A method and system for predicting arsenic make-up quantity in a heavy arsenic-doped single crystal silicon pulling process

Abstract

A method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped monocrystalline silicon, relating to the field of monocrystalline silicon preparation technology, includes: acquiring pulling data during the pulling process of monocrystalline silicon, including the time interval between the current doping and the previous doping, the number of times the burr falls off during the shoulder formation stage and the cumulative weight of the burr falling off during the constant diameter stage within the time interval; inputting the pulling data into a replenishment calculation model to calculate the actual amount of arsenic replenishment; the replenishment calculation model establishes a quantitative mapping relationship between various factors and the replenishment amount, eliminating reliance on manual experience and eliminating errors caused by subjective judgment of operators. Using the replenishment calculation model can achieve accurate calculation of the amount of arsenic replenishment, ensuring that the resistivity deviation of the crystal rod head from the target value is stably controlled within a small range, reducing the crystal rod scrap rate caused by resistivity deviation, and possessing significant economic benefits and industrial application value.

Description

Technical Field

[0001] This invention relates to the field of monocrystalline silicon preparation technology, specifically to a method and system for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped monocrystalline silicon. Background Technology

[0002] Heavy arsenic-doped monocrystalline silicon is widely used as a substrate material for power devices, MOSFETs, microwave integrated circuits, and other components due to its excellent electrical conductivity and low temperature coefficient of resistivity. As components evolve towards lower power consumption and higher voltage withstand capability, the resistivity of the required monocrystalline silicon continues to decrease. Since the equilibrium segregation coefficient of arsenic in silicon is only about 0.2, a high arsenic concentration needs to be maintained in the molten silicon to obtain low-resistivity monocrystalline silicon. However, while high arsenic concentration reduces resistivity, it also reduces the surface tension of the molten silicon, disrupting the solid-liquid interface stability and easily leading to compositional supercooling, resulting in frequent sheathing or wire breakage accidents during the pulling process. Furthermore, as the pulling time increases, the effective arsenic concentration in the molten silicon decreases non-linearly, causing the resistivity at the head of the ingot to deviate from the target value even if the initial doping is accurate. Therefore, a certain amount of arsenic needs to be added to the molten silicon during the monocrystalline silicon pulling process.

[0003] Currently, the determination of arsenic replenishment during the pulling process of heavily arsenic-doped single-crystal silicon mainly relies on manual experience. Operators roughly estimate the amount of arsenic to be replenished based on their personal experience, considering factors such as the doping time interval, the location of the detached crystal, and the weight of the detached crystal. This method has several shortcomings in practical applications. First, arsenic continuously volatilizes in the high-temperature molten silicon, and the volatilization rate decreases non-linearly over time, making it impossible to accurately estimate the amount of arsenic that has volatilized based solely on experience. Second, factors such as the doping time interval, the location of the detached crystal, and the weight of the detached crystal all affect the arsenic concentration in the molten silicon, thus affecting the determination of the replenishment amount. Furthermore, these factors are interdependent, resulting in a complex non-linear relationship between the amount of arsenic replenishment and the target resistivity. Relying on manual experience for replenishment is highly subjective and prone to significant errors. The resistivity at the head of the pulled crystal rod deviates significantly from the target resistivity, leading to a high scrap rate and substantial economic losses. Summary of the Invention

[0004] To address the shortcomings of existing technologies where the amount of arsenic added is often inaccurate, this invention provides a method and system for predicting the amount of arsenic added during the pulling process of heavily arsenic-doped single-crystal silicon.

[0005] To achieve the above objectives, the specific solution adopted by the present invention is as follows: a method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single crystal silicon, comprising: Acquire pulling data of monocrystalline silicon during the pulling process, including the time interval between the current doping and the previous doping. and time interval Number of times the buds drop during the shoulder-opening stage occurs inside The cumulative weight of bud drop during the isodiameter stage ; The pulling data is input into the doping amount calculation model to calculate the actual arsenic doping amount. The doping amount calculation model is as follows: , , , in, This is the actual amount of additive. This is the theoretical amount of additive. Basic dosage, For correction factor, For the target resistivity, Correction coefficient The fitting function, For time interval The obtained extension time, Based on the delay time lookup table mapping functions, This represents the cumulative weight of the buds that fell off during the isodiameter stage. This refers to the number of times the buds fall during the shoulder-growing stage. For indicator functions, This is the cumulative weight compensation coefficient for bud drop during the equal diameter stage. This is a compensation coefficient for the number of times the buds fall during the shoulder-growing stage. This is the offset triggered by the shedding of the bud during the equal diameter stage.

