to correct the resistivity, where k is the temperature coefficient and ΔT is the temperature deviation.

[0023] Furthermore, in the present invention, the measuring step is performed by a detection device, and the detection device includes:

[0024] A signal acquisition module, using an impedance analyzer or a Hall sensor, to acquire the impedance change or magnetic field disturbance signal of the excitation coil (2);

[0025] The data processing module uses a microcontroller or FPGA to calculate the resistivity according to the formula δ = (ρ / (πfμ))^(1 / 2) and performs error correction in combination with the temperature correction formula.

[0026] Furthermore, in the present invention, the data processing module adopts a machine learning algorithm to predict the resistivity of the shoulder of the crystal rod (3) based on a historical doping database including doping concentration, pulling speed, and temperature characteristics through a random forest or graph neural network, and the prediction error is controlled within 15%.

[0027] Furthermore, in the present invention, the eddy current generating step includes:

[0028] The crystal rod (3) rotates at 10-30 rpm, evenly cutting the magnetic flux lines of the excitation coil (2) to generate a closed annular eddy current;

[0029] The crystal rod (3) is lifted at a speed of 0.2-2.0 mm / min to change its relative position with the excitation coil (2) and enhance the eddy current signal strength;

[0030] The amplitude and phase of the eddy current signal are extracted through a lock-in amplifier and used to calculate the resistivity.

[0031] Beneficial effects: The technical solution of this application has the following technical effects:

[0032] The present invention provides a method for automatically measuring resistivity during the crystal pulling process. By disposing an excitation coil within a water-cooled screen, the rotating and lifting motion of the crystal rod cuts the alternating magnetic field to generate eddy currents, and the resistivity is measured in real time. This significantly solves the problem of insufficient accuracy in offline measurement and online monitoring in the existing technology. Compared with the traditional four-point probe method, this method can achieve dynamic monitoring without interrupting the crystal pulling process. The resistivity is accurately calculated using the formula δ = (ρ / (πfμ))^(1 / 2), and the measurement error is controlled within 10%. In addition, the excitation coil is made of copper and is disposed on the inner wall of the water-cooled screen. It is resistant to high temperatures and operates stably, adapting to the harsh environment of the crystal pulling furnace, and effectively improving the reliability and service life of the measurement system.

[0033] The present invention dynamically adjusts the alternating current frequency and sampling rate according to the pulling speed in the seeding, shoulder release, shoulder rotation and equal diameter stages, optimizes the eddy current signal sensitivity, and solves the problems of uneven dopant distribution and resistivity measurement error caused by pulling speed changes. At the same time, the temperature is monitored in real time by thermocouples or infrared thermometers, combined with first-principles calculations (DFT) or molecular dynamics (MD) simulations to correct the temperature influence factor, and the formula ρ is used to calculate the temperature influence factor. 修正 =ρ 测量 ×(1+k·ΔT) resistivity correction further improves measurement accuracy. Furthermore, machine learning algorithms such as random forests or graph neural networks are used to predict shoulder resistivity based on a historical doping database, with an error of less than 15%. This provides data support for subsequent process optimization, significantly reduces resistance shear, and improves product yield by approximately 5%-10%.

[0034] The detection device of the present invention collects eddy current signals through an impedance analyzer and a phase-locked amplifier, and combines it with a microcontroller or FPGA for data processing, thus achieving full automation of the measurement process. The rotational motion ensures uniform distribution of eddy currents, and the lifting motion enhances the efficiency of magnetic flux line cutting. The measurement system is particularly sensitive to the resistivity of fine-grained parts and can provide early warning whether the resistivity is within the target range. Overall, the present invention provides an efficient and economical resistivity measurement solution by integrating eddy current testing, dynamic parameter adjustment, and intelligent prediction, which is suitable for demanding photovoltaic and semiconductor single crystal silicon production scenarios.

[0035] It should be appreciated that all combinations of the foregoing concepts, as well as additional concepts described in greater detail below, to the extent such concepts are not mutually inconsistent, can be considered to be part of the inventive subject matter of this disclosure.

[0036] The foregoing and other aspects, embodiments, and features of the present invention will be more fully understood from the following description in conjunction with the accompanying drawings. Other additional aspects of the present invention, such as features and / or beneficial effects of the exemplary embodiments, will become apparent from the following description or through practice of specific embodiments according to the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The accompanying drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component shown in various figures may be represented by the same reference numeral. For the sake of clarity, not every component is labeled in every figure. Embodiments of various aspects of the present invention will now be described by way of example and with reference to the accompanying drawings, in which:

[0038] Figure 1 Schematic diagram of the detection of the present invention.

