Silicon dopant volatilization compensation evaluation method and system based on process analysis

Abstract

The invention relates to the technical field of monocrystalline silicon manufacturing, in particular to a silicon dopant volatilization compensation evaluation method and system based on process analysis, and the method comprises the steps: obtaining a doping target instruction in a monocrystalline silicon drawing process, analyzing the doping target instruction, and obtaining a dopant target concentration value and a dopant target uniform characteristic value of each drawing stage; aiming at each drawing stage, setting a corresponding monitoring frequency, and monitoring drawing process parameters according to the monitoring frequency to obtain a real-time process parameter set; performing doping volatilization analysis on the real-time process parameter set to obtain an actual concentration value and an actual uniform characteristic value of the dopant under the process condition; based on the dopant target concentration value, the dopant actual concentration value, the dopant target uniform characteristic value and the dopant actual uniform characteristic value, calculating concentration deviation and uniform characteristic deviation; the device can be dynamically adjusted along with the propulsion of the drawing process and the change of technological parameters, so that the high-efficiency compensation on the volatilization of the dopant is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of single-crystal silicon manufacturing, and particularly to a method and system for evaluating silicon dopant volatilization compensation based on process analysis. Background Art

[0002] As a key material for manufacturing semiconductor integrated circuits and photovoltaic devices, the doping process of single-crystal silicon directly determines the electrical properties of these devices. During the pulling process of single-crystal silicon, by precisely adding a specific concentration of dopants (such as phosphorus, boron, etc.) to the silicon melt, the conductivity type and carrier concentration of single-crystal silicon can be effectively controlled. However, in a high-temperature pulling environment, due to the influence of the vapor pressure effect, dopants are prone to volatilization. This not only causes a deviation between the actual doping concentration and the expected value, but also deteriorates the doping uniformity, thereby affecting important performance indicators such as the device threshold voltage consistency in subsequent chip manufacturing and the photoelectric conversion efficiency of photovoltaic cells.

[0003] Most of the current methods for evaluating silicon dopant volatilization compensation rely on empirical adjustment or use fixed parameter models. Existing methods are difficult to cope with the complex dynamic changes during the single-crystal silicon pulling process - including the influence of various process parameter changes in stages such as seed crystal drawing, necking, and shoulder opening on the volatilization behavior of dopants. Therefore, the existing compensation strategies often cannot accurately match the actual volatilization law of dopants, limiting the performance optimization of the final product.

[0004] In order to improve the quality of semiconductor materials and device performance, there is an urgent need to develop a method and system for evaluating silicon dopant volatilization compensation that can adapt to variable process conditions. Summary of the Invention

[0005] The present invention provides a method and system for evaluating silicon dopant volatilization compensation based on process analysis, which can dynamically adjust with the progress of the pulling process and the change of process parameters, achieve efficient compensation for dopant volatilization, and can effectively solve the problems in the background art.

[0006] To achieve the above object, in the first aspect, the present invention provides a method for evaluating silicon dopant volatilization compensation based on process analysis, including: Obtain a doping target instruction during the single-crystal silicon pulling process, and parse it to obtain the target concentration value of the dopant and the target uniformity characteristic value of the dopant for each pulling stage; For each of the pulling stages, set a corresponding monitoring frequency, and monitor the pulling process parameters based on this to obtain a set of real-time process parameters; Conduct doping volatilization analysis on the set of real-time process parameters to obtain the actual concentration value of the dopant and the actual uniformity characteristic value of the dopant under this process condition; Based on the target dopant concentration value and the actual dopant concentration value, as well as the target dopant uniformity characteristic value and the actual dopant uniformity characteristic value, a concentration deviation and a uniformity characteristic deviation are calculated. Combined with the set of real-time process parameters, compensation analysis is performed on the concentration deviation and the uniformity characteristic deviation to obtain a dopant volatilization compensation strategy, and compensation is performed on this drawing stage accordingly.

[0007] Combined with the first aspect, in a possible design, the drawing stage includes at least one of a seed crystal pulling stage, a necking stage, a shoulder broadening stage, an equal diameter growth stage, a finishing stage, and a cooling stage.

[0008] Combined with the first aspect, in a possible design, the drawing process parameters include melt temperature, crystal pulling speed, seed crystal rotation speed, crucible rotation speed, argon gas flow rate, melt liquid level height, and dopant injection amount.

[0009] Combined with the first aspect, in a possible design, the calculation formula for performing dopant volatilization analysis on the set of real-time process parameters is: ; Wherein, represents the actual dopant concentration value; represents the dopant injection amount at the beginning of the corresponding drawing stage; represents the dynamic melt volume, which is calculated from the real-time liquid level height; is a volatilization rate function, representing the volatilization rate of the dopant on the surface of the silicon melt; wherein, represents the melt temperature at time τ, represents the argon gas flow rate at time τ; τ is a virtual time variable, used to represent any moment from the start of the drawing stage τ = 0 to the current time τ = t, τ ∈ [0, t]; t represents the current moment; represents the dopant concentration on the surface of the silicon melt at time τ, reflecting the dopant concentration level participating in volatilization at the current moment; represents the contribution amount of the convective diffusion of the dopant caused by the melt flow to the actual dopant concentration from the start of the drawing stage to the current time; represents the melt flow velocity field at time τ, used to describe the flow velocity and direction of each point in the silicon melt at time τ, which is jointly determined by the seed crystal rotation speed, the crucible rotation speed, and the crystal pulling speed; represents the gradient of the dopant concentration, used to describe the change rate of the dopant concentration in space at time τ.

