Crystal bar axial resistivity control method, device, equipment and product

Abstract

The application relates to a crystal bar axial resistivity control method and device. The method comprises the following steps: predicting a first antimony evaporation amount of a crystal pulling isodiametric process in an antimony-phosphorus co-doped single crystal furnace according to the correlation between an evaporation constant and a remaining material weight in the antimony-phosphorus co-doped single crystal furnace, and controlling an antimony-phosphorus doping ratio of the isodiametric process according to the first antimony evaporation amount; predicting a second antimony evaporation amount of a crystal pulling ignition process in the antimony-phosphorus co-doped single crystal furnace according to the correlation between the evaporation constant and an ignition duration, and controlling the antimony-phosphorus doping ratio of the ignition process according to the second antimony evaporation amount; predicting a third antimony evaporation amount of a re-injection stage in the antimony-phosphorus co-doped single crystal furnace according to a target re-injection evaporation calculation model, and controlling the antimony-phosphorus doping ratio of the re-injection stage according to the third antimony evaporation amount, so that the axial resistivity uniformity of a straight-pulling obtained crystal bar is located in a target range, and at least the axial doping element uniformity in the single crystal silicon during the crystal pulling process is improved, and the axial resistivity uniformity of the crystal bar is improved.

Description

Technical Field

[0001] This disclosure belongs to the field of Czochralski silicon single crystal technology, specifically relating to a method, device, equipment and product for controlling the axial resistivity of a crystal rod. Background Technology

[0002] The Czochralski method is a relatively simple method for preparing single-crystal silicon, which involves gradually pulling single-crystal silicon using a rotating seed crystal. This method has relatively low production costs and can be mass-produced, producing high-quality, large-size semiconductor-grade or solar-grade single-crystal silicon wafers. Therefore, it is widely used in the preparation of single-crystal silicon.

[0003] However, the axial resistivity of Czochralski-grown monocrystalline silicon is difficult to control, and it has many crystal defects, which reduces minority carrier lifetime. Furthermore, the high oxygen content creates oxygen donors, leading to a decrease in solar cell conversion efficiency and limiting the potential for improvement.

[0004] Therefore, in order to ensure the quality and performance of single-crystal silicon prepared by the Czochralski method, it is necessary to provide effective control and optimization methods for the axial resistivity uniformity of Czochralski single-crystal silicon. Summary of the Invention

[0005] Based on this, it is necessary to provide a method, apparatus, equipment and product for controlling the axial resistivity of a crystal rod to address the problems mentioned above in the background art. This method can at least ensure that the uniformity of axial doped elements in single crystal silicon is improved during the crystal pulling process, thereby achieving precise control of resistivity and improving the uniformity of the axial resistivity of the crystal rod.

[0006] According to various embodiments of this disclosure, in a first aspect, this disclosure provides a method for controlling the axial resistivity of a crystal rod, comprising:

[0007] Based on the correlation between the evaporation constant and the weight of the residue in the antimony-phosphorus co-doped single crystal furnace, the first antimony evaporation amount in the crystal pulling process of the antimony-phosphorus co-doped single crystal furnace is predicted, and the antimony-phosphorus doping ratio in the process of crystal pulling is controlled according to the first antimony evaporation amount.

[0008] Based on the correlation between the evaporation constant and the release time, the second antimony evaporation amount in the crystal pulling and release process in the antimony-phosphorus co-doped single crystal furnace is predicted, and the antimony-phosphorus doping ratio in the release process is controlled based on the second antimony evaporation amount.

[0009] Based on the target re-evaporation calculation model, the third antimony evaporation amount in the re-evaporation stage of the antimony-phosphorus co-doped single crystal furnace is predicted, and the antimony-phosphorus doping ratio in the re-evaporation stage is controlled according to the third antimony evaporation amount, so that the axial resistivity uniformity of the Czochralski-grown crystal rod is within the target range.

[0010] The ingot axial resistivity control method in the above embodiments, since the Czochralski silicon single crystal fabrication process includes stages such as feeding, melting, necking, shoulder formation, and equalization, adopts the antimony-phosphorus co-doped Czochralski silicon single crystal fabrication process. Utilizing the characteristic that the amount of antimony evaporation during the equalization process, necking process, and re-doping stage has a significant impact on the uniformity of the ingot axial resistivity, the method first predicts the first amount of antimony evaporation during the equalization process in the antimony-phosphorus co-doped single crystal furnace based on the correlation between the evaporation constant and the weight of the remaining material. Based on the first amount of antimony evaporation, the antimony-phosphorus doping ratio during the equalization process is controlled to ensure accurate antimony doping during the equalization process. Based on the correlation between the evaporation constant and the necking time, the method further predicts... The second antimony evaporation amount during the crystal pulling and release process in an antimony-phosphorus co-doped single crystal furnace is measured. The antimony-phosphorus doping ratio during the release process is controlled based on the second antimony evaporation amount to ensure accurate antimony doping during the release process. Furthermore, based on the target re-evaporation calculation model, the third antimony evaporation amount during the re-evaporation stage in the antimony-phosphorus co-doped single crystal furnace is predicted. The antimony-phosphorus doping ratio during the re-evaporation stage is controlled based on the third antimony evaporation amount to ensure accurate antimony doping during the re-evaporation stage. This ensures improved uniformity of axial doped elements in single crystal silicon during crystal pulling, achieving precise control of resistivity. This ensures that the axial resistivity uniformity of the Czochralski-grown ingot is within the target range, thereby improving the uniformity of the ingot's axial resistivity.

[0011] In some embodiments, the method for controlling the axial resistivity of crystal rods further includes the step of obtaining a target re-evaporation calculation model:

[0012] Correlation analysis algorithms were used to identify irrelevant variables in the re-feeding stage whose correlation with antimony evaporation was less than a threshold.

[0013] Based on irrelevant variables, target variables related to antimony evaporation during the re-feeding stage are determined. Target variables include antimony concentration during the break-in process, residual material weight, and re-feeding time.

[0014] A linear fitting algorithm was used to determine the functional relationship between antimony evaporation and the target variable.

[0015] The ingot axial resistivity control method in the above embodiments uses a correlation analysis algorithm to determine irrelevant variables in the re-feeding stage whose correlation with antimony evaporation is less than a threshold. Based on these irrelevant variables, the target variables related to antimony evaporation in the re-feeding stage are determined. The target variables include the concentration of antimony in the broken wire, the weight of the remaining material, and the re-feeding time. Then, a linear fitting algorithm is used to determine the functional relationship between antimony evaporation and the target variables. Based on this functional relationship, the third antimony evaporation in the re-feeding stage in the antimony-phosphorus co-doped single crystal furnace can be predicted. The antimony-phosphorus doping ratio in the re-feeding stage can be controlled based on the third antimony evaporation, ensuring accurate doping of antimony in the re-feeding stage.

[0016] In some embodiments, the method for controlling the axial resistivity of the crystal rod further includes using correlation analysis to determine the constant values ​​in the target re-evaporation calculation model as follows:

[0017] P = i + kQ;

[0018] In the above formula, P is the third antimony evaporation amount, Q is the weight of the remaining material in the re-feeding stage, and i and k are constants.