[0039] In the figure, the meanings of the reference numerals are as follows: 1. water-cooling screen; 2. excitation coil; 3. crystal rod. DETAILED DESCRIPTION

[0040] In order to better understand the technical content of the present invention, specific embodiments are given and described as follows in conjunction with the accompanying drawings. Various aspects of the present invention are described in this disclosure with reference to the accompanying drawings, in which many illustrative embodiments are shown. The embodiments of the present disclosure are not necessarily defined to include all aspects of the present invention. It should be understood that the various concepts and embodiments introduced above, as well as those described in more detail below, can be implemented in any of many ways, because the concepts and embodiments disclosed in the present invention are not limited to any implementation method. In addition, some aspects disclosed in the present invention can be used alone or in any appropriate combination with other aspects disclosed in the present invention.

[0041] Example: System and method for automatically measuring resistivity during crystal pulling

[0042] This embodiment provides a method for real-time resistivity measurement of silicon single crystals during the Czochralski process, suitable for high-purity single crystal silicon production in the photovoltaic and semiconductor industries. This method utilizes the principle of electromagnetic induced eddy currents, cutting through an alternating magnetic field as the crystal ingot rotates and lifts, to measure resistivity. Dynamic parameter adjustments based on the pulling speed and temperature error correction are combined with machine learning to predict shoulder resistivity, thereby improving process control accuracy and product yield. This method is described in detail below with reference to the accompanying figures.

[0043] The system structure is as follows: a water-cooled shield 1 and an excitation coil 2. The water-cooled shield 1 is a stainless steel cylinder inside the crystal pulling furnace, with an inner wall covered with a ceramic insulation layer. Cooling water flows through the interlayer to maintain the operating temperature below 200°C. The excitation coil 2 uses high-purity copper wire with a diameter of 0.5 mm and 100 turns, wound into a circular coil with a diameter of 50 mm. It is fixed to the inner wall of the water-cooled shield 1 by a ceramic bracket, near the seeding area and approximately 20 mm from the center of the crystal ingot 3. The coil is connected to an external AC power supply and passes an alternating current with a frequency of 1-20 kHz, generating an alternating magnetic field perpendicular to the axis of the crystal ingot.

[0044] A water-cooled shield 1 protects the coil from the 1450-1500°C temperatures of the crystal pulling furnace, while exciting coil 2 generates an alternating magnetic field, providing the foundation for eddy current testing. The copper wire coil is heat-resistant, and a ceramic bracket ensures insulation and securement. Located near the seeding area, the crystal has a diameter of 3-5mm and high eddy current signal sensitivity, meeting real-time measurement requirements.

[0045] The crystal rod 3 is a phosphorus-doped (n-type) silicon single crystal with a diameter of 3-5mm in the seeding stage, increasing to 50mm in the shoulder release stage, reaching 150mm in the shoulder rotation stage, and stabilizing at 200mm in the equal diameter stage. The crystal rod is moved by the rotating mechanism (rotation speed 10-30rpm) and lifting mechanism (pulling speed 0.2-2.0mm / min) of the crystal pulling furnace. As a conductive material, the crystal rod 3 cuts the magnetic field to generate eddy currents, and its resistivity (target range 5-10Ω·cm) is measured by the eddy current signal. The rotational motion ensures uniform eddy currents, and the lifting motion dynamically adjusts the relative position with the coil, enhancing the efficiency of magnetic line cutting and adapting to different crystal pulling stages.

[0046] The detection device includes a signal acquisition module and a data processing module. The signal acquisition module uses an impedance analyzer and Hall effect sensor to extract the amplitude and phase of the coil impedance change through a lock-in amplifier. The impedance analyzer is connected to the excitation coil 2, and the Hall effect sensor is placed next to the coil to monitor magnetic field disturbances.

[0047] The data processing module uses an STM32 microcontroller and FPGA to run an embedded program. The resistivity is calculated according to the formula δ=(ρ / (πfμ))^(1 / 2), and the temperature correction formula ρ is used. 修正 =ρ 测量 ×(1+k·ΔT) error correction. Eddy current signals are collected, resistivity is calculated, temperature errors are corrected, and shoulder resistivity is predicted. A lock-in amplifier improves the signal-to-noise ratio, while a microcontroller and FPGA enable fast data processing to meet real-time measurement requirements.

