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

Abstract

The present invention relates to the technical field of single crystal silicon manufacturing, and in particular to a silicon dopant volatilization compensation evaluation method and system based on process analysis, comprising: obtaining a doping target instruction in a single crystal silicon pulling process, parsing the instruction, and obtaining a dopant target concentration value and a dopant target uniformity characteristic value for each pulling stage; setting a corresponding monitoring frequency for each pulling stage, and using the frequency to monitor the pulling process parameters to obtain a real-time process parameter set; performing a dopant volatilization analysis on the real-time process parameter set to obtain an actual dopant concentration value and an actual dopant uniformity characteristic value under the process conditions; and calculating a concentration deviation and a uniformity characteristic deviation based on the dopant target concentration value and the actual dopant concentration value, as well as the dopant target uniformity characteristic value and the actual dopant uniformity characteristic value. The method can be dynamically adjusted as the pulling process progresses and the process parameters change, thereby achieving efficient compensation for dopant volatilization.

Description

Technical Field

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

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

[0003] Current methods for evaluating silicon dopant volatilization compensation mostly rely on empirical adjustments or fixed parameter models. These methods struggle to account for the complex dynamics of the single-crystal silicon pulling process—including the impact of various process parameter changes during seeding, necking, and shoulder release on dopant volatilization. Consequently, existing compensation strategies often fail to accurately match the actual volatilization behavior of dopants, limiting the performance optimization of the final product.

[0004] In order to improve the quality of semiconductor materials and device performance, it is urgent to develop a silicon dopant volatilization compensation evaluation method and system that can adapt to changing process conditions. Summary of the Invention

[0005] The present invention provides a silicon dopant volatilization compensation evaluation method and system based on process analysis that can be dynamically adjusted as the drawing process progresses and process parameters change to achieve efficient compensation for dopant volatilization, which can effectively solve the problems in the background technology.

[0006] To achieve the above objectives, in a first aspect, the present invention provides a method for evaluating silicon dopant volatilization compensation based on process analysis, comprising:

[0007] Obtaining the doping target instructions during the single crystal silicon pulling process and parsing them to obtain the dopant target concentration value and dopant target uniformity characteristic value at each pulling stage;

[0008] For each of the drawing stages, a corresponding monitoring frequency is set, and the drawing process parameters are monitored to obtain a real-time process parameter set;

[0009] Performing doping volatilization analysis on the real-time process parameter set to obtain an actual dopant concentration value and an actual dopant uniformity characteristic value under the process conditions;

[0010] Calculating a concentration deviation and a uniformity characteristic deviation 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;

[0011] In combination with the real-time process parameter set, a compensation analysis is performed on the concentration deviation and the uniform feature deviation to obtain a dopant volatilization compensation strategy, and compensation is performed on the drawing stage accordingly.

[0012] In combination with the first aspect, in a possible design, the pulling stage includes at least one of a seeding stage, a necking stage, a shoulder release stage, an equal diameter growth stage, a finishing stage, and a cooling stage.

[0013] In combination with the first aspect, in a possible design, the pulling 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.

[0014] In conjunction with the first aspect, in one possible design, the calculation formula for performing doping volatilization analysis on the real-time process parameter set is:

[0015] ;

[0016] in, Indicates the actual concentration value of the dopant;

[0017] represents the dopant injection amount at the beginning of the corresponding drawing stage;

[0018] Indicates the dynamic melt volume, which is calculated from the real-time liquid level height;

[0019] is the volatilization rate function, which represents the volatilization rate of the dopant on the surface of the silicon melt; represents the melt temperature at time τ, represents the argon flow rate at time τ; τ is a virtual time variable used to represent any time between τ = 0 at the beginning of the drawing stage and the current time τ = t, τ∈[0,t]; t represents the current time;

[0020] It represents the dopant concentration on the surface of the silicon melt at time τ, reflecting the concentration level of the dopant participating in volatilization at the current moment;

[0021] It represents the contribution of dopant convection diffusion caused by melt flow to the actual dopant concentration from the beginning of the drawing stage to the current time;

[0022] It represents the melt flow rate field at time τ, which is used to describe the flow speed and direction of each point in the silicon melt at time τ and is determined by the seed crystal rotation speed, crucible rotation speed and crystal pulling speed;

[0023] It represents the gradient of dopant concentration and is used to describe the rate of change of dopant concentration in space at time τ.

[0024] In combination with the first aspect, in one possible design, the mathematical expression of the gradient of the dopant concentration is:

[0025] ;

[0026] in, 、 and represent the rate of change of dopant concentration in the x, y, and z directions, respectively.

[0027] In combination with the first aspect, in a possible design, the dopant distribution uniformity characteristic value is quantitatively represented by an axial concentration variation coefficient.

[0028] In combination with the first aspect, in a possible design, the calculation formula for the axial concentration coefficient of variation is:

[0029] ;

[0030] in, It represents the coefficient of variation of axial concentration. The smaller the value, the more uniform the axial concentration distribution. represents the total length of the crystal grown to time t; represents the standard deviation of the concentration at the axial position z; represents the mean concentration at the axial position z.