[0010] In combination with the first aspect, in a possible design, the mathematical expression of the gradient of the dopant concentration is as follows: ; wherein, , and respectively represent the change rates of the dopant concentration in the x, y, and z directions.

[0011] In combination with the first aspect, in a possible design, the dopant distribution uniformity eigenvalue is quantitatively represented by the axial concentration variation coefficient.

[0012] In combination with the first aspect, in a possible design, the calculation formula for the axial concentration variation coefficient is as follows: ; wherein, represents the axial concentration variation coefficient, and the smaller the value, the more uniform the axial concentration distribution; represents the total length of the crystal growth at time t; represents the concentration standard deviation at the axial position z; represents the concentration mean value at the axial position z.

[0013] In combination with the first aspect, in a possible design, the compensation logic in the seed crystal introduction stage is as follows: when the concentration deviation is greater than 0, the melt temperature is preferentially adjusted; when the concentration deviation is less than 0, the heating power is reduced to inhibit volatilization to achieve the control of the concentration; The melt turbulence is reduced by stabilizing the seed crystal rotation speed to achieve the control of the uniformity.

[0014] In combination with the first aspect, in a possible design, the compensation logic in the shoulder release stage is as follows: dynamic supplementary doping is performed according to the liquid level drop rate to achieve the control of the concentration; The melt convection is regulated by the rotation speed difference between the seed crystal and the crucible to achieve the control of the uniformity.

[0015] In the second aspect, the present invention further provides a silicon dopant volatilization compensation evaluation system based on process analysis, including: A target analysis module, configured to obtain the doping target instruction during the single crystal silicon pulling process and parse it to obtain the target concentration value of the dopant and the target uniformity eigenvalue of the dopant in each pulling stage; A parameter monitoring module, configured to set the corresponding monitoring frequency for each pulling stage and monitor the pulling process parameters based on this to obtain a real-time process parameter set; A volatilization analysis module, configured to perform doping volatilization analysis on the real-time process parameter set to obtain the actual concentration value of the dopant and the actual uniformity eigenvalue of the dopant under this process condition; A deviation calculation module, which is used to calculate the concentration deviation and the uniformity characteristic deviation according to the target concentration value and the actual concentration value of the dopant, as well as the target uniformity characteristic value and the actual uniformity characteristic value of the dopant. A compensation strategy module, which is used to perform compensation analysis on the concentration deviation and the uniformity characteristic deviation in combination with the real-time process parameter set, obtain a dopant volatilization compensation strategy, and output the strategy for compensating the corresponding drawing stage.

[0016] Through the technical solution of the present invention, the following technical effects can be achieved: Through the subdivision and targeted monitoring of the drawing stage, it is ensured to deeply understand the process; the acquisition and analysis of real-time process parameters can quickly sense the environmental changes; based on the calculation of the deviation between the target value and the actual value, the problem can be identified; by combining real-time parameters for compensation analysis and strategy implementation, the problem of dopant volatilization can be corrected in time. The cooperation of each link enables the compensation strategy to be dynamically adjusted with the progress of the drawing process and the change of process parameters, and finally realizes the efficient compensation of dopant volatilization, obtains a single-crystal silicon doping effect more in line with expectations, and thus improves the quality of semiconductor materials and device performance. Description of the Drawings

[0017] Figure 1 It is a logic flow chart of a silicon dopant volatilization compensation evaluation method based on process analysis; Figure 2 It is a structural block diagram of a silicon dopant volatilization compensation evaluation system based on process analysis. Detailed Embodiments

[0018] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0019] Next, the present application will be described in conjunction with the drawings in the present application.

[0020] As Figure 1 shown, the silicon dopant volatilization compensation evaluation method based on process analysis of the present invention specifically includes the following steps: Step S1: Obtain the doping target instruction in the single-crystal silicon drawing process and parse it to obtain the target concentration value and the target uniformity characteristic value of the dopant in each drawing stage; Step S2: For each of the drawing stages, set a corresponding monitoring frequency and monitor the drawing process parameters with this to obtain a real-time process parameter set; Step S3: Perform doping volatilization analysis on the real-time process parameter set to obtain the actual concentration value and the actual uniformity characteristic value of the dopant under this process condition; Step S4: Calculate the concentration deviation and the uniformity characteristic deviation based on the target dopant concentration value, the actual dopant concentration value, the target dopant uniformity characteristic value, and the actual dopant uniformity characteristic value. Step S5: Combine the real-time process parameter set, conduct a compensation analysis on the concentration deviation and the uniformity characteristic deviation, obtain a dopant volatilization compensation strategy, and perform compensation on this pulling stage accordingly.