[0019] The crystal rod axial resistivity control method in the above embodiments establishes a specific functional relationship expression between the antimony evaporation amount and the target variable. Based on this specific functional relationship expression, it can predict the third antimony evaporation amount in the re-doping stage of the antimony-phosphorus co-doped single crystal furnace, reduce the computational complexity of the prediction algorithm and reduce the computation time, and control the antimony-phosphorus doping ratio in the re-doping stage based on the third antimony evaporation amount, ensuring accurate doping of antimony elements in the re-doping stage.

[0020] In some embodiments, the furnace pressure and argon flow rate in the antimony-phosphorus co-doped single crystal furnace are preset pressure and flow rate values, respectively; the crystal rod axial resistivity control method further includes:

[0021] Obtain the antimony diffusion constant after a predetermined amount of antimony is doped into the silicon melt in a single crystal furnace;

[0022] Based on the antimony diffusion constant, the simulated distribution curve of the axial resistance of the crystal rod caused by antimony segregation was calculated under the condition that the resistivity at the start of crystal pulling is at the target value.

[0023] Determine the measured resistivity distribution curve based on the simulated distribution curve;

[0024] Based on the measured resistivity distribution curve, the correlation between the evaporation constant and the weight of the remaining material during the constant diameter process was determined using correlation analysis.

[0025] In the above-described method for controlling the axial resistivity of the crystal rod, the diffusion constant of antimony in molten silicon affects its distribution and concentration, thereby influencing the growth rate and quality of the single crystal. Experiments show that this diffusion constant is related to factors such as the kinematic viscosity coefficient and relative rotation speed of the molten silicon, and that this value can be determined under specific growth conditions. Therefore, by setting the furnace pressure and argon flow rate to a preset value, multiple experiments were conducted to obtain the antimony diffusion constant after a preset amount of antimony was incorporated into the silicon melt in the single crystal furnace. This confirmed that the antimony diffusion constant and the corresponding growth parameters meet the requirements of current mass production. Then, based on the aforementioned antimony diffusion constant, the simulated distribution curve of the axial resistivity of the crystal rod caused by antimony segregation is calculated under the condition that the resistivity at the starting point of crystal pulling is the target value. The measured resistivity distribution curve is determined based on the simulated distribution curve, so that the fitting degree between the measured resistivity distribution curve and the simulated distribution curve is greater than or equal to a preset threshold. Then, based on the measured resistivity distribution curve, the correlation between the evaporation constant and the weight of the remaining material during the constant diameter process is determined by the correlation analysis method. Thus, the corresponding antimony evaporation constant can be accurately calculated based on the real-time weight of the remaining material in the single crystal furnace and this correlation, thereby accurately calculating the predicted antimony evaporation amount during the Czochralski constant diameter process.

[0026] In some embodiments, correlation analysis is used to determine the constant value in the relationship between the evaporation constant and the weight of the residue in the following constant diameter process:

[0027] Ev = a + bW + cW 2 +dW 3 ;

[0028] In the above formula, Ev is the antimony evaporation constant of the constant diameter process, W is the weight of the residue of the constant diameter process, and a, b, c and d are all constants.

[0029] The ingot axial resistivity control method in the above embodiments, after determining that the antimony evaporation constant is mainly related to the weight of the residue using correlation analysis, determines the constant value in the correlation between the evaporation constant and the weight of the residue in the equal diameter process after obtaining a large amount of actual data, and determines the functional expression of the evaporation constant and the weight of the residue in the equal diameter process. This enables the accurate calculation of the corresponding antimony evaporation constant based on the real-time weight of the residue in the single crystal furnace and the functional expression. Based on the antimony evaporation constant and the correlation between the antimony evaporation amount in the Czochralski equal diameter process and the antimony evaporation constant, the predicted antimony evaporation amount in the Czochralski equal diameter process can be accurately calculated, thus achieving accurate dynamic prediction of the predicted antimony evaporation amount in the Czochralski equal diameter process.

[0030] In some embodiments, the temperature during the crystal pulling and release process is a preset temperature value; the crystal rod axial resistivity control method further includes:

[0031] Obtain the curve of antimony evaporation constant during the ignition process as a function of ignition time in the single crystal furnace;

[0032] The functional expression between the antimony evaporation constant and the release time is determined based on the variation curve.

[0033] In the above embodiments, the method for controlling the axial resistivity of the crystal rod allows for the determination of a functional expression between the antimony evaporation constant and the release time in the single crystal furnace after obtaining the curve of the antimony evaporation constant versus the release time. This functional expression, along with the real-time release time, enables the accurate calculation of the current antimony evaporation constant during the Czochralski release process. Based on this function expression and the real-time release time, the predicted antimony evaporation amount during the Czochralski release process can be accurately calculated or predicted.

[0034] In some embodiments, determining the functional expression between the antimony evaporation constant and the release time includes:

[0035] Determine the constant values ​​in the following formulas:

[0036] Ev=m *t n ;

[0037] In the above formula, Ev is the antimony evaporation constant during the release process, t is the release time, and m and n are both constants.

[0038] The ingot axial resistivity control method in the above embodiments, after determining that the antimony evaporation constant in the Czochralski-de-arrival process is mainly related to the de-arrival time, can determine the constant value in the functional expression between the antimony evaporation constant and the de-arrival time based on a large amount of real data, thereby determining the specific functional expression between the antimony evaporation constant and the de-arrival time in the Czochralski-de-arrival process.

[0039] Secondly, this disclosure provides a crystal rod axial resistivity control device, including a constant diameter process control module, a lead-out process control module, and a re-doping stage control module. The constant diameter process control module is used to predict the first antimony evaporation amount in the constant diameter pulling process in the antimony-phosphorus co-doped single crystal furnace based on the correlation between the evaporation constant and the weight of the remaining material, and to control the antimony-phosphorus doping ratio in the constant diameter process based on the first antimony evaporation amount. The lead-out process control module is used to predict the second antimony evaporation amount in the lead-out process in the antimony-phosphorus co-doped single crystal furnace based on the correlation between the evaporation constant and the lead-out time, and to control the antimony-phosphorus doping ratio in the lead-out process based on the second antimony evaporation amount. The re-doping stage control module is used to predict the third antimony evaporation amount in the re-doping stage in the antimony-phosphorus co-doped single crystal furnace based on a target re-doping evaporation calculation model, and to control the antimony-phosphorus doping ratio in the re-doping stage based on the third antimony evaporation amount, so that the axial resistivity uniformity of the Czochralski-grown crystal rod is within the target range.