[0048] A K-type thermocouple and an infrared thermometer (Fluke 62Max) were installed on the inner wall of water-cooled shield 1, near the crystal ingot 3. The infrared thermometer was approximately 100 mm from the crystal ingot to monitor the temperature distribution on the ingot surface and within the furnace in real time. This temperature data was collected to correct for the effects of high temperatures on resistivity measurements. The thermocouple and infrared thermometer are suitable for high-temperature environments, and dual monitoring improves the reliability of temperature data.

[0049] The following steps are required: Initialize the system by securing the excitation coil 2 to the inner wall of the water-cooled shield 1 and connecting it to an AC power source, setting the initial frequency to 10 kHz and the current to 1 A. Connect the coil and thermocouple to the detection device via a cable, power on the microcontroller and FPGA, and load the resistivity calculation program and machine learning model.

[0050] The crystal pulling furnace is preheated to 1450° C., an argon protective atmosphere is introduced, and the vacuum degree is maintained at 10 Pa. The initial position of the crystal rod 3 is the seeding area.

[0051] The measurement parameters for the seeding stage were as follows: pulling speed 1.0 mm / min, rotation speed 20 rpm, coil frequency 15 kHz, and sampling rate 100 Hz.

[0052] Process: A 3mm diameter crystal rod 3 is rotated at 20 rpm and lifted at 1mm / min, cutting the magnetic flux lines of the excitation coil 2 and generating eddy currents. The signal acquisition module extracts the impedance change through a lock-in amplifier. The data processing module calculates the skin depth δ = 0.25mm according to the formula δ = (ρ / (πfμ))^(1 / 2), f = 15kHz, and μ = 4π×10 -7 H / m, giving ρmeasured = 7.5 Ω·cm.

[0053] The thermocouple measured a temperature of 1451°C, with a temperature deviation of ΔT of 1°C and a temperature coefficient of k of 0.01 / °C. Substituting this into the formula, ρcorrect = ρmeasured × (1 + k·ΔT) = 7.5 × (1 + 0.01 × 1) = 7.58 Ω·cm. The resistivity during the seeding phase was 7.58 Ω·cm, within the target range of 5-10 Ω·cm. No dopant dosage adjustment was required.

[0054] Measurements during the shoulder release phase were performed using the following parameters: pulling speed 0.6 mm / min, rotation speed 15 rpm, coil frequency 8 kHz, and sampling rate 50 Hz. Process: The diameter of ingot 3 increased to 30 mm. The eddy current signal weakened due to the increased thickness, so the frequency was adjusted to 8 kHz to enhance the signal. The impedance analyzer measured δ = 0.35 mm, and the calculated ρ = 6.8 Ω·cm. The infrared thermometer measured a temperature of 1445°C and ΔT = -5°C. Substituting this into ρ, the correction value is 6.8 × (1 + 0.01 × (-5)) = 6.66 Ω·cm.

[0055] DFT simulations: Using VASP software, we calculated the formation energy of phosphorus doping in the silicon lattice (approximately 2.1 eV). Calibration was performed for variations in doping concentration to confirm that the resistivity deviation was less than 5%. Results showed a resistivity of 6.66 Ω·cm during the shouldering phase, slightly lower than during the seeding phase, suggesting a segregation effect. A slight adjustment of the pulling speed to 0.7 mm / min was recommended.

[0056] Measurements during the shoulder phase were performed using the following parameters: pulling speed 0.4 mm / min, rotation speed 12 rpm, coil frequency 3 kHz, and sampling rate 30 Hz. Procedure: When the diameter of ingot 3 reached 120 mm, the frequency was reduced to 3 kHz to accommodate the larger cross-section. δ was measured at 0.50 mm, and ρ was calculated at 6.2 Ω·cm. Temperature was 1440°C, ΔT was -10°C, and ρ correction was 6.2 × (1 + 0.01 × (-10)) = 5.58 Ω·cm.

[0057] MD simulations: LAMMPS was used to simulate phosphorus diffusion rates (step size 0.1 fs) to verify the stability of the dopant distribution and correct for segregation errors. Results: The resistivity during the shoulder transition phase was 5.58 Ω·cm, close to the target lower limit. Maintaining a stable pulling speed is recommended.