[0031] In conjunction with the first aspect, in one possible design, the compensation logic in the seeding stage is as follows: when the concentration deviation is greater than 0, the melt temperature is adjusted first; when the concentration deviation is less than 0, the heating power is reduced to suppress volatilization in order to achieve concentration control;

[0032] The uniformity can be controlled by stabilizing the seed crystal rotation speed and reducing the melt turbulence.

[0033] Combined with the first aspect, in a possible design, the compensation logic of the shoulder release stage is: dynamic addition according to the liquid level drop rate to achieve concentration control;

[0034] The melt convection is regulated by the rotational speed difference between the seed crystal and the crucible to achieve control of uniformity.

[0035] In a second aspect, the present invention further provides a silicon dopant volatilization compensation evaluation system based on process analysis, comprising:

[0036] The target parsing module is used to obtain the doping target instructions during the single crystal silicon pulling process and parse them to obtain the dopant target concentration value and dopant target uniformity characteristic value at each pulling stage;

[0037] The parameter monitoring module is used to set the corresponding monitoring frequency for each drawing stage, and thereby monitor the drawing process parameters to obtain a real-time process parameter set;

[0038] The volatilization analysis module is used 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 characteristic value of the dopant under the process conditions;

[0039] a deviation calculation module, configured to calculate a concentration deviation and a uniformity characteristic deviation based on a target dopant concentration value and an actual dopant concentration value, as well as a target uniformity characteristic value and an actual uniformity characteristic value of the dopant;

[0040] The compensation strategy module is used to combine the real-time process parameter set to perform compensation analysis on the concentration deviation and uniform feature deviation, obtain the dopant volatilization compensation strategy, and output the strategy to compensate the corresponding drawing stage.

[0041] The technical solution of the present invention can achieve the following technical effects:

[0042] Through segmented and targeted monitoring of the pulling phase, a deep understanding of the process is ensured. Real-time acquisition and analysis of process parameters enable rapid perception of environmental changes. Problems are identified based on the calculation of deviations between target and actual values. Compensation analysis and strategy implementation, combined with real-time parameters, enable timely correction of dopant volatilization issues. The coordinated implementation of these links enables dynamic adjustment of compensation strategies as the pulling process progresses and process parameters change, ultimately achieving efficient compensation for dopant volatilization and achieving more consistent single-crystal silicon doping results, thereby improving semiconductor material quality and device performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A logic flow chart of a silicon dopant volatilization compensation evaluation method based on process analysis;

[0044] Figure 2 The block diagram of the silicon dopant volatilization compensation evaluation system based on process analysis is shown in FIG. DETAILED DESCRIPTION

[0045] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0046] The present application is described below in conjunction with the accompanying drawings.

[0047] like Figure 1 As shown, the silicon dopant volatilization compensation evaluation method based on process analysis of the present invention specifically includes the following steps:

[0048] Step S1: obtaining the doping target instruction during the single crystal silicon pulling process, and analyzing it to obtain the dopant target concentration value and the dopant target uniformity characteristic value at each pulling stage;

[0049] Step S2: for each of the drawing stages, a corresponding monitoring frequency is set, and the drawing process parameters are monitored to obtain a real-time process parameter set;

[0050] Step S3: performing doping volatilization analysis on the real-time process parameter set to obtain an actual dopant concentration value and an actual dopant uniformity characteristic value under the process conditions;

[0051] Step S4, calculating a concentration deviation and a uniformity characteristic deviation 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;

[0052] Step S5: combining the real-time process parameter set, performing compensation analysis on the concentration deviation and the uniform characteristic deviation, obtaining a dopant volatilization compensation strategy, and compensating the drawing stage accordingly.

[0053] In this embodiment, the single crystal silicon pulling process is divided into multiple specific stages, such as seeding, necking, and shouldering. Dedicated monitoring frequencies are set for each stage based on the process characteristics. This allows for capturing the differential impact of process parameter changes at different stages on dopant volatilization. For example, the dopant volatilization patterns differ significantly between the prolonged high-temperature environment of the constant diameter growth stage and the sudden diameter change during the shouldering stage. By analyzing the doping target for each stage and matching it with a corresponding monitoring strategy, the entire process from the initial crystal growth to cooling is covered, avoiding the problem of traditional fixed models' lack of adaptability to complex dynamic processes.

[0054] By collecting key process parameters such as melt temperature and crystal pulling speed in real time, combined with calculations of deviations between target and actual doping concentrations and uniformity, a closed-loop feedback mechanism for monitoring, analysis, and compensation is established. Specifically, the real-time process parameter set provides dynamic input for volatilization analysis, enabling real-time identification of volatilization characteristics at the current stage. Calculations of concentration and uniformity deviations directly inform the formulation of compensation strategies, ensuring that these strategies can be adjusted instantly as process conditions change. This improves the accuracy of tracking the dynamic process of dopant volatilization in high-temperature environments compared to traditional methods that rely on historical experience or fixed parameters.