[0006] An optimized scheme for the aforementioned method of predicting arsenic replenishment during the pulling process of heavily arsenic-doped single-crystal silicon: based on time intervals. Obtaining extended time The methods include: , in, This is the offset constant for the pulling process of heavily arsenic-doped single-crystal silicon.

[0007] Another optimization scheme for the above-mentioned method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single crystal silicon: offset constant. It takes 3.9 to 4.1 hours.

[0008] As an optimization scheme for the above-mentioned method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single crystal silicon: a cumulative weight compensation coefficient for burr shedding during the constant diameter stage. The compensation coefficient for the number of bud drops during the shoulder-growing stage is 2.8~3.2. The offset for triggering the sheath drop during the equal-diameter stage is 9.5~10.5. It is 9.5~10.5g.

[0009] As an optimization scheme for the above-mentioned method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single crystal silicon: indicator function The method for determining the value is as follows: The cumulative weight of bud drop during the equal diameter stage When the value is greater than 0, the indicator function takes the value of 1; The cumulative weight of bud drop during the equal diameter stage When the value is 0, the indicator function takes the value 0.

[0010] As an optimization scheme for the above-mentioned method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single crystal silicon: based on a lookup table mapping function. Obtain the basic amount of additive The methods include: Using a pre-built mapping table for lookup and extension time Corresponding basic dosage Based on multiple delay times Compared with the basic amount of additive The scatter plot yields a mapping table.

[0011] As an alternative optimization scheme for the above-mentioned method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single-crystal silicon: fitting function The construction methods include: Calculate the resistivity of multiple targets without bud drop using a doping amount calculation model. Corresponding theoretical dosage ; To achieve the target resistivity at the tip of the crystal rod. Required actual amount of additive Based on the actual amount of additives Compared with theoretical dosage The ratio of to is used as a candidate value for the correction coefficient. Finally, multiple sets of candidate values ​​for the correction coefficient were obtained. Compared with the actual amount of additive ; For multiple sets of candidate correction coefficient values Compared with the actual amount of additive The least squares fitting is used to obtain the fitting function. .

[0012] A prediction system for arsenic doping amount during the pulling process of heavily arsenic-doped single crystal silicon includes a data acquisition module, a data processing module, and a data display module; The data acquisition module is used to acquire pulling data of monocrystalline silicon during the pulling process. The pulling data includes the time interval between the current doping and the previous doping. and in the time interval Number of times the buds drop during the shoulder-opening stage occurs inside The cumulative weight of bud drop during the isodiameter stage ; The data processing module is used to calculate the actual amount of arsenic added based on the pulling data using the doping amount calculation model; The data display module is used to visualize the actual amount of arsenic added.

[0013] Compared with the prior art, the present invention has the following advantages: The present invention calculates the actual amount of arsenic added based on the pulling data using a doping amount calculation model, and the doping amount calculation model comprehensively considers the doping time interval. Number of times the buds fall during the shoulder-growing stage Cumulative weight of bud drop during the equal diameter stage By considering the influence of multiple factors, a quantitative mapping relationship between each factor and the amount of arsenic doping is established, eliminating reliance on manual experience and removing errors caused by operators' subjective judgment. The arsenic doping calculation model enables precise calculation of the arsenic doping amount, ensuring that the resistivity deviation of the crystal rod head from the target value is stably controlled within 1%, reducing the crystal rod scrap rate caused by resistivity deviation, and demonstrating significant economic benefits and industrial application value. Attached Figure Description

[0014] Figure 1 This is a flowchart of the prediction method of the present invention. Detailed Implementation

[0015] The technical solution of the present invention will be further described in detail below with reference to specific embodiments. Parts not described or disclosed in detail in the following embodiments of the present invention should be understood as prior art known or should be known by those skilled in the art.

[0016] like Figure 1 As shown, the present invention provides a method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single crystal silicon, including steps S1 to S2.

[0017] S1. Obtain pulling data of single-crystal silicon during the pulling process. The pulling data includes the time interval between the current doping and the previous doping. and time interval Number of times the buds drop during the shoulder-opening stage occurs inside The cumulative weight of bud drop during the isodiameter stage .