[0021] In this embodiment, the single-crystal silicon pulling process is divided into multiple specific stages such as seed crystal pulling, necking down, and shoulder forming. Exclusive monitoring frequencies are set for the process characteristics of each stage, which can capture the differential effects of process parameter changes in different stages on dopant volatilization. For example, during the equal-diameter growth stage with a long-time high-temperature environment and the diameter sudden change process in the shoulder forming stage, there are significant differences in the dopant volatilization rules; by separately analyzing the doping target for each stage and matching the corresponding monitoring strategies, full-process coverage from the initial stage of crystal growth to cooling is achieved, avoiding the problem of insufficient adaptability of traditional fixed models to complex dynamic processes. By collecting key process parameters such as melt temperature and crystal pulling speed in real time, and combining with the calculation of the deviation between the target and actual doping concentrations and uniformity, a closed-loop feedback mechanism for monitoring, analysis, and compensation is formed; specifically, the real-time process parameter set provides dynamic input for volatilization analysis, which can identify the volatilization characteristics of the current stage in real time, while the calculation of the concentration and uniformity deviation directly points to the formulation of the compensation strategy, ensuring that the compensation strategy can be adjusted immediately with the change of process conditions. Compared with the traditional method relying on historical experience or fixed parameters, the tracking accuracy of the dynamic process of dopant volatilization in a high-temperature environment is improved. The method simultaneously focuses on the dopant concentration deviation and the uniformity characteristic deviation, and conducts a comprehensive compensation analysis in combination with real-time process parameters; the concentration deviation reflects the volatilization loss of the total amount of dopant, and the uniformity characteristic deviation reflects the consistency problem of the doping distribution. The two together determine the electrical performance stability of single-crystal silicon; by associating the above two types of deviations with specific process parameters, the compensation strategy can formulate a differential adjustment plan for the dominant influencing factors in different stages. For example, by adjusting the argon flow rate to control the furnace pressure to inhibit volatilization, or by optimizing the crucible rotation speed to improve doping uniformity, it breaks through the limitation of the traditional method that only focuses on a single concentration index, and improves the compensation effect from two levels of total amount control and distribution uniformity. Due to the non-linear dynamic changes in the process parameters at each stage during the single-crystal silicon pulling process, it is difficult for traditional fixed models to accurately describe the time-varying law of dopant volatilization. This method captures parameter fluctuations in real time by setting monitoring frequencies in stages, and through the correlation analysis of deviation calculation and process parameters, the compensation strategy can automatically adapt to the volatilization characteristics in different scenarios such as the low-temperature initial contact in the seeding stage, the rapid pulling in the necking stage, and the long-term stable growth in the constant-diameter stage. For example, when the melt volume decreases in the finishing stage, resulting in a change in the volatilization interface, the compensation amount can be adjusted through real-time liquid level height data to avoid the impact of the sudden change in the volatilization rate caused by the change in the melt surface area on the doping uniformity. This enables the method to effectively handle complex volatilization behaviors in high-temperature environments and solve the problem of insufficient compensation accuracy in existing technologies under variable process conditions. In summary, this method forms an intelligent compensation system covering the entire process of single-crystal silicon pulling through the logical series of phased target analysis, real-time dynamic monitoring, multi-dimensional deviation analysis, and process parameter coupling compensation. The coordinated action of each step not only realizes the accurate quantitative evaluation of dopant volatilization, but also constructs a closed-loop control mechanism from data acquisition to strategy execution. Ultimately, while improving the accuracy and uniformity of doping concentration, it significantly enhances the stability of the semiconductor material manufacturing process.

[0022] In some embodiments of the present invention, the doping target instruction is determined by the preliminary process design of semiconductor or photovoltaic device manufacturing, and includes the target parameters of the electrical properties of single-crystal silicon, such as conduction type, carrier concentration, resistivity, etc., as well as the concentration distribution requirements of dopants (such as phosphorus, boron, etc.) in the crystal. It exists in the form of process documents or digital models, clearly specifying the doping effects to be achieved at each stage during the pulling process. The instruction needs to cover all stages of the single-crystal silicon pulling process, including but not limited to: Seeding stage: The initial stage where the seed crystal contacts the silicon melt and starts to grow, and it is necessary to ensure that the concentration of the dopant in the starting part of the crystal meets the requirements. Necking stage: A thin neck is formed by rapidly pulling the crystal to eliminate crystal defects. The doping uniformity in this stage needs to meet the basic conditions for subsequent growth. Shoulder opening stage: The crystal diameter gradually expands to the target size, and it is necessary to control the stability of the dopant concentration with the changes in the melt liquid level and temperature. Constant-diameter growth stage: The crystal diameter remains constant, which is the key stage determining the doping performance of the crystal body and has the highest requirement for concentration uniformity. Finishing stage: The diameter contraction stage before the end of crystal growth, and it is necessary to avoid abnormal enrichment or depletion of dopants in the finishing area. Cooling stage: During the crystal cooling process, it is necessary to consider the influence of the temperature gradient on the dopant diffusion to ensure the final concentration stability.

[0023] Specifically, for each drawing stage, the target concentration of dopants in the single crystal silicon at the end of this stage is analyzed, such as atomic concentration, mass fraction, etc.; for example, the phosphorus doping concentration is required to be 1×10 15 cm −3 during the equal-diameter growth stage, while in the seed crystal pulling stage, due to the small melt volume and fast evaporation rate, the target concentration may be slightly higher than the theoretical value to compensate for the initial evaporation; The target uniformity eigenvalue of the dopant is used to quantify the spatial distribution uniformity of the dopant in the crystal, and is a combination of any one or more of the concentration standard deviation, coefficient of variation, radial / axial concentration gradient threshold, etc.; in chip manufacturing, if the dopant distribution is uneven, it will lead to differences in the transistor threshold voltages in different regions, affecting the overall performance and reliability of the chip. For example, the target uniformity eigenvalue stipulates that the coefficient of variation of the doping concentration in the equal-diameter section does not exceed 5% to ensure the consistency of the device threshold voltage; Through structured data processing (such as reading process files in XML and JSON formats) or industrial control system (such as SCADA) interfaces, the target parameters of each stage are extracted; if the target instructions exist in the form of empirical formulas or models, such as the doping distribution function deduced based on device performance, they need to be transformed into discrete target values executable in each stage through mathematical analysis.