[0055] This method simultaneously focuses on dopant concentration deviation and uniformity characteristic deviation, and combines real-time process parameters for comprehensive compensation analysis. Concentration deviation reflects the volatilization loss of the total dopant, while uniformity characteristic deviation reflects the consistency of the doping distribution. Together, they determine the stability of the electrical properties of single-crystal silicon. By correlating these two types of deviations with specific process parameters, the compensation strategy can formulate differentiated adjustment plans for the dominant influencing factors at different stages. For example, adjusting the argon flow rate to control the furnace pressure to suppress volatilization, or optimizing the crucible rotation speed to improve doping uniformity, breaking through the limitations of traditional methods that only focus on a single concentration indicator, and simultaneously improving the compensation effect from both the total amount control and distribution uniformity levels.

[0056] Because the process parameters at each stage of the single-crystal silicon pulling process exhibit nonlinear dynamic changes, traditional fixed models are unable to accurately describe the time-varying laws of dopant volatilization. However, this method captures parameter fluctuations in real time by setting the monitoring frequency in stages. Combining deviation calculation with correlation analysis of 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 equal diameter stage. For example, when the melt volume decreases in the final stage, causing the volatilization interface to change, the compensation amount can be adjusted using real-time liquid level data to avoid the impact of sudden changes in the volatilization rate caused by changes in the melt surface area on doping uniformity. This enables the method to effectively cope with complex volatilization behaviors in high-temperature environments and solves the problem of insufficient compensation accuracy of existing technologies under variable process conditions.

[0057] In summary, this method forms an intelligent compensation system covering the entire process of single-crystal silicon pulling through the logical series connection of phased target analysis, real-time dynamic monitoring, multi-dimensional deviation analysis and process parameter coupling compensation; the synergistic effect 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 significantly enhancing the stability of the semiconductor material manufacturing process while improving the accuracy and uniformity of doping concentration.

[0058] In some embodiments of the present invention, the doping target instructions are determined by the early process design of semiconductor or photovoltaic device manufacturing, and include target parameters of the electrical properties of single crystal silicon, such as conductivity type, carrier concentration, resistivity, etc., as well as the concentration distribution requirements of dopants (such as phosphorus and boron) in the crystal. They exist in the form of process documents or digital models, clearly specifying the doping effects to be achieved at each stage of the pulling process. The instructions must cover the entire process stage of single crystal silicon pulling, including but not limited to:

[0059] Seeding stage: The initial stage when the seed crystal contacts the silicon melt and begins to grow. It is necessary to ensure that the concentration of the dopant in the initial part of the crystal meets the requirements;

[0060] Neck shrinkage: Rapid crystal pulling forms a thin neck to eliminate crystal defects. During this stage, doping uniformity must meet the basic conditions for subsequent growth.

[0061] Shouldering stage: The crystal diameter is gradually expanded to the target size, and the stability of the dopant concentration with changes in melt level and temperature needs to be controlled;

[0062] Constant diameter growth stage: The crystal diameter remains constant. This is the key stage that determines the doping performance of the crystal body and places the highest requirements on concentration uniformity.

[0063] Finishing stage: The diameter shrinkage stage before the end of crystal growth. It is necessary to avoid abnormal enrichment or depletion of dopants in the finishing area;

[0064] Cooling stage: During the crystal cooling process, the effect of temperature gradient on dopant diffusion needs to be considered to ensure the final concentration is stable.

[0065] Specifically, for each pulling stage, the target concentration of dopants in the single crystal silicon at the end of the stage is analyzed, such as atomic concentration, mass fraction, etc. For example, the isodiameter growth stage requires a phosphorus doping concentration of 1×10 15 cm −3 , while in the seeding stage, due to the small melt volume and fast volatilization rate, the target concentration may be slightly higher than the theoretical value to compensate for the initial volatilization;

[0066] The dopant target uniformity characteristic value is used to quantify the spatial distribution uniformity of the dopant in the crystal. It uses any one of the following characteristics, such as concentration standard deviation, coefficient of variation, and radial / axial concentration gradient threshold, or a combination of two or more. In chip manufacturing, if the dopant distribution is uneven, it will lead to differences in transistor threshold voltages in different regions, affecting the overall performance and reliability of the chip. For example, the target uniformity characteristic value stipulates that the coefficient of variation of the dopant concentration in equal-diameter segments does not exceed 5% to ensure the consistency of the device threshold voltage.

[0067] The target parameters for each stage are extracted through structured data processing (such as reading process files in XML or JSON format) or industrial control system (such as SCADA) interfaces. If the target instructions exist in the form of empirical formulas or models, such as the doping distribution function based on device performance, they need to be converted into discrete target values that can be executed at each stage through mathematical analysis.

[0068] In this embodiment, through precise analysis of the doping target instructions, the abstract device performance requirements are converted into quantifiable doping targets for each drawing stage; through phased and refined design, it is ensured that the target parameters match the dynamic characteristics of the drawing process, so that the compensation evaluation method can adapt to changing process conditions.