[0018] S2. Input the pulling data into the doping amount calculation model to calculate the actual arsenic doping amount. The doping amount calculation model is as follows: , , , in, This is the actual amount of additive. This is the theoretical amount of additive. Basic dosage, For correction factor, For the target resistivity, Correction coefficient The fitting function, For time interval The obtained extension time, Based on the delay time lookup table mapping functions, This represents the cumulative weight of the buds that fell off during the isodiameter stage. This refers to the number of times the buds fall during the shoulder-growing stage. For indicator functions, This is the cumulative weight compensation coefficient for bud drop during the equal diameter stage. This is a compensation coefficient for the number of times the buds fall during the shoulder-growing stage. This refers to the offset triggered by the shedding of the bud during the equal diameter stage. The method for calculating the amount of admixture based on the pulling data includes S21 to S24.

[0019] S21. Calculate the delay time. Based on time interval Obtaining extended time The methods include: , in, This is the offset constant for the pulling process of heavily arsenic-doped single-crystal silicon; for the arsenic system, The typical duration is 3.9~4.1 hours. In this embodiment, Take 4 hours.

[0020] S22, Calculate the basic amount of admixture. Based on lookup table mapping function Obtain the basic amount of additive The methods include: using a pre-built mapping table for lookup and time extension. Corresponding basic dosage Based on multiple delay times Compared with the basic amount of additive The scatter plot yields a mapping table.

[0021] The specific process for obtaining the mapping table is as follows: The feed amount is fixed at 105 kg, and the target resistivity is... The number of bud drops during the shoulder-opening stage is 0.002 Ω·cm. The cumulative weight of bud drop during the 0th and equal diameter stages is 0. 0 kg, change the time interval This extends the time. Take 5h, 6h, 7h..., 50h respectively, for each extension time Record the resistivity at the head of the crystal rod. The amount of additive required to achieve 0.002 ± 0.00005 Ω·cm, this additive amount is the basic additive amount. For the data ( , Draw a scatter plot to identify the basic amount of admixture. With delay time The arsenic exhibits piecewise linear growth, meaning the slope gradually increases, consistent with the characteristic that the arsenic volatilization rate accelerates with increasing concentration. Cubic spline interpolation was used to obtain the basic addition amount for each integer hour. A mapping table is formed. The error is confirmed to be ≤2% through three sets of independent verification batches. In this embodiment, the mapping table is shown in Table 1.

[0022] Table 1. Delay Time Compared with the basic amount of additive mapping table

[0023] The pattern of the mapping table is illustrated using a portion of the data in Table 1 as an example, as shown in Table 2.

[0024] Table 2. Explanation of Patterns

[0025] As shown in Table 2, the delay time Compared with the basic amount of additive It shows a strong positive correlation, and the correlation increases with the extension time. As the concentration of arsenic in the molten silicon increases, the required incremental doping per unit hour gradually increases, rising from 4-5 g / h in the early stages to 12-13 g / h in the later stages. This is because even after the concentration of arsenic in the molten silicon decreases over time, the volatilization rate remains high, requiring additional compensation. The mapping table is essentially a discretized and precise model of the cumulative effect of arsenic volatilization loss over time.

[0026] S23, Calculate the theoretical amount of additive. .

[0027] , Cumulative weight compensation coefficient for bud drop during equal diameter stage Compensation coefficient for the number of times the buds fall during the shoulder-dropping stage Equal diameter stage bud drop trigger offset All were obtained through calibration, and the target resistivity was determined during the calibration process. The value is 0.002 Ω·cm, and the calibration process is as follows.

[0028] Cumulative weight compensation coefficient for bud drop during equal diameter stage Calibration: Number of bud drops during the fixed shoulder-drop stage 0 times, cumulative weight of bud drop during the equal diameter stage 0 kg, change the time interval This extends the time. The resistivity at the head of the crystal rod was recorded at 20h, 30h, and 40h respectively during the single-crystal silicon pulling process without additional doping. The offset is used to deduce the required compensation amount. Then, a constant-diameter clipping is manufactured to... Take 5kg, 10kg, 15kg, and 20kg of crystal rods and record the resistivity at the head of the rod. Achieve target resistivity Additional dosage required For data points ( , A linear regression was performed, and the slope was the compensation coefficient for the cumulative weight of bud drop during the isodiameter stage. Cumulative weight compensation coefficient for bud drop during the equal diameter stage The value is 2.8~3.2. In this embodiment, the cumulative weight compensation coefficient for bud drop during the equal diameter stage is 2.8~3.2. It is version 3.0.