[0040] The ingot axial resistivity control device in the above embodiments, since the Czochralski silicon single crystal manufacturing process includes stages such as feeding, melting, necking, shoulder setting, and equalization, and adopts the antimony-phosphorus co-doped Czochralski silicon single crystal manufacturing process, utilizes the characteristic that the amount of antimony evaporation in the equalization process, the necking process, and the re-doping stage has a significant impact on the uniformity of the ingot axial resistivity. First, based on the equalization process control module, the correlation between the evaporation constant in the antimony-phosphorus co-doped single crystal furnace and the weight of the remaining material is used to predict the first amount of antimony evaporation in the equalization process of crystal pulling in the antimony-phosphorus co-doped single crystal furnace. The antimony-phosphorus doping ratio in the equalization process is controlled according to the first amount of antimony evaporation to ensure accurate doping of antimony element in the equalization process. Then, based on the necking process control module, the correlation between the evaporation constant and the necking time is used to determine the first amount of antimony evaporation in the equalization process. The correlation is used to predict the second antimony evaporation amount during the crystal pulling and release process in the antimony-phosphorus co-doped single crystal furnace. Based on the second antimony evaporation amount, the antimony-phosphorus doping ratio during the release process is controlled to ensure accurate antimony doping during the release process. Furthermore, based on the re-addition stage control module and the target re-addition evaporation calculation model, the third antimony evaporation amount during the re-addition stage in the antimony-phosphorus co-doped single crystal furnace is predicted, and the antimony-phosphorus doping ratio during the re-addition stage is controlled based on the third antimony evaporation amount to ensure accurate antimony doping during the re-addition stage. This ensures improved uniformity of axial doped elements in single crystal silicon during crystal pulling, achieving precise control of resistivity. This ensures that the axial resistivity uniformity of the Czochralski-grown ingot is within the target range, thereby improving the uniformity of the ingot's axial resistivity.

[0041] Thirdly, this disclosure provides a crystal rod axial resistivity control device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the method described in any embodiment of this disclosure.

[0042] Fourthly, this disclosure provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in any embodiment of this disclosure.

[0043] Fifthly, this disclosure provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described in any embodiment of this disclosure. Attached Figure Description

[0044] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this disclosure. For those skilled in the art, other embodiments can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a schematic flowchart of a method for controlling the axial resistivity of a crystal rod provided in one embodiment of the present disclosure;

[0046] Figure 2 This is a schematic diagram comparing the axial resistivity variation curves of antimony-phosphorus co-doped single crystals under three furnace pressure states in one embodiment of this disclosure.

[0047] Figure 3a The present invention discloses, in one embodiment of the present invention, simulated and measured axial resistivity distribution curves of a crystal rod without adjusting growth parameters.

[0048] Figure 3b The present invention discloses, in one embodiment, a simulated distribution curve of axial resistivity of a crystal rod and a measured distribution curve of axial resistivity of a crystal rod obtained by adjusting growth parameters.

[0049] Figure 4 In one embodiment of this disclosure, when obtaining Figure 3b The curve shown is the curve of the evaporation constant as a function of crystal length.

[0050] Figure 5 This is a correlation curve between the weight of residual material and the evaporation constant in one embodiment of this disclosure;

[0051] Figure 6 In order to be in Figure 5 The variation curves correspond to the two antimony evaporation constant variation curves obtained based on the first calculation method and the second calculation method under the experimental conditions;

[0052] Figure 7 This is a curve showing the variation of the antimony evaporation constant with the release time during the Czochralski release process, obtained in one embodiment of this disclosure.

[0053] Figure 8 This is a schematic diagram of the structure of a crystal rod axial resistivity control device provided in one embodiment of the present disclosure.

[0054] Figure labels and descriptions:

[0055] 10. Equal diameter process control module; 20. Induction and release process control module; 30. Re-injection stage control module. Detailed Implementation

[0056] To facilitate understanding of this disclosure, a more complete description will now be given with reference to the accompanying drawings, in which preferred embodiments of the present disclosure are shown. However, this disclosure may be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that a thorough and complete understanding of the disclosure will be achieved.

[0057] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of this disclosure. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0058] When using the terms “including,” “having,” and “comprising” as described herein, another component may be added unless explicitly qualifying terms such as “only,” “consisting of,” etc. are used. Unless otherwise stated, singular terms may include plural forms and should not be construed as having a quantity of one.

[0059] The segregation principle of antimony-phosphorus co-doped single crystals mainly involves the concentration distribution changes of the dopant elements during crystal growth. During the growth of single-crystal silicon, the introduction of dopant elements (such as antimony and phosphorus) significantly affects the physical and chemical properties of the crystal. These dopant elements exhibit differences in solubility in melts and solids, typically having higher solubility in liquids than in solids; this is defined as the segregation coefficient 1. Antimony's equilibrium segregation coefficient in silicon is also very small (approximately 0.023), resulting in poor axial resistivity uniformity in antimony-doped Czochralski single-crystal silicon.

[0060] Segregation refers to the phenomenon where, when a crystalline substance containing impurities is melted and recrystallized, the concentration of impurities differs between the solid and uncrystallized forms. In the growth of antimony-phosphorus co-doped single crystals, the different segregation coefficients of antimony and phosphorus lead to variations in their distribution within the crystal.

[0061] Specifically, the incorporation of antimony and phosphorus into the silicon lattice leads to lattice distortion, thereby affecting dislocation dynamics. At high temperatures, these doped atoms can interact with dislocation nuclei to form complexes, which act as pinning centers, suppressing dislocation slip. However, due to the different segregation coefficients of antimony and phosphorus, their distribution in the crystal exhibits a certain gradient. For example, phosphorus has a smaller segregation coefficient, meaning that phosphorus atoms are more likely to accumulate at the tail of the crystal during growth, while antimony may have a relatively larger segregation coefficient, resulting in a more uniform or different distribution characteristics.

[0062] In antimony-phosphorus co-doped single crystals, the simultaneous presence of the two doping elements leads to their interaction, which further affects the crystal's properties. For example, antimony and phosphorus may jointly influence the crystal's electrical conductivity, mechanical strength, and other properties by forming complexes or altering dislocation behavior.

[0063] Antimony co-doped semiconductors possess excellent photoelectric properties and have broad application prospects in fields such as solar cells, light-emitting diodes, and lasers. Especially in the field of solar cells, phosphorus-antimony co-doped semiconductors can enhance photoelectric conversion efficiency and improve the performance of solar cells.

[0064] Existing control methods often rely on preset fixed growth parameters, which are difficult to adapt to small changes in the actual growth process. They lack real-time monitoring and dynamic adjustment of growth parameters during the growth process, lack precision and controllability, and are difficult to achieve the optimal resistivity distribution, resulting in uneven resistivity distribution and affecting device performance.

[0065] The embodiments disclosed herein aim to provide a method, apparatus, device, and product for controlling the axial resistivity of a crystal rod, which can at least ensure the uniformity of axial doped elements in single crystal silicon during crystal pulling, achieve precise control of resistivity, and improve the uniformity of the axial resistivity of the crystal rod.

[0066] Please see Figure 1 In some embodiments, a method for controlling the axial resistivity of a crystal rod is provided, comprising:

[0067] Step S20: Based on the correlation between the evaporation constant and the weight of the remaining material in the antimony-phosphorus co-doped single crystal furnace, predict the first antimony evaporation amount in the crystal pulling process of the antimony-phosphorus co-doped single crystal furnace, and control the antimony-phosphorus doping ratio in the process of the equal diameter process based on the first antimony evaporation amount.

[0068] Step S40: Based on the correlation between the evaporation constant and the release time, predict the second antimony evaporation amount during the crystal pulling and release process in the antimony-phosphorus co-doped single crystal furnace, and control the antimony-phosphorus doping ratio during the release process based on the second antimony evaporation amount;

[0069] Step S60: Based on the target re-evaporation calculation model, predict the third antimony evaporation amount in the re-evaporation stage of the antimony-phosphorus co-doped single crystal furnace, and control the antimony-phosphorus doping ratio in the re-evaporation stage according to the third antimony evaporation amount, so that the axial resistivity uniformity of the Czochralski-grown crystal rod is within the target range.