[0069] In some embodiments of the present invention, the process dynamics at different stages of the single crystal silicon pulling process vary significantly, and differentiated monitoring frequencies are required to ensure the timeliness and validity of data. The specific divisions are as follows:

[0070] During the rapid change phase, including seeding, necking, and shouldering, the crystal morphology adjusts rapidly. For example, during seeding, the seed crystal first contacts the melt; during necking, the pulling speed suddenly increases to form a thin neck; during shouldering, the crystal diameter gradually expands. Parameters such as the melt surface area, temperature, and pulling speed may fluctuate frequently. During this phase, dopant volatilization is significantly affected by changes in process parameters, requiring high-frequency monitoring to capture even the smallest parameter changes in real time. For example, during the seeding phase, instantaneous fluctuations in melt temperature can lead to sudden changes in the volatilization rate. High-frequency monitoring can prevent lags in compensation strategies.

[0071] The stable growth stage, including the constant diameter growth stage, is a stage in which the crystal diameter is constant and process parameters tend to be stable (such as pulling speed and rotation speed). However, long-term growth may still cause slow volatilization changes due to factors such as melt consumption and temperature drift. The use of medium frequency monitoring can not only ensure data continuity to track the gradual change process, but also reduce the system data processing load;

[0072] In the final stage, crystal growth is nearing completion, and the parameter adjustment range is reduced. The main focus is on the residual concentration when the melt is almost consumed. In the cooling stage, the temperature is mainly slowly dropped, and the volatilization of the dopant basically stops. The focus is on monitoring the impact of the cooling rate on the concentration diffusion. At this time, low-frequency monitoring is used to reduce redundant data collection, while recording key parameters such as the final melt level and cooling temperature.

[0073] More specifically, the pulling process parameters corresponding to each pulling stage include melt temperature, crystal pulling speed, seed crystal rotation speed, crucible rotation speed, argon gas flow rate, melt level height and dopant injection amount, as follows:

[0074] Melt temperature: Under high temperature conditions, the vapor pressure of dopants increases significantly with increasing temperature. For example, the volatilization rate of phosphorus at 1420°C is about 30% higher than that at 1400°C. Use an infrared thermometer or thermocouple installed on the periphery of the crucible to obtain real-time melt surface and center temperatures.

[0075] Crystal pulling speed: The crystal pulling speed directly affects the melt flow state at the crystal growth interface. Rapid crystal pulling intensifies melt convection, prompting dopants to migrate to the melt surface and increasing the probability of volatilization. A stable pulling speed in the constant diameter stage corresponds to a relatively balanced volatilization rate. The servo motor encoder of the monitoring equipment can be accurate to the micron / second level, providing real-time feedback on the current crystal pulling speed.

[0076] Seed crystal and crucible rotational speeds: The rotational speeds of the seed crystal and crucible jointly determine the vortex morphology of the melt. Changes in rotational speed can affect melt mixing uniformity, thereby altering the distribution and volatilization path of the dopant. For example, as the rotational speed difference increases, melt turbulence intensifies, potentially leading to changes in the dopant concentration gradient at the surface, thus affecting the volatilization rate. A rotational speed sensor collects the rotational speed values of both in real time.

[0077] Argon flow rate: The argon protective atmosphere in the crystal pulling furnace not only isolates oxygen but also affects the transport efficiency of volatilized dopant molecules through airflow velocity. A high argon flow rate accelerates the detachment of surface-volatilized dopant molecules from the area above the melt, reducing the probability of recondensation. A low flow rate may lead to local concentration enrichment and increase 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 correction of the gas phase transport parameters in the volatilization model.

[0078] Melt level: As crystals grow, the melt is continuously consumed. A drop in the melt level causes changes in the exposed melt surface area. For example, the surface area increases during the shouldering phase and decreases during the tailing phase, directly affecting the total surface area for volatilization. For example, for every 1 cm drop in the melt level, the surface area may change by several square centimeters, thus affecting the overall volatilization rate. The melt level should be monitored with a laser rangefinder or capacitive sensor with millimeter-level accuracy to correct for deviations in volatilization calculations caused by surface area changes in real time.

[0079] Dopant injection amount: The seeding stage is the starting stage of single crystal silicon pulling. At this stage, the crystal has not yet been fully formed, and the demand for dopants is relatively low. Since the seed crystal and the melt have just started to contact, a certain dopant concentration needs to be guaranteed to form a stable crystal core, but too high a dopant concentration may cause initial crystallization defects. Therefore, the injection amount is usually set to a lower level to meet the needs of forming high-quality crystal nuclei. In the necking stage, a thin neck is formed by rapid crystal pulling. The main purpose is to eliminate defects such as dislocations in the crystal. The control of the dopant injection amount is relatively strict and is generally maintained at a relatively stable low level. Because rapid crystal pulling will intensify the convection of the melt, if the dopant injection amount is too much, it may cause uneven distribution of dopants in the crystal, affecting the necking effect and crystal quality. In the shouldering stage, the crystal diameter gradually expands, the thermal field and flow field distribution of the melt change, 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 crystal growth. At the same time, the increase in injection volume needs to match the convection and volatilization of the melt to ensure uniform distribution of dopants in the crystal; the equal-diameter growth stage is a key stage in the pulling of single crystal silicon. The crystal diameter remains constant, and the concentration uniformity of the dopant is extremely high. At this stage, the dopant injection volume needs to be precisely controlled, and is usually dynamically adjusted according to factors such as the melt consumption rate and temperature distribution. Since the equal-diameter growth stage lasts for a long time, the volatilization and temperature changes of the melt will affect the concentration of the dopant. Therefore, it is necessary to monitor and adjust the injection volume in real time to ensure the stability of the dopant concentration. In the final stage, the crystal growth is nearing the end, and the melt volume gradually decreases. At this time, the injection volume of the dopant needs to be reduced, because if the dopant continues to be injected at the normal rate, the dopant concentration in the final area will be too high, affecting the overall performance of the crystal. At the same time, the injection volume needs to be precisely controlled according to the remaining amount of the melt and the growth of the crystal to avoid local enrichment or deficiency of the dopant.