[0024] In this embodiment, through the precise analysis of the doping target instructions, the abstract device performance requirements are transformed into quantifiable doping targets for each drawing stage; through stage-by-stage refined design, it is ensured that the target parameters match the dynamic characteristics of the drawing process, enabling the compensation evaluation method to adapt to variable process conditions.

[0025] In some embodiments of the present invention, the process dynamics in different stages of the single crystal silicon drawing process are significantly different, and different monitoring frequencies are required to ensure the timeliness and effectiveness of data. The specific division is as follows: The rapid change stage includes the seed crystal pulling, necking, and shoulder opening stages. In these stages, the crystal morphology is rapidly adjusted. For example, when pulling the seed crystal, the seed crystal first contacts the melt; when necking, the pulling speed suddenly increases to form a thin neck; when opening the shoulder, the crystal diameter gradually expands, and parameters such as the melt surface area, temperature, and pulling speed may fluctuate frequently; at this time, the evaporation of the dopant is significantly affected by the change of process parameters, and high-frequency monitoring is required to capture the minute changes of parameters in real time; for example, in the seed crystal pulling stage, the instantaneous fluctuation of the melt temperature may cause a sudden change in the evaporation rate, and high-frequency monitoring can avoid the lag of the compensation strategy; The stable growth stage includes the equal-diameter growth stage. In this stage, the crystal diameter is constant, and the process parameters tend to be stable (such as the pulling speed and rotation speed), but slow evaporation changes may still be caused by factors such as melt consumption and temperature drift during long-term growth; medium-frequency monitoring is adopted, which can not only ensure the data continuity to track the gradual change process, but also reduce the system data processing load; In the final stage, crystal growth is approaching completion, the amplitude of parameter adjustment decreases, and the residual concentration when the melt is almost exhausted is mainly concerned; in the cooling stage, the temperature slowly decreases, and the volatilization of the dopant basically stops. The focus is on monitoring the influence of the cooling rate on concentration diffusion; at this time, low-frequency monitoring is adopted to reduce redundant data acquisition, and key parameters such as the final melt level and cooling temperature are recorded.

[0026] More specifically, the pulling process parameters corresponding to each pulling stage include melt temperature, crystal pulling speed, seed rotation speed, crucible rotation speed, argon flow rate, melt level height, and dopant injection amount, as follows: Melt temperature: In a high-temperature environment, the vapor pressure of the dopant increases significantly with the increase in temperature. For example, the volatilization rate of phosphorus is about 30% higher at 1420 °C than at 1400 °C; the surface and central temperatures of the melt are obtained in real time through an infrared thermometer or thermocouple installed on the periphery of the crucible. Crystal pulling speed: The crystal pulling speed directly affects the melt flow state at the crystal growth interface; rapid crystal pulling will intensify melt convection, promote the migration of the dopant to the melt surface, and increase the probability of volatilization; the stable pulling speed in the equal-diameter stage corresponds to a relatively balanced volatilization rate; the monitoring device servo motor encoder can be accurate to the micron / second level and feedback the current crystal pulling speed in real time. Seed and crucible rotation speeds: The rotation speeds of the seed and the crucible jointly determine the eddy current pattern of the melt; the change in rotation speed will affect the melt mixing uniformity, and then change the distribution and volatilization path of the dopant; for example, when the rotation speed difference increases, the melt turbulence intensifies, which may lead to changes in the concentration gradient of the dopant on the surface, thus affecting the volatilization rate; the rotation speed values of both are collected in real time through a rotation speed sensor. Argon flow rate: The argon protective atmosphere in the crystal pulling furnace is not only used to isolate oxygen, but also affects the transfer efficiency of volatilized dopant molecules through the gas flow rate; a high argon flow rate will accelerate the volatilized dopant molecules on the surface to leave the area above the melt, reducing the probability of recondensation; a low flow rate may lead to local concentration enrichment, increasing the uncertainty of volatilization; a mass flow meter monitors the argon flow rate in real time and synchronizes the data to the control system for correcting the gas phase transfer parameters in the volatilization model. Melt level height: As the crystal grows, the melt is continuously consumed, and the change in the exposed melt surface area due to the decrease in the liquid level, such as the surface area increases in the shoulder stage and decreases in the final stage, directly affects the total surface area of volatilization; for example, when the melt level drops by 1 centimeter, the surface area may change by several square centimeters, thereby affecting the overall volatilization amount; the liquid level is monitored by a laser rangefinder or a capacitive sensor, and the accuracy needs to reach the millimeter level to correct the calculation deviation of the volatilization amount caused by the surface area change in real time. Dopant injection amount: The seed crystal pulling stage is the starting stage of single crystal silicon pulling. At this stage, the crystal has not been fully formed, and the demand for dopants is relatively low. Since the seed crystal and the melt have just come into contact, a certain dopant concentration needs to be ensured to form a stable crystallization nucleus. However, too high a dopant concentration may lead to initial crystallization defects. Therefore, the injection amount is usually set at a relatively low level to meet the requirement of forming high-quality crystal nuclei. In the necking stage, a thin neck is formed by quickly pulling the crystal. The main purpose is to eliminate defects such as dislocations in the crystal. The control of the dopant injection amount is relatively strict and generally maintained at a relatively stable low level because the rapid crystal pulling will intensify the melt convection. If the dopant injection amount is too large, it may cause uneven distribution of the dopant in the crystal, affecting the necking effect and crystal quality. In the shoulder broadening stage, the crystal diameter gradually expands, and the distribution of the thermal field and flow field of the melt changes, and the consumption of dopants also increases accordingly. At this time, the dopant injection amount will gradually increase with the expansion of the crystal diameter to meet the demand for dopants during the crystal growth process. At the same time, the increase in the injection amount needs to match the convection and volatilization conditions of the melt to ensure uniform distribution of the dopant in the crystal. The constant diameter growth stage is the key stage of single crystal silicon pulling. The crystal diameter remains constant, and extremely high requirements are placed on the concentration uniformity of the dopant. In this stage, the dopant injection amount needs to be precisely controlled and is usually dynamically adjusted according to factors such as the consumption rate of the melt and the temperature distribution. Since the constant diameter growth stage lasts for a long time, the volatilization and temperature change of the melt will affect the dopant concentration. Therefore, it is necessary to monitor and adjust the injection amount in real time to ensure the stability of the dopant concentration. In the finishing stage, the crystal growth is approaching the end, and the melt volume gradually decreases. At this time, the dopant injection amount needs to be reduced because if the dopant is injected at the normal rate, it will cause too high a dopant concentration in the finishing area, affecting the overall performance of the crystal. At the same time, it is necessary to precisely control the injection amount according to the remaining amount of the melt and the growth situation of the crystal to avoid local enrichment or lack of dopants.