[0070] For example, since the Czochralski silicon single crystal fabrication process includes stages such as feeding, melting, necking, shoulder formation, and equalization, the antimony-phosphorus co-doped Czochralski silicon single crystal fabrication process utilizes the characteristic that the amount of antimony evaporation during the equalization process, necking process, and re-doping stage has a significant impact on the uniformity of the axial resistivity of the crystal rod. Firstly, based on the correlation between the evaporation constant in the antimony-phosphorus co-doped single crystal furnace and the weight of the remaining material, the first amount of antimony evaporation during the equalization process in the antimony-phosphorus co-doped single crystal furnace is predicted. The antimony-phosphorus doping ratio during the equalization process is then controlled based on the first amount of antimony evaporation to ensure accurate antimony doping during the equalization process. Finally, based on the correlation between the evaporation constant and the necking time, the antimony-phosphorus co-doped single crystal is predicted... The second antimony evaporation amount during the crystal pulling and release process in the crystal furnace is used to control the antimony-phosphorus doping ratio during the release process, ensuring precise doping of antimony during the release process. Furthermore, based on the target re-evaporation calculation model, the third antimony evaporation amount during the re-evaporation stage in the antimony-phosphorus co-doped single crystal furnace is predicted, and the antimony-phosphorus doping ratio during the re-evaporation stage is controlled based on the third antimony evaporation amount, ensuring precise doping of antimony during the re-evaporation stage. This ensures improved uniformity of axial doped elements in single crystal silicon during the crystal pulling process, achieving precise control of resistivity, and ensuring that the axial resistivity uniformity of the Czochralski-grown ingot is within the target range, thereby improving the uniformity of the axial resistivity of the ingot.

[0071] The diffusion behavior and diffusion constant of antimony in silicon single crystals are influenced by various factors, including temperature, doping concentration, and other doping elements. The incorporation of antimony affects the properties of silicon single crystals through its interaction with dislocations. This influence is significant for the application and processing of silicon single crystals, particularly in the integrated circuit manufacturing process, where it plays a crucial role in improving the mechanical strength of silicon wafers and the performance of devices.

[0072] However, in the antimony-phosphorus co-doped crystal pulling process, the diffusion constants and evaporation constants of P and Sb are all fixed values ​​as shown in Table 1 below.

[0073] Table 1

[0074]

[0075] As shown in Table 1, the diffusion and evaporation constants of P and Sb are values ​​obtained from tests conducted in solid silicon at 1200℃. In actual Czochralski processes, the temperature at which P and Sb are doped into molten silicon reaches over 1400℃, thus reducing the applicability of the diffusion constants in Table 1. The diffusion constant of phosphorus has been experimentally verified to be approximately 2.80E-5, which differs from the values ​​in the table by seven orders of magnitude.

[0076] In some embodiments of this disclosure, the process of determining the diffusion constant of antimony in molten silicon through multiple experiments mainly includes:

[0077] Sample preparation: Antimony-containing silicon single crystals were prepared by the Czochralski method. During the process, a predetermined amount of antimony was added to the silicon melt as a dopant and incorporated into the silicon lattice during crystal growth.

[0078] Cooling and slicing: After diffusion treatment, the silicon single crystal is slowly cooled to fix the distribution of antimony atoms in the lattice. Subsequently, the silicon single crystal is sliced ​​into a series of thin slices for subsequent resistivity measurements.

[0079] Data processing and analysis: A four-probe resistivity / sheet resistance meter was used to collect resistivity data of the profile. The diffusion constant of antimony was calculated based on the measured resistivity data. This process usually involves calculations such as effective segregation. The diffusion constant was determined by fitting the test data with theoretical values. The diffusion constant of antimony in molten silicon was found to be 2.914E-6.

[0080] Results Verification: To ensure the accuracy of the experimental results, multiple experiments were conducted to verify the repeatability of the data. The influence of experimental conditions (such as temperature, pressure, purity of silicon and antimony) on the diffusion constant was also considered. The diffusion constant of antimony in molten silicon was found to be 2.914E-6, which can meet the current mass production requirements.

[0081] Please see Figure 2 In some embodiments, the preset states include a furnace pressure of a preset pressure value and an argon flow rate of a preset flow rate value; the crystal rod axial resistivity control method further includes the step of obtaining a first correlation relationship:

[0082] Step S12: Obtain the antimony diffusion constant after a preset amount of antimony is doped into the silicon melt in the single crystal furnace;

[0083] Step S14: Based on the antimony diffusion constant, simulate the axial resistivity distribution curve of the crystal rod caused by antimony segregation when the resistivity at the start of crystal pulling is at the target value.

[0084] Step S16: Determine the measured resistivity distribution curve based on the simulated distribution curve;

[0085] Step S18: Based on the measured resistivity distribution curve, the first correlation between the antimony evaporation constant and the weight of the remaining material in the single crystal furnace is determined using the correlation analysis method.

[0086] For example, step S12 can refer to the aforementioned experimental steps to determine the antimony diffusion constant as 2.914E-6.

[0087] For example, in the preset states: the preset pressure value of the furnace is 3 torr-15 torr, such as 3 torr, 7 torr, 12 torr or 15 torr, etc.; the preset flow rate value of the argon gas flow is 30 slpm-170 slpm, such as 30 slpm, 60 slp, 90 slp, 110 slp, 140 slp, 160 slp or 170 slpm, etc.; the size of the hot zone inside the single crystal furnace is 28 inches-42 inches, such as 28 inches, 32 inches, 36 inches, 40 inches or 42 inches, etc.

[0088] In step S14, antimony-containing silicon single crystals can be prepared using the Czochralski method. During the process, a certain amount of antimony is added to the silicon melt as a dopant and incorporated into the silicon lattice during crystal growth. Three furnace pressing processes can be used for verification. Then, a portable four-probe analyzer is used to measure and collect axial resistivity data of the pulled crystal rod at three points equidistantly distributed along the circumference of the concentric circles in the cross-section, for example, at 50mm intervals along the axial direction. Figure 2 The resistivity curve shown is a function of crystal length. Figure 2 In the figure, the unit of resistivity on the vertical axis is ohm-meter (Ω·m), and the unit of crystal length on the horizontal axis is mm.

[0089] like Figure 2 As shown, the BSL line represents the axial resistivity distribution of phosphorus-doped single crystals. The yellow BSL line indicates that the axial resistivity of phosphorus-doped single crystals is minimally affected by furnace pressure changes. Since the evaporation effect of antimony is greater than its segregation effect, reducing the furnace pressure from 9.4 Torr to 2 Torr yields... Figure 2 The green curve in the image; maintaining the furnace pressure at 6 Torr to 7 Torr yields... Figure 2 The orange curve in the image; increasing the furnace pressure from 7 Torr to 10 Torr yields... Figure 2 The gray curve in the figure shows that antimony evaporation can be controlled by preset furnace pressure and argon parameters, indicating that the evaporation effect of antimony can be enhanced or suppressed by changing the furnace pressure.