[0080] In this embodiment, the differentiated monitoring frequency in different stages enables the system to capture transient events missed by traditional fixed-frequency methods during rapid changes, such as a surge in volatilization caused by a sudden rise in melt temperature. The real-time fusion of multi-dimensional parameters such as 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 release stage, the compensation strategy is optimized by monitoring the coordinated changes in the liquid level drop rate and the crucible rotation speed. By dynamically adjusting the monitoring frequency and collaboratively collecting multiple parameters in different stages, a high-precision real-time process parameter set is constructed to enhance the ability to capture volatilization behavior.

[0081] In some embodiments of the present invention, based on the real-time collected melt temperature, crystal pulling speed, seed crystal rotation speed, crucible rotation speed, argon flow rate, melt liquid level and the initially designed dopant injection amount, the actual dopant concentration value and its distribution uniformity characteristic value under the current process conditions are calculated through the fusion analysis of the physical model and the data-driven algorithm.

[0082] First, based on the initial dopant injection amount and real-time parameters, a concentration dynamic model is established as follows:

[0083] ;

[0084] in, Indicates the actual concentration value of the dopant;

[0085] It indicates the dopant injection amount at the beginning of the corresponding drawing stage, which is predetermined by the process recipe;

[0086] Indicates the dynamic melt volume, which is calculated from the real-time liquid level height. The calculation formula is: V=πr 2 h melt (t), h melt (t) represents the real-time liquid level;

[0087] represents the volatilization rate function, which describes the volatilization rate of the dopant on the surface of the silicon melt and is a function of temperature and argon flow rate, where represents the melt temperature at time τ. The increase in temperature will significantly increase the vapor pressure of the dopant, thereby accelerating the volatilization rate. represents the argon flow rate at time τ. The argon flow rate affects the transport efficiency of dopant molecules after volatilization. A high flow rate will accelerate the evaporation of volatile molecules from the melt surface and increase the volatilization loss.

[0088] τ is a virtual time variable, which is used to represent any time between the beginning of the drawing stage 0 and the current time t, τ∈[0,t];

[0089] It represents the dopant concentration on the surface of the silicon melt at time τ, reflecting the concentration level of the dopant participating in volatilization at the current moment;

[0090] It represents the contribution of dopant convection and diffusion caused by melt flow to the actual concentration of dopant from the beginning of the drawing stage to the current time. The cumulative effect of convection and diffusion in the entire time period is calculated by integration.

[0091] represents the melt flow rate 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 correspond to the flow velocities in the three directions of space, which are determined by the seed crystal rotation speed, crucible rotation speed, and crystal pulling speed. An increase in the seed crystal rotation speed will drive the melt to flow upward; the difference between the crucible rotation speed and the seed crystal rotation speed will affect the radial convection intensity of the melt; and the crystal pulling speed will affect the flow of the melt toward the solid-liquid interface.

[0092] represents the concentration gradient vector, which is the rate of change of the dopant concentration in space at time τ. The mathematical expression is: , respectively represent the rate of change of dopant concentration in the x, y, and z directions;

[0093] More specifically, in the above formula, the first term Used to indicate the initial concentration reference, the second Used to express the cumulative loss of volatilization during the entire drawing stage, the third Used to express the effect of the interaction between the melt flow rate field and the concentration gradient on the dopant concentration at different times during the entire drawing stage; the calculation dimensions of the above three are (amount of substance / volume) or (mass / volume), which are the same as the dimensions of concentration.

[0094] On the other hand, the characteristic value of dopant distribution uniformity is quantitatively expressed by the axial concentration variation coefficient, which is calculated as follows:

[0095] ;

[0096] in, It represents the coefficient of variation of axial concentration. The smaller the value, the more uniform the axial concentration distribution. represents the total length of the crystal grown to time t; represents the standard deviation of the concentration at the axial position z; represents the mean concentration at the axial position z.