[0027] In this embodiment, the phased differential monitoring frequency enables the system to capture transient events missed by the traditional fixed frequency method in the rapidly changing stage, such as a sharp increase in volatilization caused by a sudden rise in the melt temperature; the real-time fusion of multi-dimensional parameters such as the melt temperature, argon flow rate, and crystal pulling speed can identify the dominant factors of volatilization under complex working conditions. For example, in the shoulder broadening stage, by monitoring the coordinated change of the liquid level drop rate and the crucible rotation speed, the compensation strategy is optimized; by dynamically adjusting the monitoring frequency in phases and collecting multi-parameters in a coordinated manner, a high-precision real-time process parameter set is constructed to improve the capture ability of the volatilization behavior.

[0028] In some embodiments of the present invention, based on the melt temperature, crystal pulling speed, seed rotation speed, crucible rotation speed, argon gas flow rate, melt level height, and the initially designed dopant injection amount collected in real time, through the fusion analysis of a physical model and a data-driven algorithm, the actual concentration value of the dopant and its distribution uniformity characteristic value under the current process conditions are calculated.

[0029] First, based on the initial dopant injection amount and real-time parameters, a concentration dynamic model is established as follows: ; Wherein, represents the actual concentration value of the dopant; represents the dopant injection amount at the initial stage of the corresponding crystal pulling stage, which is pre-determined by the process recipe; represents the dynamic melt volume, which is calculated from the real-time liquid level height, and the calculation formula is: V = πr 2 h melt (t), h melt (t) represents the real-time liquid level height; represents the evaporation rate function, which describes the evaporation rate of the dopant on the surface of the silicon melt and is a function of temperature and argon gas flow rate. Among them, represents the melt temperature at time τ. The increase in temperature will significantly increase the vapor pressure of the dopant, thereby accelerating the evaporation rate. represents the argon gas flow rate at time τ. The argon gas flow rate affects the molecular transport efficiency of the evaporated dopant. A high flow rate will accelerate the detachment of the evaporated molecules from the melt surface and increase the evaporation loss. τ is a virtual time variable used to represent any moment between 0 and the current time t from the start of the crystal pulling stage, τ ∈ [0, t]; represents the dopant concentration on the surface of the silicon melt at time τ, reflecting the concentration level of the dopant participating in evaporation at the current moment; represents the contribution amount of the convective diffusion of the dopant due to the melt flow to the actual concentration of the dopant from the start of the crystal pulling stage to the current time, and the cumulative effect of the convective diffusion effect during the entire time period is calculated through integration; represents the melt flow velocity field at time τ. As a vector, it describes the flow velocity and direction of each point in the silicon melt at time τ. Its three components respectively correspond to the flow velocities in the three spatial directions and are jointly determined by the seed rotation speed, crucible rotation speed, and crystal pulling speed. An increase in the seed rotation speed will drive the melt to flow upward; the difference between the crucible rotation speed and the seed rotation speed will affect the radial convective intensity of the melt; the crystal pulling speed will affect the flow of the melt towards the solid-liquid interface; represents the concentration gradient vector, which is the spatial change rate of the dopant concentration at time τ. Its mathematical expression is: , representing the change rates of the dopant concentration in the x, y, and z directions respectively; More specifically, in the above formula, the first term is used to represent the initial concentration reference, the second term is used to represent the cumulative loss due to volatilization during the entire drawing stage, and the third term is used to represent the influence of the interaction between the melt flow velocity field and the concentration gradient at different times on the dopant concentration during the entire drawing stage; the calculation dimensions of the above three are all (amount of substance / volume) or (mass / volume), which are the same as the dimension of the concentration.

[0030] On the other hand, the dopant distribution uniformity characteristic value is quantitatively represented by the axial concentration variation coefficient, and the calculation formula is: ; where represents the axial concentration variation coefficient, and the smaller the value, the more uniform the axial concentration distribution; represents the total length of the crystal when it grows to time t; represents the concentration standard deviation at the axial position z; represents the concentration mean value at the axial position z.