[0029] Compensation coefficient for the number of times the buds fall during the shoulder-dropping stage Calibration: Cumulative weight of bud drop during the fixed equal diameter stage 0kg, extension time The duration is 30 hours, and the number of bud drops during the shoulder-dropping phase is changed. ,make Take values ​​1, 2, and 3 respectively, and record the resistivity at the head of the crystal rod. Achieve target resistivity Additional dosage required For data points ( , Perform linear regression; the slope is the compensation coefficient for the number of bud drops during the shoulder-growing stage. Compensation coefficient for the number of times the buds fall during the shoulder-dropping stage The value is 9.5~10.5. In this embodiment, the compensation coefficient for the number of bud drops during the shoulder-opening stage is... It is 10.0.

[0030] equal diameter stage bud drop trigger offset Calibration: Number of bud drops during the fixed shoulder-drop stage 0 times, extension time The experiment lasted 30 hours. Two groups were set up: Group A: cumulative weight of bud drop during the isodiameter stage. Group B: Total weight of bud drop during the equal diameter stage (0 kg); The experimental results showed that group B needed an additional 10g of arsenic compared to group A, with a dose of 0.5kg. This value was consistent with... The size is weakly correlated, and the offset is triggered by the sheath falling during the equal diameter stage. The weight is 9.5~10.5g. In this embodiment, the offset amount triggered by the sheath falling during the equal diameter stage is... It is 10.0.

[0031] S24. Calculate the actual amount of admixture added. .

[0032] , Fitting function The construction methods include: Calculate the resistivity of multiple targets without bud drop using a doping amount calculation model. Corresponding theoretical dosage .

[0033] Obtain the resistivity of the crystal rod head Achieving each target resistivity Required actual amount of additive Based on the actual amount of additives Compared with theoretical dosage The ratio of to is used as a candidate value for the correction coefficient. Finally, multiple sets of candidate values ​​for the correction coefficient were obtained. Compared with the actual amount of additive .

[0034] For multiple sets of candidate correction coefficient values Compared with the actual amount of additive The least squares fitting is used to obtain the fitting function. .

[0035] More specifically: Calculate the resistivity of multiple targets without bud drop using a doping amount calculation model. Corresponding theoretical dosage Target resistivity Measure 0.001 Ω·cm, 0.0015 Ω·cm, 0.002 Ω·cm, 0.0025 Ω·cm, 0.003 Ω·cm, 0.004 Ω·cm, and 0.005 Ω·cm respectively. Maintain a fixed extension time. The number of times the buds fall during the shoulder-growing stage (30 hours). 0 times, cumulative weight of bud drop during the equal diameter stage The weight is 0 kg, using the cumulative weight compensation coefficient for bud drop during the equal diameter stage, which has been calibrated in step S23. Compensation coefficient for the number of times the buds fall during the shoulder-dropping stage Equal diameter stage bud drop trigger offset The theoretical amount of additive was calculated. Record the resistivity at the head of the crystal rod. Achieve target resistivity Required actual amount of additive Based on the actual amount of additives Compared with theoretical dosage The ratio of to is used as a candidate value for the correction coefficient. Multiple sets of data points were obtained. , (as shown in Table 3).

[0036] Table 3 Different target resistivity Corresponding candidate values ​​of correction coefficients

[0037] For data points ( , The least squares fitting is used to obtain the fitting function. .

[0038] Goodness-of-fit verification: Calculate the sum of squared residuals = 0.991, indicating that the calculation model for the amount of additives has high interpretability.

[0039] Ultimately, the actual amount of additive was used. Perform the arsenic doping operation.

[0040] Due to factors such as differences in single-crystal furnaces, fluctuations in raw material impurities, and aging of graphite components, even the same doping amount calculation model parameters may produce slight deviations. Therefore, the doping amount calculation model of this invention can be based on the resistivity of the pulled crystal ingot head. Compensation coefficient for cumulative weight loss during the equal diameter stage Compensation coefficient for the number of times the buds fall during the shoulder-dropping stage Equal diameter stage bud drop trigger offset The adaptive correction is performed as follows.

[0041] After each batch of crystal pulling is completed, the resistivity of the crystal ingot head is measured. And calculate the head resistivity With target resistivity Relative deviation: , in, Head resistivity With target resistivity Relative deviation.