[0097] In this embodiment, the constructed concentration dynamic model comprehensively considers the initial dopant injection amount, dynamic melt level height, volatilization rate function, and the convection effect of the melt flow field and concentration gradient during the drawing stage. For example, the melt volume is calculated by real-time liquid level height, which can dynamically reflect the change of dopant concentration during the melt consumption process. The volatilization rate function adjusts the volatilization loss calculation in real time according to parameters such as temperature and argon flow rate, which is more in line with the volatilization situation caused by multi-parameter changes in the actual drawing process, rather than using fixed parameter calculation. It can more accurately calculate the actual dopant concentration value and overcome the defect of the existing technology that cannot adapt to variable process conditions. By integrating physical models and data-driven algorithms for analysis, the model is not only based on theoretical physical models, but also optimized in combination with actual collected data. For example, the volatilization rate function is experimentally calibrated to specific parameter values under conditions such as different argon flow rates, making the model calculation closer to actual production conditions. Compared with relying solely on experience or simple fixed models, it can more accurately reflect the actual situation of dopant concentration under complex working conditions and improve calculation accuracy.

[0098] The axial concentration variation coefficient is used to quantify the characteristic value of the uniformity of the dopant distribution. Through a clear calculation formula, the crystal growth length, the standard deviation and the mean of the concentration at different axial positions are comprehensively considered. Compared with existing methods that may lack quantitative evaluation or rely solely on qualitative judgment, this quantification method can more accurately and intuitively evaluate the uniformity of the dopant distribution 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 uniformity through the size of the variation coefficient. Compared with existing technologies that may not be able to accurately capture subtle differences in axial concentration, it can more keenly discover doping unevenness problems caused by changes in process parameters. For example, local concentration fluctuations caused by abnormal process parameters at certain stages of the drawing process can be discovered in time and targeted adjustments can be made through this quantitative value to improve product quality stability.

[0099] In some embodiments of the present invention, two types of deviation calculations are performed based on the dopant target concentration value and the dopant target uniformity characteristic value obtained in step S1 and the dopant actual concentration value and the dopant actual uniformity characteristic value obtained in step S3:

[0100] Concentration deviation calculation: Compare and analyze the target concentration value of the dopant with the actual concentration value of the dopant; for example, if the target concentration value of the dopant at a certain drawing stage is The actual concentration of the dopant obtained by analysis in 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;

[0101] Uniform characteristic deviation calculation: compare the target uniform characteristic value of the dopant with the actual uniform characteristic value of the dopant; if the target uniform characteristic value of the dopant is , the actual uniform eigenvalue is , then the uniform characteristic deviation ; This deviation quantifies the gap between the actual performance of doping uniformity and the target requirement, indicating the degree of deterioration of doping uniformity.

[0102] In some embodiments of the present invention, a dynamic and executable compensation strategy is generated based on the concentration deviation and uniformity characteristic deviation calculated in step S4, combined with real-time process parameters. This process requires comprehensive consideration of the multi-parameter linkage effect, the process characteristics of different drawing stages, and the impact of real-time environmental changes on volatilization behavior, as follows:

[0103] First, it is necessary to conduct deviation analysis on the concentration deviation and uniformity characteristic deviation. For a positive concentration deviation, i.e., ΔC>0, it means that the actual concentration is lower than the target concentration and it is necessary to add dopants or suppress volatilization. For a negative concentration deviation, i.e., ΔC<0, it means that the actual concentration is too high and it is necessary to reduce the injection volume or extend the volatilization time. For a positive uniformity deviation, i.e., ΔCV>0, it means that the uniformity does not meet the standard and it is necessary to optimize the melt convection or thermal field distribution. For a negative uniformity deviation, i.e., ΔCV<0, it means that the uniformity is better than expected and it is possible to maintain the current parameters or reduce the adjustment range.

[0104] Afterwards, the compensation weights for concentration and uniformity are dynamically allocated based on the process sensitivity of different drawing stages. For example, in the shoulder release stage, due to the nonlinear increase in volatilization rate, the concentration compensation weight accounts for 70% and the uniformity weight accounts for 30%. In the equal diameter stage, the weights of the two are 50% each.

[0105] Then, through regression analysis or machine learning models, the weight of each process parameter's impact on the deviation is quantified. For example, if a 10°C increase in melt temperature results in a 60% contribution to ΔC, and a decrease in argon flow rate results in a 30% contribution to ΔC, then the temperature adjustment is prioritized. The deviation is mapped to the specific process parameter adjustment, such as ΔC per +1×10¹. 5 atoms / cm³, the implant volume increased by 5%.

[0106] More specifically, due to the differences in process characteristics at different drawing stages, compensation logic needs to be designed specifically as follows:

[0107] 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 suppress volatilization. The melt turbulence is reduced by stabilizing the seed crystal rotation speed to ensure the uniformity of the initial crystal nucleus.

[0108] Shouldering stage: The crystal diameter expands rapidly, the melt surface area grows nonlinearly, and the volatilization rate surges. The compensation logic is: dynamic doping according to the rate of liquid level drop, for example, for every 1mm drop in liquid level, the injection volume increases by 0.8% to achieve concentration control. The melt convection is regulated by the speed difference between the seed crystal and the crucible to achieve uniformity control.

[0109] Constant diameter stage: Steady-state growth occurs, but prolonged pulling results in a cumulative volatilization effect. Compensation logic is as follows: injection rate is adjusted based on a closed-loop feedback loop of melt resistivity. For every +0.1Ω·cm in resistivity, the injection rate is increased by 2% to achieve concentration control. The pulling speed is maintained stable, for example, with fluctuations of <±0.05mm / min and axial temperature gradients controlled to <5°C / cm to achieve uniformity control.