[0090] For example, in step S14, based on the antimony diffusion constant, the simulated resistivity distribution curve of the crystal rod caused by antimony segregation is calculated. This is achieved when the resistivity at the crystal pulling initiation (head-controlled resistivity) is consistent with the target value. Figure 3a As shown, the horizontal axis represents the crystal length in mm, and the vertical axis represents the axial resistivity in Ω·cm; Figure 3a The green curve represents the simulated axial resistivity distribution curve of the crystal rod caused by antimony segregation; Figure 3aThe red curve represents the simulated distribution curve of the axial resistivity of the crystal rod. In the actual process, the segregation effect of antimony is smaller than the evaporation effect of antimony. The segregation effect and the evaporation effect of antimony together affect the axial resistivity distribution of the crystal rod.

[0091] For example, in step S16, the measured resistivity distribution curve is determined based on the simulated distribution curve. For instance, the antimony evaporation constant (Ev) and evaporation amount (N) at different lengths (along the axial direction) are calculated by simulation to obtain the simulated resistivity curve and the measured resistivity curve shown in Figure 3b, such that the fitting degree between the simulated resistivity curve and the measured resistivity curve shown in Figure 3b is ≥99.8%.

[0092] In the process of obtaining the simulated resistivity curve and the measured resistivity curve shown in Figure 3b, the evaporation constant for different crystal lengths was obtained as follows: Figure 4 As shown in the image.

[0093] Furthermore, in step S18, it can be based on Figure 3b The measured resistivity distribution curve shown in the figure, and Figure 4 The curve of the evaporation constant as a function of crystal length shown in the figure was used to determine the first correlation between the antimony evaporation constant (Ev) and the weight of the residue in the single crystal furnace using correlation analysis.

[0094] In the correlation analysis method, the relevant independent variables include furnace background monitoring data, such as crystal length, remaining material weight, growth rate setting, crystal growth rate, main heater power, diameter value, actual argon flow rate, main chamber pressure value, actual crystal pulling speed, crystal weight, auxiliary chamber pressure value, crucible rotation speed output, crystal rotation speed output, average furnace pressure, average liquid surface temperature, actual crucible rotation speed, actual crystal rotation speed, water flow rate of the second water jacket, liquid surface temperature measurement, and equal diameter time, etc.

[0095] Statistical methods were used to determine the correlation between the antimony evaporation constant (Ev) and at least one of the aforementioned furnace background monitoring data. After performing correlation analysis, the magnitude, direction, and significance of the correlation coefficients needed to be interpreted. A positive correlation coefficient indicates that an increase in one variable is accompanied by an increase in another variable, while a negative correlation coefficient indicates that an increase in one variable is accompanied by a decrease in another variable. The closer the absolute value of the correlation coefficient is to 1 or -1, the stronger the correlation. The significance level is usually set to 0.05 or 0.01; if the p-value is less than these thresholds, the correlation is considered statistically significant. Based on the stratification of the above significance level thresholds, the independent variables with a significance level of P ≤ 0.05 were identified as follows: crystal length, residual material weight, actual argon flow rate, main chamber pressure, average liquid surface temperature, and constant diameter duration.

[0096] Through regression analysis, after removing the constant term, the independent variables included: actual argon flow rate, main chamber pressure, and average liquid surface temperature. Further, by using the variance expansion factor (VIF) method to remove crystal length and constant diameter duration, the relationship between residual material weight and evaporation constant was finally established as follows:

[0097] Ev = a + bW + cW 2 +dW 3 ;

[0098] In the above formula, Ev is the antimony evaporation constant, W is the weight of the remaining material, and a, b, c and d are all constants.

[0099] based on Figure 3b , Figure 4 The test data from the same experiment yielded the correlation curve between the residual material weight and the evaporation constant, as shown below. Figure 5 As shown, Figure 5 The horizontal axis represents the weight of the remaining material in grams, and the vertical axis represents the evaporation constant in cm / s.

[0100] Correlation analysis was used to determine the constant values ​​in the first correlation relationship, resulting in the specific functional expression between the residual material weight and the evaporation constant:

[0101] Ev=0.000301638354296996-2.847079761568·10 -11 W+2.374013120331233•10 - 15 W 2 -2.82524056437763•10 -21 W 3 .

[0102] In some embodiments, obtaining the first predicted antimony evaporation rate for the Czochralski constant-diameter process includes:

[0103] The first predicted antimony evaporation amount N1 is calculated using the following formula:

[0104] N1 = Ev•A•C1 (First calculation method);

[0105] In the above formula, Ev is the antimony evaporation constant, A is the antimony evaporation surface area, and C1 is the antimony concentration in the single crystal furnace.

[0106] In the aforementioned embodiments, after determining that the antimony evaporation constant is mainly related to the weight of the residual material using correlation analysis, and after obtaining a large amount of actual data, the constant value in the first correlation relationship is determined, and the functional expression of the first correlation relationship is determined. This enables the accurate calculation of the corresponding antimony evaporation constant based on the real-time weight of the residual material in the single crystal furnace and the first correlation relationship. Based on the antimony evaporation constant and the correlation between the antimony evaporation amount in the Czochralski equal diameter process and the antimony evaporation constant, the first predicted antimony evaporation amount in the Czochralski equal diameter process is accurately calculated, thereby achieving accurate dynamic prediction of the first predicted antimony evaporation amount in the Czochralski equal diameter process.

[0107] The diffusion constant of antimony in molten silicon affects its distribution and concentration, thus influencing the growth rate and quality of single crystals. Experiments show that this diffusion constant is related to factors such as the kinematic viscosity coefficient of molten silicon and relative rotation speed, and that this value can be determined under specific growth conditions. Therefore, by setting the furnace pressure and argon flow rate to preset values, multiple experiments were conducted to obtain the antimony diffusion constant after a preset amount of antimony was incorporated into the silicon melt in the single crystal furnace. This confirmed that the antimony diffusion constant and the corresponding growth parameters meet the requirements of current mass production. Then, based on the aforementioned antimony diffusion constant, the simulated distribution curve of the axial resistivity of the crystal rod caused by antimony segregation is calculated under the condition that the resistivity at the starting point of crystal pulling is the target value. The measured resistivity distribution curve is determined based on the simulated distribution curve, so that the fitting degree between the measured resistivity distribution curve and the simulated distribution curve is greater than or equal to a preset threshold. Then, based on the measured resistivity distribution curve, the first correlation between the antimony evaporation constant and the weight of the residual material in the single crystal furnace is determined by the correlation analysis method. Thus, the corresponding antimony evaporation constant can be accurately calculated based on the real-time weight of the residual material in the single crystal furnace and the first correlation, thereby accurately calculating the first predicted antimony evaporation amount in the Czochralski equal diameter process.

[0108] Compared to the calculation of the first predicted antimony evaporation amount N1 under the constant diameter state of Czochralski pulling, the changes in the weight of the remaining material in the single crystal furnace, power, furnace pressure, and argon flow rate are relatively small in other crystal pulling states and stages. Therefore, considering the latent heat of evaporation, a different calculation method (second calculation method) is used to calculate the second predicted antimony evaporation amount N2, which is different from the above calculation method for antimony evaporation in the constant diameter process.

[0109] C = C0e^-(Ev•A / U);

[0110] N2 = (C0 - C) • V;

[0111] In the above formula, C is the antimony concentration after antimony evaporation, C0 is the antimony concentration after time t, Ev is the antimony evaporation constant, A is the antimony evaporation surface area, U is the silicon mass in the single crystal furnace, and V is the residual volume in the single crystal furnace.