[0042] like If so, no correction is needed; if If this occurs, the adaptive correction process will be triggered.

[0043] Cumulative weight compensation coefficient for bud drop during equal diameter stage Compensation coefficient for the number of times the buds fall during the shoulder-dropping stage Equal diameter stage bud drop trigger offset The correction is for long-term drift calibration.

[0044] When multiple batches of the same sign show relative deviations For example, if five consecutive batches are all above the recommended level, multiple linear regression is used to collect the cumulative weight of bud drop during the equal diameter stage of the past 20 heats. Number of times the buds fall during the shoulder-growing stage Indicator functions The value and relative deviation Using the data, solve for the optimal increment. , , .

[0045] , Updated cumulative weight compensation coefficient for bud drop during equal diameter stage Compensation coefficient for the number of times the buds fall during the shoulder-dropping stage Equal diameter stage bud drop trigger offset for: , , .

[0046] It should be noted that the doping amount calculation model of this invention can be transferred to heavily phosphorus-doped and heavily antimony-doped systems. Only the mapping table for the arsenic system needs to be replaced with that for the phosphorus or antimony system, and the cumulative weight compensation coefficient for shedding during the isodiameter stage needs to be recalibrated. Compensation coefficient for the number of times the buds fall during the shoulder-dropping stage Equal diameter stage bud drop trigger offset It can be used for pulling single crystals that are heavily doped with phosphorus or antimony. The offset constant of the phosphorus system is generally taken as 6h, and the offset constant of the antimony system is generally taken as 5h. This calculation model for the amount of doping can significantly reduce the development cost of new dopant processes.

[0047] This invention provides an embodiment of the applicant's actual operation process.

[0048] Known data: Feed rate is 105 kg, target resistivity The value is 0.002 Ω·cm. The last doping time was 01:20:00 on 2025-07-02. The expected doping time this time is 09:10:00 on 2025-07-03. The number of times the bud breaks off during the shoulder formation stage... The number of times the buds fell during the isodiameter stage was 0, and the cumulative weight of the buds fell was It weighs 23kg.

[0049] Time interval It takes 31.83 hours.

[0050] Calculate the delay time The hour is rounded up to 36 hours.

[0051] Refer to Table 1 for the extension time. Basic dosage corresponding to 36 hours It weighs 320g.

[0052] Calculate the theoretical amount of additive The cumulative weight compensation coefficient for bud drop during the diameter stage Take 3.0 as the compensation coefficient for the number of times the buds fall during the shoulder placement phase. Take 10.0, the offset for triggering the sheath drop during the equal diameter stage. Take 10.0g, indicator function The value is 1.

[0053] Theoretical dosage .

[0054] Target resistivity Corresponding correction factor It is 1.21.

[0055] Actual amount of admixture .

[0056] Implementation results: Based on the above actual amount of admixture. After additional doping of 482.8g, the head resistivity of the crystal rod... The measured value was 0.00199 Ω·cm, which is consistent with the target resistivity. The difference is -0.5% for a 0.002 Ω·cm.

[0057] The applicant also conducted a cumulative weight measurement of bud drop at different diameter stages. and different target resistivity The experimental data are shown in Tables 4 and 5.

[0058] Table 4. Cumulative weight of bud drop at different diameter stages The results of the supplementary doping

[0059] Table 5 Different target resistivity Results of supplementary mixing

[0060] Table 4 shows the target resistivity. 0.002 Ω·cm, extension time The experiment was conducted over a period of 35 hours. Table 5 shows the number of bud drops during the shoulder-opening stage. The cumulative weight of bud drop during one equal-diameter stage. For 12kg, extension time It was performed over a period of 35 hours.

[0061] Based on long-term data statistics, As a standard, the head resistivity of the doping ingot calculated using the doping amount calculation model of this invention is used to determine the doping amount. The pass rate was 96.7%, and the head resistivity of the crystal rods that relied on manual experience for doping was [not specified]. The pass rate was only 55%.

[0062] The doping amount calculation model of this invention can reduce the production cost per kilogram of crystal rod by about 23%, and save about 38% of arsenic dopant per furnace per year. This invention can also reduce the head resistivity. With target resistivity The deviation is controlled within 1%, which has significant economic benefits and industrial application value.