[0110] Finishing and cooling stage: The amount of residual melt is small, and concentration enrichment is likely to occur at the tail. The compensation logic is: reduce the injection amount in a step-by-step manner, such as reducing the injection amount by 8% for every 10% reduction in diameter, to achieve concentration control; limit the cooling rate and suppress the lattice stress at the tail to achieve uniformity control.

[0111] In this embodiment, through positive and negative deviation judgment and targeted processing, such as supplementing or reducing dopants when concentration deviation occurs, and optimizing convection or thermal field when uniformity deviation occurs, the compensation strategy goal is clear and blind adjustment is avoided; compensation weights are dynamically allocated based on the characteristics of different pulling stages, such as differentiated weight settings for shoulder release and equal diameter stages, which meet the process requirements of each stage and improve compensation efficiency; regression analysis or machine learning is used to quantify the influence weights of process parameters to achieve precise adjustment, accurately map the deviation amount and the parameter adjustment amount, and enhance the operability of the compensation strategy; exclusive compensation logic is designed for each pulling stage, from seeding to final cooling, fully considering the changes in the melt and crystal state at different stages, so that the compensation strategy is more in line with actual production, effectively improving the doping accuracy and uniformity of single crystal silicon, and thus improving the quality of semiconductor materials and device performance.

[0112] like Figure 2 As shown, the present invention also provides a silicon dopant volatilization compensation evaluation system based on process analysis, which specifically includes the following modules;

[0113] The target parsing module is used to obtain the doping target instructions during the single crystal silicon pulling process and parse them to obtain the dopant target concentration value and dopant target uniformity characteristic value at each pulling stage;

[0114] The parameter monitoring module is used to set the corresponding monitoring frequency for each drawing stage, and thereby monitor the drawing process parameters to obtain a real-time process parameter set;

[0115] The volatilization analysis module is used 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 characteristic value of the dopant under the process conditions;

[0116] a deviation calculation module, configured to calculate a concentration deviation and a uniformity characteristic deviation based on a target dopant concentration value and an actual dopant concentration value, as well as a target uniformity characteristic value and an actual uniformity characteristic value of the dopant;

[0117] The compensation strategy module is used to combine the real-time process parameter set to perform compensation analysis on the concentration deviation and uniform feature deviation, obtain the dopant volatilization compensation strategy, and output the strategy to compensate the corresponding drawing stage.

[0118] In this embodiment, the target analysis module obtains the doping target instructions during the single crystal silicon pulling process and analyzes them to obtain the dopant target concentration values and dopant target uniformity characteristic values for each pulling stage, such as seeding, necking, shouldering, isodiametric growth, finishing, and cooling, providing benchmark data for subsequent evaluation. The parameter monitoring module sets a matching monitoring frequency based on the process characteristics of each pulling stage, such as high-frequency monitoring in the isodiametric growth stage and low-frequency monitoring in the cooling stage, and collects process parameters such as melt temperature, pulling speed, seed crystal rotation speed, crucible rotation speed, argon flow rate, and melt level height during the crystal pulling process in real time to form a real-time process parameter set to ensure coverage of dynamic change characteristics at 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. It calculates the actual dopant concentration value and the actual dopant uniformity characteristic value, such as the radial concentration standard deviation and the axial concentration gradient, to quantify the impact of volatilization on the doping effect. The deviation calculation module compares the dopant target concentration value of each pulling stage with the actual concentration. The target uniformity characteristic value is compared with the actual uniformity characteristic value. Through difference calculation, variance analysis and other methods, the concentration deviation and uniformity characteristic deviation are obtained to clarify the difference between the current process status and the target requirement. The compensation strategy module combines the real-time process parameter set and the deviation calculation results to establish a multivariable coupling compensation model. For example, the volatilization rate correction algorithm based on process parameters is used to generate targeted compensation strategies for the volatilization laws of different pulling stages, such as the volatilization rate fluctuation caused by the change of melt surface area in the shoulder release stage. Such strategies include adjusting the dopant replenishment amount, optimizing the gas flow rate or pulling speed, and outputting the compensation instructions to the crystal pulling equipment to achieve dynamic control of the doping process at each stage. Each module forms a closed-loop control through data interaction. The target analysis module provides a benchmark, the parameter monitoring module provides real-time status feedback, the volatilization analysis module quantifies the impact, the deviation calculation module locates the problem, and the compensation strategy module outputs the solution. Ultimately, the whole process from target setting to compensation execution is coordinated, effectively addressing the dopant volatilization problem caused by multi-stage and multi-parameter changes in the single crystal silicon pulling process, and improving the control accuracy of doping concentration and uniformity.

[0119] The above shows and describes 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 to the above embodiments, and the above embodiments and descriptions are only for illustrating the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements fall within the scope of the present invention to be protected; the scope of protection claimed in the present invention is defined by the attached claims and their equivalents.