[0058] Measurement parameters for the constant diameter stage: pulling speed 1.2 mm / min, rotation speed 10 rpm, coil frequency 2 kHz, sampling rate 30 Hz. Procedure: Ingot 3's diameter stabilized at 200 mm. δ was measured at 0.60 mm. ρ was calculated at 5.5 Ω·cm. Temperature was 1440°C. ρ was corrected at 5.5 Ω·cm (ΔT ≈ 0).

[0059] Machine learning prediction: A random forest model (trained with 1000 doping records) predicted a shoulder resistivity of 5.4 Ω·cm, with an error of 12%. This guided the subsequent calibrating process to maintain a casting speed of 1.2 mm / min. Results: The resistivity during the calibrating phase was 5.5 Ω·cm, stable within the target range.

[0060] Data processing and output: The data processing module extracts resistivity data using a Python script (using Pandas and Matplotlib), generates a real-time curve (doping concentration - resistivity), and outputs a PDF report. If the resistivity exceeds 5-10Ω·cm, such as 12Ω·cm during the seeding phase, the system automatically issues an alert, prompting adjustments to the dopant dosage or casting speed.

[0061] Working Principle: Eddy Current Generation: An alternating current (1-20kHz) is passed through excitation coil 2, generating an alternating magnetic field. Crystal ingot 3 rotates at 10-30 rpm and lifts at 0.2-2.0 mm / min, cutting through the magnetic flux lines and generating closed eddy currents on the surface. Rotation ensures uniform eddy currents, while lifting adjusts the relative position of the crystal ingot and coil, enhancing signal strength.

[0062] Resistivity measurement: Eddy current changes the impedance of the excitation coil 2. The signal acquisition module extracts the amplitude and phase through the lock-in amplifier and calculates the skin depth δ. The data processing module calculates the skin depth δ according to the formula δ=(ρ / (πfμ))^(1 / 2)(μ=4π×10 -7 H / m) to calculate the resistivity ρ.

[0063] Adjustment of pulling speed parameters: Dynamically adjust the frequency and sampling rate in the seeding (0.5-1.5 mm / min, high frequency 15 kHz), shoulder release (0.3-1.0 mm / min, 8 kHz), shoulder rotation (0.2-0.8 mm / min, 3 kHz), and equal diameter (0.5-2.0 mm / min, 2 kHz) stages to optimize the eddy current signal.

[0064] Temperature correction: The temperature (1440-1451°C) was monitored by thermocouples and infrared thermometers. DFT (VASP) and MD (LAMMPS) were used to simulate the dopant behavior. The error was corrected by substituting the formula: ρcorrect = ρmeasured × (1 + k·ΔT) (k = 0.01 / °C).

[0065] Machine learning prediction: The random forest model predicts shoulder resistivity based on a historical doping database (including pulling speed, temperature, and phosphorus concentration), with an error within 15%, guiding process optimization.

[0066] Implementation Effect

[0067] Measurement accuracy: Resistivity in the seeding stage is 7.58Ω·cm, shoulder release is 6.66Ω·cm, shoulder rotation is 5.58Ω·cm, and equal diameter is 5.5Ω·cm. The error compared with the four-point probe method is less than 10%, meeting the requirements of photovoltaic silicon single crystals.

[0068] Yield improvement: Real-time warning reduces resistance back-cutting, and the yield is increased by about 8%.

[0069] Stability: The excitation coil runs continuously for 500 hours without failure under the protection of the water-cooling screen, and the detection device automatically processes data to reduce manual intervention.

[0070] Process Guidance: Machine learning predicts shoulder resistivity with an error of 12%, optimizes pulling speed and dopant dosage, and reduces process adjustment costs by approximately 10%.