[0031] In this embodiment, the constructed concentration dynamic model comprehensively considers the initial dopant injection amount in the drawing stage, the dynamic melt level height, the volatilization rate function, and the convective effect of the melt flow field and the concentration gradient; for example, by calculating the melt volume based on the real-time liquid level height, it can dynamically reflect the change of the dopant concentration during the melt consumption process; the volatilization rate function adjusts the calculation of the volatilization loss in real time according to parameters such as temperature and argon flow rate, which is more in line with the volatilization situation caused by the multi-parameter changes in the actual drawing process, rather than using fixed parameters for calculation, and can more accurately calculate the actual concentration value of the dopant, overcoming the defect that the existing technology cannot adapt to the changing process conditions; by using the fusion analysis of the physical model and the data-driven algorithm, the model is not only based on the theoretical physical model, but also optimized by combining the actual collected data; for example, the volatilization rate function calibrates the specific parameter values under different argon flow rate and other conditions through experiments, making the model calculation closer to the actual production working conditions. Compared with simply relying on experience or a simple fixed model, it can more accurately reflect the actual situation of the dopant concentration under complex working conditions and improve the calculation accuracy; The axial coefficient of variation of concentration is used to quantify the characteristic value of the dopant distribution uniformity. Through a clear calculation formula, the crystal growth length, the standard deviation and the mean value of the concentration at different axial positions are comprehensively considered. Compared with the existing methods that may lack quantitative evaluation or rely only on qualitative judgment, this quantification method can more accurately and intuitively evaluate the distribution uniformity of the dopant in the axial direction of the crystal. This calculation method can effectively reflect the concentration difference of the dopant at different axial positions of the crystal, and intuitively reflect the quality of the uniformity through the magnitude of the coefficient of variation. Compared with the situation where the prior art may not be able to accurately capture the subtle differences in axial concentration, it can more sensitively detect the problem of non-uniform doping caused by changes in process parameters. For example, local concentration fluctuations caused by abnormal process parameters at certain stages during the drawing process can be detected in time through this quantitative value and adjusted accordingly to improve the quality stability of the product.

[0032] In some embodiments of the present invention, based on the target concentration value of the dopant, the target uniformity characteristic value of the dopant obtained in step S1, and the actual concentration value of the dopant and the actual uniformity characteristic value of the dopant obtained in step S3, two types of deviation calculations are performed: Concentration deviation calculation: The target concentration value of the dopant is compared and analyzed with the actual concentration value of the dopant. For example, if the target concentration value of the dopant at a certain drawing stage is and the actual concentration value of the dopant analyzed through step S3 is , then the concentration deviation . This deviation directly reflects the difference between the actual doping concentration and the expected target concentration, and is used to measure the degree of deviation of the doping concentration. Uniformity characteristic deviation calculation: The target uniformity characteristic value of the dopant is compared with the actual uniformity characteristic value of the dopant. If the target uniformity characteristic value of the dopant is and the actual uniformity characteristic value is , then the uniformity characteristic deviation . This deviation quantifies the gap between the actual performance of the doping uniformity and the target requirements, and represents the degree of deterioration of the doping uniformity.

[0033] In some embodiments of the present invention, according to the concentration deviation and the uniformity characteristic deviation calculated in step S4, combined with real-time process parameters, a dynamic and executable compensation strategy is generated. This process needs to comprehensively consider the multi-parameter coupling effect, the process characteristics of different drawing stages, and the influence of real-time environmental changes on the volatilization behavior, as follows: First, deviation analysis needs to be carried out on the concentration deviation and the uniformity characteristic deviation. Among them, for the positive concentration deviation, that is, ΔC>0, it means that the actual concentration is lower than the target concentration, and dopants need to be supplemented or volatilization needs to be inhibited; for the negative concentration deviation, that is, ΔC<0, it means that the actual concentration is too high, and the injection amount needs to be reduced or the volatilization time needs to be extended; for the positive uniformity deviation, that is, ΔCV>0, it means that the uniformity does not meet the standard, and the melt convection or the thermal field distribution needs to be optimized; for the negative uniformity deviation, that is, ΔCV<0, it means that the uniformity is better than expected, and the current parameters can be maintained or the adjustment range can be reduced. After that, according to the process sensitivity in different drawing stages, the compensation weights of concentration and uniformity are dynamically allocated; for example, in the shoulder-forming stage, due to the non-linear increase in the volatilization rate, the concentration compensation weight accounts for 70% and the uniformity accounts for 30%; in the equal-diameter stage, the weights of both are 50%. Then, through regression analysis or machine learning models, the influence weights of each process parameter on the deviation are quantified; for example, if the melt temperature increases by 10°C resulting in a 60% contribution to ΔC, and the argon flow rate decreases resulting in a 30% contribution to ΔC, then the temperature is adjusted first; map the deviation amount to the specific process parameter adjustment amount, such as for every +1×10¹ 5 atoms / cm³ of ΔC, the injection amount is increased by 5%.

[0034] More specifically, due to the differences in process characteristics in different drawing stages, compensation logics need to be designed specifically as follows: Seeding stage: When the melt initially contacts the seed crystal, the temperature fluctuates greatly and the volatilization rate is unstable; the compensation logic is: when ΔC>0, the melt temperature is adjusted first; when ΔC<0, the heating power is reduced to inhibit volatilization; ensure the uniformity of the initial crystal nuclei by stabilizing the seed crystal rotation speed to reduce melt turbulence. Shoulder-forming stage: The crystal diameter expands rapidly, the melt surface area grows non-linearly, and the volatilization rate surges; the compensation logic is: dynamically supplement doping according to the liquid level drop rate, such as when the liquid level drops by 1 mm, the injection amount is increased by 0.8% to achieve the control of concentration; control the melt convection by the rotation speed difference between the seed crystal and the crucible to achieve the control of uniformity. Equal-diameter stage: Steady-state growth, but long-term drawing leads to the cumulative effect of volatilization; the compensation logic is: based on the feedback of the melt resistivity, adjust the injection amount in a closed-loop manner. When the resistivity increases by +0.1 Ω·cm, the injection amount is increased by 2% to achieve the control of concentration; maintain the stability of the crystal pulling speed, for example, the fluctuation is <±0.05 mm / min, and the axial temperature gradient is controlled <5°C / cm to achieve the control of uniformity. Ending and cooling stage: The residual amount of the melt is small, and concentration enrichment is likely to occur at the tail; the compensation logic is: reduce the injection amount step by step, such as when the diameter is shortened by 10% each time, the injection amount is reduced by 8% to achieve the control of concentration; limit the cooling rate to inhibit the lattice stress at the tail to achieve the control of uniformity.