[0063] Finally, this invention provides a prediction system for the arsenic doping amount during the pulling process of heavily arsenic-doped single-crystal silicon, including a data acquisition module, a data processing module, and a data display module.

[0064] The data acquisition module is used to acquire pulling data of monocrystalline silicon during the pulling process. The pulling data includes the time interval between the current doping and the previous doping. and in that time interval Number of times the buds drop during the shoulder-opening stage occurs inside The cumulative weight of bud drop during the isodiameter stage .

[0065] The data processing module is used to calculate the actual amount of arsenic added based on the pulling data using the doping amount calculation model. The doping amount calculation model is as shown above and will not be repeated here.

[0066] The data display module is used to visualize the actual amount of arsenic added.

[0067] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. 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 the invention. Therefore, the invention 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 predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single-crystal silicon, characterized in that, include: Acquire pulling data of monocrystalline silicon during the pulling process, including the time interval between the current doping and the previous doping. and time interval Number of times the buds drop during the shoulder-opening stage occurs inside The cumulative weight of bud drop during the isodiameter stage ; The actual amount of arsenic added is calculated by inputting the pulling data into the doping amount calculation model. The doping amount calculation model is as follows: ， ， ， in, This is the actual amount of additive. This is the theoretical amount of additive. Basic dosage, For correction factor, For the target resistivity, Correction coefficient The fitting function, For time interval The obtained extension time, Based on the delay time lookup table mapping functions, This represents the cumulative weight of bud drop during the isodiameter stage. This refers to the number of times the buds fall during the shoulder-growing stage. For indicator functions, This is the cumulative weight compensation coefficient for bud drop during the equal diameter stage. This is a compensation coefficient for the number of times the buds fall during the shoulder-growing stage. This is the offset triggered by the shedding of the bud during the equal diameter stage.

2. The method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single crystal silicon according to claim 1, characterized in that, Based on time interval Obtaining extended time The methods include: ， in, This is the offset constant for the pulling process of heavily arsenic-doped single-crystal silicon.

3. The method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single crystal silicon according to claim 2, characterized in that, Offset constant It takes 3.9 to 4.1 hours.

4. The method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single crystal silicon according to claim 1, characterized in that, Cumulative weight compensation coefficient for bud drop during equal diameter stage The compensation coefficient for the number of bud drops during the shoulder-growing stage is 2.8~3.

2. The offset for triggering the sheath drop during the equal-diameter stage is 9.5~10.

5. It is 9.5~10.5g.

5. The method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single crystal silicon according to claim 1, characterized in that, Indicator Function The method for determining the value is as follows: The cumulative weight of bud drop during the equal diameter stage When the value is greater than 0, the indicator function takes the value of 1; The cumulative weight of bud drop during the equal diameter stage When the value is 0, the indicator function takes the value 0.

6. The method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single crystal silicon according to claim 1, characterized in that, Based on table lookup mapping function Obtain the basic amount of additive The methods include: Using a pre-built mapping table for lookup and extension time Corresponding basic dosage Based on multiple extension times Compared with the basic amount of additive The scatter plot yields a mapping table.

7. The method for predicting the amount of arsenic replenishment during the pulling process of heavily arsenic-doped single crystal silicon according to claim 1, characterized in that, Fitting function The construction methods include: Calculate the resistivity of multiple targets without bud drop using a doping amount calculation model. Corresponding theoretical dosage ; To achieve the target resistivity at the tip of the crystal rod. Required actual amount of additive Based on the actual amount of additives Compared with theoretical dosage The ratio of to is used as a candidate value for the correction coefficient. Finally, multiple sets of candidate values ​​for the correction coefficient were obtained. Compared with the actual amount of additive ; For multiple sets of candidate correction coefficient values Compared with the actual amount of additive The least squares fitting is used to obtain the fitting function. .

8. A system for predicting the arsenic doping level during the pulling process of heavily arsenic-doped single-crystal silicon, characterized in that, It includes a data acquisition module, a data processing module, and a data display module; The data acquisition module is used to acquire pulling data of monocrystalline silicon during the pulling process. The pulling data includes the time interval between the current doping and the previous doping. and in the time interval Number of times the buds fall during the shoulder-opening stage inside the body The cumulative weight of bud drop during the isodiameter stage ; The data processing module is used to calculate the actual amount of arsenic added based on the pulling data using the doping amount calculation model; The data display module is used to visualize the actual amount of arsenic added.

Images