[0112] As water temperature rises, the latent heat of vaporization gradually decreases, making water evaporation more difficult; the evaporation phenomenon of antimony is similar to that of water. Using data from the aforementioned experimental conditions, the change in the antimony evaporation constant during the Czochralski-drawn constant-diameter process was simulated and calculated, and the results are as follows: Figure 6 As shown in the image. Figure 6 In the figure, the horizontal axis represents the weight of the remaining material in g, and the vertical axis represents the evaporation constant in cm / s. The antimony evaporation constants obtained by the two calculation methods show significant differences in the first interval, while the latter intervals are basically the same. It is determined that this difference is caused by the latent heat of vaporization of antimony in silicon, and the latent heat of vaporization of antimony in silicon satisfies a similar change relationship to that of water.

[0113] Since the temperature is basically constant in other crystal pulling states except for the Czochralski constant diameter process, such as the temperature of the Czochralski release process being a preset temperature value; the ingot axial resistivity control method also includes the following step of obtaining the second correlation relationship:

[0114] Step S52: Obtain the curve of antimony evaporation constant as a function of the induction time in the single crystal furnace;

[0115] Step S54: Determine the functional expression between the antimony evaporation constant and the release time based on the change curve.

[0116] For example, after obtaining the curve of the antimony evaporation constant changing with the ignition time in the single crystal furnace, the functional expression between the antimony evaporation constant and the ignition time can be determined based on the curve. Thus, based on the functional expression and the real-time ignition time, the current antimony evaporation constant of the Czochralski ignition process can be accurately calculated. Based on the current antimony evaporation constant and the correlation between the amount of antimony evaporated in the Czochralski ignition process and the concentration of antimony after evaporation, the second predicted amount of antimony evaporation in the Czochralski ignition process can be accurately calculated or predicted.

[0117] Data from the aforementioned experimental conditions can be used to simulate and calculate the variation curve of the antimony evaporation constant with the release time during the direct pull-out process, such as... Figure 7 As shown in the image. Figure 7 In the figure, the horizontal axis represents the release time in minutes, and the vertical axis represents the evaporation constant in cm / s.

[0118] In some embodiments, determining the functional expression between the antimony evaporation constant and the release time includes:

[0119] Determine the constant values ​​in the following formulas:

[0120] Ev=m •t n ;

[0121] In the above formula, Ev is the antimony evaporation constant, t is the release time, and m and n are both constants.

[0122] For example, after determining that the antimony evaporation constant in the Czochralski release process is mainly related to the release duration, it can be based on... Figure 7 By fitting the curve, the constant value in the functional expression between the antimony evaporation constant and the release time t is determined, thus determining the specific functional expression between the antimony evaporation constant Ev and the release time t in the Czochralski release process as follows:

[0123] Ev=0.000104194 •t 0.463774 .

[0124] In some embodiments, combining the first correlation between the antimony evaporation constant and the weight of the residue in the single crystal furnace, and the first calculation method, the optimal antimony-phosphorus doping ratio is calculated using the least squares method. Combining the correlation between the amount of antimony evaporation in the Czochralski-de-arrival process and the concentration of antimony after evaporation, the second predicted amount of antimony evaporation in the Czochralski-de-arrival process is accurately calculated or predicted, thereby achieving optimized control of the axial resistivity of the Czochralski constant diameter process and the Czochralski-de-arrival process in the antimony-phosphorus co-doping process.

[0125] The Czochralski equal-diameter process and the Czochralski release process are relatively fixed and repetitive. Compared with the calculation of antimony evaporation in the Czochralski equal-diameter process and the calculation of antimony evaporation in the Czochralski release process, the re-feeding stage is diverse and is affected by a variety of factors such as the weight of the remaining material in the single crystal furnace (residual material amount), the remaining concentration of antimony, the amount of re-feeding material, furnace pressure, and temperature.

[0126] In some embodiments, the method for controlling the axial resistivity of crystal rods further includes the step of obtaining a target re-evaporation calculation model:

[0127] Step S52: Use a correlation analysis algorithm to determine irrelevant variables in the re-feeding stage whose correlation with antimony evaporation is less than a threshold;

[0128] Step S54: Determine the target variables related to the antimony evaporation rate in the re-feeding stage based on irrelevant variables. The target variables include the concentration of antimony in the broken wire, the weight of the remaining material, and the re-feeding time.

[0129] Step S56: Use a linear fitting algorithm to determine the functional relationship between antimony evaporation and the target variable.

[0130] For example, by using a correlation analysis algorithm to identify irrelevant variables in the re-feeding stage whose correlation with antimony evaporation is less than a threshold, the target variables in the re-feeding stage related to antimony evaporation can be determined based on the irrelevant variables. The target variables include the concentration of antimony in the broken line, the weight of the remaining material, and the re-feeding time. Then, a linear fitting algorithm can be used to determine the functional relationship between antimony evaporation and the target variables. Based on this functional relationship, the third antimony evaporation in the re-feeding stage in the antimony-phosphorus co-doped single crystal furnace can be predicted, and the antimony-phosphorus doping ratio in the re-feeding stage can be controlled based on the third antimony evaporation to ensure accurate doping of antimony in the re-feeding stage.

[0131] After collecting a large amount of relevant data, conducting correlation analysis and eliminating irrelevant variables, the relationship between the three variables—antimony concentration at break (unit: atoms / cm³), residual amount (unit: kg), and re-use time (unit: min)—and the evaporation rate Y (unit: atoms) was confirmed as shown in Table 2.

[0132] The established average deviation between the concentration of antimony in the broken wire, the amount of remaining material, the time of re-injection, and the evaporation rate Y is ≤1%, which meets the usage requirements. However, the correlation model between the concentration of antimony in the broken wire, the amount of remaining material, the time of re-injection, and the evaporation rate includes the relationship between three independent variables (concentration of antimony in the broken wire, amount of remaining material, and time of re-injection) and one dependent variable Y (evaporation rate). When the amount of original training data is small, the deviation calculated without training can reach 50% or more, which is not convenient for actual production use.

[0133] Table 2

[0134]

[0135] To establish the optimal relationship between the amount of residual material and the amount of re-evaporization, the constant values ​​in the target re-evaporization calculation model can be determined using correlation analysis:

[0136] P = i + kQ;

[0137] In the above formula, P is the amount of evaporation after re-feeding, Q is the weight of the remaining material in the re-feeding stage (the amount of leftover material), and i and k are constants.

[0138] The specific functional expressions for the remaining material amount and the re-evaporation amount can be determined using a correlation fitting algorithm, as follows:

[0139] P = 1.1891 - 0.001Q.