[0035] In this embodiment, through positive and negative deviation judgment and targeted processing, such as supplementing or reducing dopants in case of concentration deviation, and optimizing convection or thermal field in case of uniformity deviation, the target of the compensation strategy is clear, avoiding blind adjustment; dynamically allocating compensation weights based on the characteristics of different drawing stages, such as differential weight settings in the shoulder and equal-diameter stages, to meet the process requirements of each stage and improve the compensation efficiency; using regression analysis or machine learning to quantify the influence weights of process parameters, realizing precise adjustment, accurately mapping the deviation amount and the parameter adjustment amount, and enhancing the operability of the compensation strategy; designing exclusive compensation logics for each drawing stage, fully considering the changes in the melt and crystal states in different stages from crystal seeding to finishing cooling, making the compensation strategy more suitable for actual production, effectively improving the doping accuracy and uniformity of single crystal silicon, and further enhancing the quality of semiconductor materials and device performance.

[0036] As Figure 2 shown, the present invention also provides a silicon dopant volatilization compensation evaluation system based on process analysis, specifically including the following modules; A target parsing module, configured to obtain the doping target instruction during the pulling of single crystal silicon and parse it to obtain the target concentration value of the dopant and the target uniformity characteristic value of the dopant for each pulling stage; A parameter monitoring module, configured to set corresponding monitoring frequencies for each pulling stage and monitor the pulling process parameters based on these frequencies to obtain a set of real-time process parameters; A volatilization analysis module, configured to perform doping volatilization analysis on the set of real-time process parameters to obtain the actual concentration value of the dopant and the actual uniformity characteristic value of the dopant under this process condition; A deviation calculation module, configured to calculate the concentration deviation and the uniformity characteristic deviation based on the target concentration value of the dopant and the actual concentration value of the dopant, as well as the target uniformity characteristic value of the dopant and the actual uniformity characteristic value of the dopant; A compensation strategy module, configured to combine the set of real-time process parameters, perform compensation analysis on the concentration deviation and the uniformity characteristic deviation, obtain the dopant volatilization compensation strategy, and output this strategy for compensating the corresponding pulling stage.

[0037] In this embodiment, the target parsing module obtains the doping target instruction during the single-crystal silicon pulling process and parses it to obtain the target concentration values and target uniformity characteristic values of the dopant for each pulling stage such as crystal seeding, necking, shoulder opening, equal-diameter growth, tailing, and cooling, providing benchmark data for subsequent evaluation; the parameter monitoring module sets a matching monitoring frequency according to the process characteristics of each pulling stage, such as high-frequency monitoring during the equal-diameter growth stage and low-frequency monitoring during the cooling stage, and real-time collects process parameters such as the melt temperature, crystal pulling speed, seed crystal rotation speed, crucible rotation speed, argon gas flow rate, and melt level height during the crystal pulling process to form a real-time process parameter set, ensuring coverage of the dynamic change characteristics of different stages; the volatilization analysis module receives the real-time process parameter set and analyzes the volatilization behavior of the dopant in the silicon melt under the current process conditions based on the thermodynamic volatilization model, Fick's diffusion law, and historical process data, and calculates the actual concentration value and actual uniformity characteristic value of the dopant, such as the radial concentration standard deviation and axial concentration gradient, to quantify the impact of volatilization on the doping effect; the deviation calculation module compares the target concentration value of the dopant with the actual concentration value for each pulling stage, and at the same time matches and analyzes the target uniformity characteristic value with the actual uniformity characteristic value, and obtains the concentration deviation and uniformity characteristic deviation through methods such as difference calculation and variance analysis to clarify the difference between the current process state and the target requirements; the compensation strategy module combines the real-time process parameter set and the deviation calculation result to establish a multivariable coupling compensation model, such as a volatilization rate correction algorithm based on process parameters, and generates targeted compensation strategies for the volatilization laws of different pulling stages, such as the volatilization rate fluctuation caused by the change in the melt surface area during the shoulder opening stage, such as adjusting the dopant supplement amount, optimizing the gas flow rate or pulling speed, and outputs the compensation instruction to the crystal pulling equipment to achieve dynamic control of the doping process in each stage; each module forms a closed-loop control through data interaction. The target parsing module provides the benchmark, the parameter monitoring module real-time feedbacks the state, the volatilization analysis module quantifies the impact, the deviation calculation module locates the problem, and the compensation strategy module outputs the solution, ultimately realizing the full-process coordination from target setting to execution of compensation, effectively coping with the dopant volatilization problem caused by multi-stage and multi-parameter changes during the single-crystal silicon pulling process, and improving the control accuracy of doping concentration and uniformity.