[0071] While the present invention has been disclosed above with reference to preferred embodiments, this is not intended to limit the present invention. Persons skilled in the art will readily appreciate that various modifications and variations can be made without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A method for automatically measuring resistivity during crystal pulling, characterized in that: The following processes are included: An excitation coil (2) is provided in a water-cooled panel (1) of a crystal pulling furnace, and an alternating current is passed through the excitation coil (2) to generate an alternating magnetic field; During the crystal pulling process, the alternating magnetic field is cut by the rotation and lifting movement of the crystal rod (3), thereby generating eddy currents; measuring the impedance change or magnetic field disturbance of the excitation coil (2) caused by the eddy current, and calculating the resistivity of the crystal rod (3); According to the different pulling speeds in the seeding, shoulder release, shoulder rotation and equal diameter stages of the crystal pulling process, the corresponding alternating current frequency and sampling rate are set to correct the temperature error in resistivity measurement; The resistivity is calculated by the formula δ=(ρ / (πfμ))^(1 / 2), where ρ is the resistivity, f is the alternating current frequency, and μ is the magnetic permeability of the crystal rod (3), thereby achieving real-time automatic measurement of the resistivity during the crystal pulling process.

2. The method for automatically measuring resistivity during crystal pulling according to claim 1, wherein: The excitation coil (2) is arranged on the inner wall of the water-cooling screen (1), close to the seeding area of ​​the crystal rod (3); the excitation coil (2) is made of copper, has 50-200 turns, and is 10-50 mm away from the crystal rod (3), and is used to measure the resistivity of the fine grain part during the seeding stage.

3. The method for automatically measuring resistivity during crystal pulling according to claim 1 or 2, wherein: The pulling speed and corresponding parameters include: During the seeding stage, the pulling speed is 0.5-1.5 mm / min, the alternating current frequency is 10-20 kHz, and the sampling rate is 100 Hz; During the shoulder release phase, the pulling speed was 0.3-1.0 mm / min, the alternating current frequency was 5-10 kHz, and the sampling rate was 50 Hz; During the shoulder rotation phase, the pulling speed was 0.2-0.8 mm / min, the alternating current frequency was 2-5 kHz, and the sampling rate was 30 Hz; In the constant diameter stage, the pulling speed is 0.5-2.0 mm / min, the alternating current frequency is 1-3 kHz, and the sampling rate is 30 Hz; The parameters are adjusted according to the pulling speed to optimize the sensitivity of the eddy current signal and the resistivity measurement accuracy.

4. The method for automatically measuring resistivity during crystal pulling according to claim 1, wherein: The rotation and lifting motion of the crystal rod (3) include: a rotation speed of 10-30 rpm and a lifting speed of 0.2-2.0 mm / min, the rotation motion ensures uniform eddy current distribution, and the lifting motion adjusts the relative position of the crystal rod (3) and the excitation coil (2), thereby enhancing the magnetic flux line cutting efficiency.

5. The method for automatically measuring resistivity during crystal pulling according to claim 1 or 3, wherein: The temperature error correction includes: The temperature distribution in the crystal pulling furnace is monitored in real time by a thermocouple or an infrared thermometer to obtain the surface temperature of the crystal rod (3); Combined with first-principles calculations (DFT) or molecular dynamics (MD) simulations, the formation energy or diffusion rate of dopants in the silicon lattice is calculated to determine the influence of temperature on resistivity; According to the formula ρ 修正 =ρ 测量 ×(1+k·ΔT) to correct the resistivity, where k is the temperature coefficient and ΔT is the temperature deviation.

6. The method for automatically measuring resistivity during crystal pulling according to claim 1, wherein: The measuring step is performed by a detection device, and the detection device includes: A signal acquisition module, using an impedance analyzer or a Hall sensor, to acquire the impedance change or magnetic field disturbance signal of the excitation coil (2); The data processing module uses a microcontroller or FPGA to calculate the resistivity according to the formula δ = (ρ / (πfμ))^(1 / 2) and performs error correction in combination with the temperature correction formula.

7. The method for automatically measuring resistivity during crystal pulling according to claim 6, wherein: The data processing module adopts a machine learning algorithm to predict the resistivity of the shoulder of the crystal rod (3) based on a historical doping database, including doping concentration, pulling speed, and temperature characteristics, through a random forest or graph neural network, and the prediction error is controlled within 15%.

8. The method for automatically measuring resistivity during crystal pulling according to claim 1 or 4, characterized in that: The eddy current generating step comprises: The crystal rod (3) rotates at 10-30 rpm, evenly cutting the magnetic flux lines of the excitation coil (2) to generate a closed annular eddy current; The crystal rod (3) is lifted at a speed of 0.2-2.0 mm / min to change its relative position with the excitation coil (2) and enhance the eddy current signal strength; The amplitude and phase of the eddy current signal are extracted through a lock-in amplifier and used to calculate the resistivity.

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