[0140] Please refer to Table 3. Combining the first correlation and calculation method between the antimony evaporation constant and the weight of the remaining material in the single crystal furnace, the optimal antimony-phosphorus doping ratio for preparing N-type single crystal silicon using the Czochralski method is calculated using the least squares method. Combining the correlation between the antimony evaporation amount during the Czochralski extraction process and the antimony concentration after evaporation, the second predicted antimony evaporation amount during the Czochralski extraction process is accurately calculated or predicted to ensure precise doping of antimony during extraction. Furthermore, based on the target re-expansion evaporation calculation model, the third antimony evaporation amount during the re-expansion stage in the antimony-phosphorus co-doped single crystal furnace is predicted, and the antimony-phosphorus doping ratio during the re-expansion stage is controlled according to the third antimony evaporation amount to ensure precise doping of antimony during the re-expansion stage. Finally, the axial resistivity of the crystal rod is obtained as 0.952Ω·m-0.964Ω·m, effectively achieving optimized control of the axial resistivity of the whole furnace crystal pulling process for antimony-phosphorus co-doped crystals.

[0141] Table 3

[0142]

[0143] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0144] Please see Figure 8 In some embodiments, a crystal rod axial resistivity control device is provided, including a constant diameter process control module 10, a lead-out process control module 20, and a re-doping stage control module 30. The constant diameter process control module 10 is used to predict the first antimony evaporation amount in the constant diameter pulling process in the antimony-phosphorus co-doped single crystal furnace based on the correlation between the evaporation constant and the weight of the remaining material, and to control the antimony-phosphorus doping ratio in the constant diameter process based on the first antimony evaporation amount. The lead-out process control module 20 is used to predict the second antimony evaporation amount in the lead-out process in the antimony-phosphorus co-doped single crystal furnace based on the correlation between the evaporation constant and the lead-out time, and to control the antimony-phosphorus doping ratio in the lead-out process based on the second antimony evaporation amount. The re-doping stage control module 30 is used to predict the third antimony evaporation amount in the re-doping stage in the antimony-phosphorus co-doped single crystal furnace based on the target re-doping evaporation calculation model, and to control the antimony-phosphorus doping ratio in the re-doping stage based on the third antimony evaporation amount, so that the axial resistivity uniformity of the Czochralski-grown crystal rod is within the target range.

[0145] Please continue reading. Figure 8Since the Czochralski silicon single crystal fabrication process includes stages such as feeding, melting, necking, shoulder formation, and equalization, the antimony-phosphorus co-doped Czochralski silicon single crystal fabrication process utilizes the characteristic that the amount of antimony evaporation during the equalization process, the necking process, and the re-doping stage has a significant impact on the uniformity of the axial resistivity of the crystal rod. First, based on the relationship between the evaporation constant and the weight of the remaining material in the antimony-phosphorus co-doped single crystal furnace, the equalization process control module 10 predicts the first amount of antimony evaporation during the equalization process in the antimony-phosphorus co-doped single crystal furnace. The antimony-phosphorus doping ratio in the equalization process is controlled according to the first amount of antimony evaporation to ensure accurate doping of antimony during the equalization process. Then, based on the relationship between the evaporation constant and the necking time, the antimony doping ratio is predicted by the necking process control module 20. The second antimony evaporation amount during the crystal pulling and release process in the phosphorus co-doped single crystal furnace is used to control the antimony-phosphorus doping ratio during the release process, ensuring accurate doping of antimony during the release process. Furthermore, based on the target re-addition evaporation calculation model, the re-addition stage control module 30 predicts the third antimony evaporation amount during the re-addition stage in the antimony-phosphorus co-doped single crystal furnace, and controls the antimony-phosphorus doping ratio during the re-addition stage based on the third antimony evaporation amount, ensuring accurate doping of antimony during the re-addition stage. This ensures improved uniformity of axial doped elements in single crystal silicon during the crystal pulling process, achieving precise control of resistivity, and ensuring that the axial resistivity uniformity of the Czochralski-grown ingot is within the target range, thereby improving the uniformity of the ingot's axial resistivity.

[0146] In some embodiments, the crystal rod axial resistivity control device further includes a re-feeding evaporation calculation model acquisition module, which is used to determine irrelevant variables in the re-feeding stage whose correlation with antimony evaporation is less than a threshold using a correlation analysis algorithm; determine the target variable related to antimony evaporation in the re-feeding stage based on the irrelevant variables, the target variable including the concentration of antimony in the broken wire, the weight of the remaining material, and the re-feeding time; and determine the functional relationship between antimony evaporation and the target variable using a linear fitting algorithm.

[0147] The crystal rod axial resistivity control device in the above embodiment uses a correlation analysis algorithm to determine irrelevant variables whose correlation with antimony evaporation is less than a threshold during the re-feeding stage. Based on these irrelevant variables, it determines the target variables related to antimony evaporation during the re-feeding stage. The target variables include the concentration of antimony in the broken wire, the weight of the remaining material, and the re-feeding time. Then, it can use a linear fitting algorithm to determine the functional relationship between antimony evaporation and the target variables. Based on this functional relationship, it can predict the third antimony evaporation during the re-feeding stage in the antimony-phosphorus co-doped single crystal furnace, and control the antimony-phosphorus doping ratio during the re-feeding stage based on the third antimony evaporation, ensuring accurate doping of antimony elements during the re-feeding stage.

[0148] In some embodiments, the preset state includes a furnace pressure of a preset pressure value and an argon flow rate of a preset flow rate value; a crystal rod axial resistivity control device further includes a first correlation acquisition module, used to acquire the antimony diffusion constant after a preset amount of antimony is doped into the silicon melt in the single crystal furnace, and based on the antimony diffusion constant, to simulate and calculate the simulated distribution curve of the crystal rod axial resistivity caused by antimony segregation under the condition that the resistivity at the start of crystal pulling is the target value, to determine the measured resistivity distribution curve based on the simulated distribution curve, and to determine the first correlation between the antimony evaporation constant and the weight of the remaining material in the single crystal furnace using the correlation analysis method based on the measured resistivity distribution curve.

[0149] By setting the furnace pressure and argon flow rate to preset values, multiple experiments were conducted to obtain the antimony diffusion constant after a preset amount of antimony was incorporated into the silicon melt in the single crystal furnace. This confirmed that the antimony diffusion constant and corresponding growth parameters met the requirements of current mass production. Then, based on the aforementioned antimony diffusion constant, a simulated distribution curve of the axial resistivity of the crystal rod caused by antimony segregation was calculated under the condition that the resistivity at the crystal pulling initiation was at the target value. The measured resistivity distribution curve was then determined based on the simulated distribution curve, ensuring that the fit between the measured and simulated resistivity distribution curves was greater than or equal to a preset threshold. Finally, based on the measured resistivity distribution curve, a correlation analysis method was used to determine the first correlation between the antimony evaporation constant and the weight of the remaining material in the single crystal furnace. This allowed for accurate calculation of the corresponding antimony evaporation constant based on the real-time weight of the remaining material in the single crystal furnace and this first correlation, thereby accurately calculating the predicted antimony evaporation amount for the Czochralski equal-diameter process.

[0150] In some embodiments, the temperature of the Czochralski release process is a preset temperature value; a crystal rod axial resistivity control device further includes a second correlation acquisition module, used to acquire the variation curve of the antimony evaporation constant with the release time in the single crystal furnace; and to determine the functional expression between the antimony evaporation constant and the release time based on the variation curve. Since the temperature of other crystal pulling states, except for the Czochralski constant diameter process, is basically constant, after acquiring the variation curve of the antimony evaporation constant with the release time in the single crystal furnace, the functional expression between the antimony evaporation constant and the release time can be determined based on the variation curve. Thus, based on the functional expression and the real-time release time, the current antimony evaporation constant of the Czochralski release process can be accurately calculated, and based on the current antimony evaporation constant and the correlation between the antimony evaporation amount and the antimony concentration after antimony evaporation in the Czochralski release process, the predicted antimony evaporation amount of the Czochralski release process can be accurately calculated or predicted.