Claims

1. A silicon dopant volatilization compensation evaluation method based on process analysis, characterized in that: include: Obtaining the doping target instructions during the single crystal silicon pulling process and parsing them to obtain the dopant target concentration value and dopant target uniformity characteristic value at each pulling stage; For each of the drawing stages, a corresponding monitoring frequency is set, and the drawing process parameters are monitored to obtain a real-time process parameter set; Performing doping volatilization analysis on the real-time process parameter set to obtain an actual dopant concentration value and an actual dopant uniformity characteristic value under the process conditions; Calculating a concentration deviation and a uniformity characteristic deviation 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; Combining the real-time process parameter set, performing compensation analysis on concentration deviation and uniform feature deviation, obtaining a dopant volatilization compensation strategy, and compensating for the drawing stage accordingly; The calculation formula for doping volatilization analysis of the real-time process parameter set is: ； in, Indicates the actual concentration value of the dopant; represents the dopant injection amount at the beginning of the corresponding drawing stage; Indicates the dynamic melt volume, which is calculated from the real-time liquid level height; is the volatilization rate function, which represents the volatilization rate of the dopant on the surface of the silicon melt; represents the melt temperature at time τ, Indicates time Argon flow rate at 1 hour; Is a virtual time variable, used to indicate the time from the drawing stage =0 to current time = any time between t, ∈[0,t]; t represents the current time; It represents the dopant concentration on the surface of the silicon melt at time τ, reflecting the concentration level of the dopant participating in volatilization at the current moment; It represents the contribution of dopant convection diffusion caused by melt flow to the actual dopant concentration from the beginning of the drawing stage to the current time; It represents the melt flow rate field at time τ, which is used to describe the flow speed and direction of each point in the silicon melt at time τ and is determined by the seed crystal rotation speed, crucible rotation speed and crystal pulling speed; represents the gradient of the dopant concentration, which is used to describe the rate of change of the dopant concentration in space at time τ; The compensation logic during the seeding phase is as follows: when the concentration deviation is greater than 0, the melt temperature is adjusted first; when the concentration deviation is less than 0, the heating power is reduced to suppress volatilization to achieve concentration control; and melt turbulence is reduced by stabilizing the seed crystal rotation speed to achieve uniformity control. The compensation logic during the shoulder release phase is as follows: dynamic doping according to the liquid level drop rate to achieve concentration control; melt convection is regulated by the speed difference between the seed crystal and the crucible to achieve uniformity control; The compensation logic in the constant diameter stage is as follows: the injection volume is adjusted based on the melt resistivity feedback closed loop to achieve concentration control; and uniformity is controlled by maintaining the stability of the crystal pulling speed. The compensation logic of the finishing and cooling stages is: reduce the injection amount in a step-by-step manner to achieve concentration control; and suppress the tail lattice stress by limiting the cooling rate to achieve uniformity control.

2. The silicon dopant volatilization compensation evaluation method based on process analysis according to claim 1, characterized in that: The pulling stage includes at least one of a seeding stage, a necking stage, a shoulder-releasing stage, an equal-diameter growth stage, a finishing stage, and a cooling stage.

3. The silicon dopant volatilization compensation evaluation method based on process analysis according to claim 2, characterized in that: The pulling 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.

4. The silicon dopant volatilization compensation evaluation method based on process analysis according to claim 3, characterized in that: The mathematical expression of the gradient of the dopant concentration is: ； in, 、 ,and represent the rate of change of dopant concentration in the x, y, and z directions, respectively.

5. The silicon dopant volatilization compensation evaluation method based on process analysis according to claim 4, characterized in that: The dopant distribution uniformity characteristic value is quantitatively represented by the axial concentration variation coefficient.

6. The silicon dopant volatilization compensation evaluation method based on process analysis according to claim 5, characterized in that: The calculation formula for the axial concentration coefficient of variation is: ； in, It represents the coefficient of variation of axial concentration. The smaller the value, the more uniform the axial concentration distribution. represents the total length of the crystal grown to time t; represents the standard deviation of the concentration at the axial position z; represents the mean concentration at the axial position z.

7. A silicon dopant volatilization compensation evaluation system based on process analysis, characterized in that: The system is applied to the silicon dopant volatilization compensation evaluation method based on process analysis as claimed in claim 1, comprising: The target parsing module is used to obtain the doping target instructions during the single crystal silicon pulling process and parse them to obtain the dopant target concentration value and dopant target uniformity characteristic value at each pulling stage; The parameter monitoring module is used to set the corresponding monitoring frequency for each drawing stage, and thereby monitor the drawing process parameters to obtain a real-time process parameter set; The volatilization analysis module is used 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 characteristic value of the dopant under the process conditions; a deviation calculation module, configured to calculate a concentration deviation and a uniformity characteristic deviation based on a target dopant concentration value and an actual dopant concentration value, as well as a target uniformity characteristic value and an actual uniformity characteristic value of the dopant; The compensation strategy module is used to combine the real-time process parameter set to perform compensation analysis on the concentration deviation and uniform feature deviation, obtain the dopant volatilization compensation strategy, and output the strategy to compensate the corresponding drawing stage.

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