[0038] The foregoing has shown and described the basic principles, main features, and advantages of the present invention; those skilled in the art should understand that the present invention is not limited by the above embodiments, and what is described in the above embodiments and the specification is only to illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed; the scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for evaluating silicon dopant volatilization compensation based on process analysis, characterized in that, Including: Obtain the doping target instruction during the single-crystal silicon drawing process, and parse it to obtain the target concentration value of the dopant and the target uniformity characteristic value of the dopant for each drawing stage; For each of the above-mentioned drawing stages, set the corresponding monitoring frequency, and monitor the drawing process parameters based on this to obtain a set of real-time process parameters; Conduct doping volatilization analysis on the set of real-time process parameters to obtain the actual concentration value of the dopant and the actual uniformity characteristic value of the dopant under this process condition; Based on the target concentration value of the dopant and the actual concentration value of the dopant, as well as the target uniformity characteristic value of the dopant and the actual uniformity characteristic value of the dopant, calculate the concentration deviation and the uniformity characteristic deviation; Combined with the set of real-time process parameters, conduct compensation analysis on the concentration deviation and the uniformity characteristic deviation to obtain a doping volatilization compensation strategy, and compensate the corresponding drawing stage accordingly.

2. The method for evaluating silicon dopant volatilization compensation based on process analysis according to claim 1, wherein The drawing stage includes at least one of the seed crystal pulling stage, the necking stage, the shoulder releasing stage, the equal-diameter growth stage, the ending stage, and the cooling stage.

3. The method for evaluating silicon dopant volatilization compensation based on process analysis according to claim 2, wherein The drawing process parameters include the melt temperature, the crystal pulling speed, the seed crystal rotation speed, the crucible rotation speed, the argon gas flow rate, the melt level height, and the dopant injection amount.

4. The method for evaluating silicon dopant volatilization compensation based on process analysis according to claim 3, wherein The calculation formula for conducting doping volatilization analysis on the set of real-time process parameters is: ； Among them, represents the actual concentration value of the dopant; Indicates the dopant injection amount corresponding to the start of the drawing stage; Indicates the dynamic melt volume, which is calculated from the real-time liquid level height; is a function of the volatilization rate, representing the volatilization rate of the dopant on the surface of the silicon melt; wherein, represents the melt temperature at time τ, represents the argon gas flow rate at time τ; τ is a virtual time variable used to represent any moment between τ = 0 at the start of the drawing stage and the current time τ = t, τ ∈ [0, t]; t represents the current moment; represents the dopant concentration on the surface of the silicon melt at time τ, reflecting the level of the dopant concentration participating in volatilization at the current moment; Represents the contribution amount of the convective diffusion of the dopant due to the melt flow to the actual concentration of the dopant from the start of the drawing stage to the current time; Denotes the melt flow velocity field at time τ, which is used to describe the flow velocity and direction of each point in the silicon melt at time τ, and is jointly determined by the seed rotation speed, crucible rotation speed, and crystal pulling speed; Represents the gradient of the dopant concentration, which is used to describe the spatial rate of change of the dopant concentration at time τ.

5. The method for evaluating silicon dopant evaporation compensation based on process analysis according to claim 4, characterized in that, The mathematical expression for the gradient of the dopant concentration is: ； Among them, , and respectively represent the change rates of the dopant concentration in the x, y, and z directions.

6. The method for evaluating silicon dopant volatilization compensation based on process analysis according to claim 5, wherein The doping distribution uniformity characteristic value is quantitatively represented by the axial concentration variation coefficient.

7. The method for evaluating silicon dopant evaporation compensation based on process analysis according to claim 6, wherein The calculation formula for the axial concentration variation coefficient is: ； Among them, represents the axial concentration variation coefficient. The smaller the value, the more uniform the axial concentration distribution; represents the total length of the crystal when it grows to time t; represents the concentration standard deviation at the axial position z; represents the concentration mean value at the axial position z.

8. The method for evaluating silicon dopant volatilization compensation based on process analysis according to claim 1, wherein The compensation logic for the seed crystal pulling stage is: when the concentration deviation is greater than 0, preferentially adjust the melt temperature; when the concentration deviation is less than 0, reduce the heating power to suppress volatilization to achieve the control of the concentration; Reduce the melt turbulence by stabilizing the seed crystal rotation speed to achieve the control of the uniformity.

9. The method for evaluating silicon dopant volatilization compensation based on process analysis according to claim 8, wherein The compensation logic for the shoulder releasing stage is: dynamically supplement doping according to the liquid level drop rate to achieve the control of the concentration; Regulate the melt convection through the rotation speed difference between the seed crystal and the crucible to achieve the control of the uniformity.

10. A silicon dopant volatilization compensation evaluation system based on process analysis, characterized in that, Including: A target parsing module, which is used to obtain the doping target instruction during the single-crystal silicon drawing process, and parse it to obtain the target concentration value of the dopant and the target uniformity characteristic value of the dopant for each drawing stage; A parameter monitoring module, which is used to set the corresponding monitoring frequency for each drawing stage, and monitor the drawing process parameters based on this to obtain a set of real-time process parameters; A volatilization analysis module, which is used to conduct doping volatilization analysis on the set of real-time process parameters to obtain the actual concentration value of the dopant and the actual uniformity characteristic value of the dopant under this process condition; A deviation calculation module, which is used to calculate the concentration deviation and the uniformity characteristic deviation according to the target concentration value of the dopant and the actual concentration value of the dopant, as well as the target uniformity characteristic value of the dopant and the actual uniformity characteristic value of the dopant; A compensation strategy module, which is used to combine the set of real-time process parameters, conduct compensation analysis on the concentration deviation and the uniformity characteristic deviation to obtain a doping volatilization compensation strategy, and output this strategy for compensating the corresponding drawing stage.

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