[0151] For example, a crystal rod axial resistivity control device can be applied to fields such as solar cells, light-emitting diodes, and lasers.

[0152] In some embodiments of this disclosure, an energy storage device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the axial resistivity control method for crystal rods in any embodiment of this disclosure.

[0153] In some embodiments of this disclosure, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the steps of the ingot axial resistivity control method in any embodiment of this disclosure.

[0154] In some embodiments of this disclosure, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps of the ingot axial resistivity control method in any embodiment of this disclosure.

[0155] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0156] The embodiments described above are merely illustrative of several implementations of this disclosure, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this disclosure, and these all fall within the scope of protection of this disclosure. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for controlling the axial resistivity of a crystal rod, characterized in that, include: Based on the correlation between the evaporation constant in the antimony-phosphorus co-doped single crystal furnace and the weight of the remaining material, the first antimony evaporation amount in the crystal pulling process of the antimony-phosphorus co-doped single crystal furnace is predicted, and the antimony-phosphorus doping ratio in the process of the equal diameter is controlled according to the first antimony evaporation amount. Based on the correlation between the evaporation constant and the release time, the second antimony evaporation amount in the crystal pulling and release process in the antimony-phosphorus co-doped single crystal furnace is predicted, and the antimony-phosphorus doping ratio in the release process is controlled based on the second antimony evaporation amount. Based on the target re-addition evaporation calculation model, the third antimony evaporation amount in the re-addition stage of the antimony-phosphorus co-doped single crystal furnace is predicted, and the antimony-phosphorus doping ratio in the re-addition stage is controlled according to the third antimony evaporation amount, so that the axial resistivity uniformity of the Czochralski-grown crystal rod is within the target range. The process also includes the following steps for obtaining the target re-evaporization calculation model: Correlation analysis algorithms were used to identify irrelevant variables in the re-feeding stage whose correlation with antimony evaporation was less than a threshold. Based on the irrelevant variables, target variables related to the antimony evaporation amount in the re-feeding stage are determined, including the concentration of antimony in the broken wire, the weight of the remaining material, and the re-feeding time. A linear fitting algorithm was used to determine the functional relationship between the antimony evaporation rate and the target variable; The furnace pressure and argon flow rate in the antimony-phosphorus co-doped single crystal furnace are preset values; the method further includes: Obtain the antimony diffusion constant after a preset amount of antimony is incorporated into the silicon melt in the antimony-phosphorus co-doped single crystal furnace; Based on the antimony diffusion constant, the simulated distribution curve of the axial resistance of the crystal rod caused by antimony segregation was calculated under the condition that the resistivity at the start of crystal pulling is at the target value. The measured resistivity distribution curve is determined based on the simulated distribution curve. Based on the measured resistivity distribution curve, the correlation between the evaporation constant and the weight of the remaining material during the constant diameter process was determined using correlation analysis. The temperature during the crystal pulling and release process is a preset temperature value; the method for controlling the axial resistivity of the crystal rod also includes: Obtain the curve of the antimony evaporation constant during the antimony-phosphorus co-doped single crystal process as a function of the duration of the induction process in the furnace; The functional expression between the antimony evaporation constant and the release duration is determined based on the change curve.

2. The method for controlling the axial resistivity of a crystal rod according to claim 1, characterized in that, This also includes using correlation analysis to determine the constant values ​​in the target re-evaporization calculation model as follows: P = i + kQ; In the above formula, P is the third antimony evaporation amount, Q is the weight of the remaining material in the re-feeding stage, and i and k are constants.

3. The method for controlling the axial resistivity of a crystal rod according to claim 1, characterized in that, The constant value in the relationship between the evaporation constant and the weight of the remaining material in the constant diameter process was determined using correlation analysis: Ev = a + bW + cW 2 +dW 3 ; In the above formula, Ev is the antimony evaporation constant of the constant diameter process, W is the residual weight of the constant diameter process, and a, b, c and d are all constants.

4. The method for controlling the axial resistivity of a crystal rod according to claim 1, characterized in that, Determining the functional expression between the antimony evaporation constant and the release duration includes: Determine the constant values ​​in the following formulas: Ev=m *t n ; In the above formula, Ev is the antimony evaporation constant of the release process, t is the release duration, and m and n are both constants.

5. A device for controlling the axial resistivity of a crystal rod, characterized in that, include: The equal diameter process control module is used to predict the first antimony evaporation amount in the equal diameter process of crystal pulling in the antimony-phosphorus co-doped single crystal furnace based on the correlation between the evaporation constant and the weight of the remaining material in the antimony-phosphorus co-doped single crystal furnace, and to control the antimony-phosphorus doping ratio in the equal diameter process based on the first antimony evaporation amount. The release process control module is used to predict the second antimony evaporation amount in the crystal pulling and release process in the antimony-phosphorus co-doped single crystal furnace according to the correlation between the evaporation constant and the release time, and to control the antimony-phosphorus doping ratio in the release process according to the second antimony evaporation amount; The re-feeding stage control module is used to predict the third antimony evaporation amount in the re-feeding stage of the antimony-phosphorus co-doped single crystal furnace according to the target re-feeding evaporation calculation model, and control the antimony-phosphorus doping ratio in the re-feeding stage according to the third antimony evaporation amount, so that the axial resistivity uniformity of the Czochralski-grown crystal rod is within the target range. The crystal rod axial resistivity control device further includes: The re-feeding evaporation calculation model acquisition module is used to determine irrelevant variables in the re-feeding stage whose correlation with the antimony evaporation amount is less than a threshold using a correlation analysis algorithm; determine the target variable in the re-feeding stage that is correlated with the antimony evaporation amount based on the irrelevant variables, the target variable including the antimony concentration of the broken line, the weight of the remaining material, and the re-feeding time; and determine the functional relationship between the antimony evaporation amount and the target variable using a linear fitting algorithm. The furnace pressure and argon flow rate in the antimony-phosphorus co-doped single crystal furnace are preset values; the crystal rod axial resistivity control device further includes: The first correlation acquisition module is used to acquire the antimony diffusion constant after a preset amount of antimony is incorporated into the silicon melt in the antimony-phosphorus co-doped single crystal furnace; based on the antimony diffusion constant, it simulates and calculates the simulated distribution curve of the axial resistance of the crystal rod caused by antimony segregation under the condition that the resistivity at the start of crystal pulling is the target value; based on the simulated distribution curve, it determines the measured resistivity distribution curve; based on the measured resistivity distribution curve, it uses correlation analysis to determine the correlation between the evaporation constant and the weight of the remaining material during the constant diameter process; The temperature during the crystal pulling and release process is a preset temperature value; the crystal rod axial resistivity control device further includes: The second correlation acquisition module is used to acquire the variation curve of the antimony evaporation constant in the antimony-phosphorus co-doped single crystal furnace with the duration of the release process; and to determine the functional expression between the antimony evaporation constant and the release duration based on the variation curve.

6. A device for controlling the axial resistivity of a crystal rod, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 4.

7. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 4.

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