Self-adaptive fuzzy temperature control method based on large-diameter, low-defect and high-uniformity germanium single crystal growth

Abstract

The invention belongs to the technical field of semiconductor processing and preparation, and particularly relates to a large-diameter, low-defect and high-uniformity germanium single crystal growth self-adaptive fuzzy temperature control method. A local thermal field is optimized through 6-inch germanium single crystal thermal field simulation and unsteady state single crystal growth simulation; by establishing a large-diameter, low-defect and high-uniformity germanium single crystal growth model and an adaptive fuzzy PID algorithm, real-time monitoring of single crystal growth key parameters, namely actual temperature or cooling rate, and model parameters is realized, and deviation automatic fitting correction control is combined; the influence of uncontrollable factors such as thermal field attenuation between different single crystal furnaces and different rounds in production scheduling is avoided, the controllability of thermal field and single crystal growth is improved, and the deviation range of the growth temperature or the cooling rate in the germanium single crystal growth process is controlled.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor processing and preparation technology, specifically relating to an adaptive fuzzy temperature control method for the growth of large-diameter, low-defect, and highly uniform germanium single crystals. Background Technology

[0002] Germanium single crystals are the mainstream substrate for solar cells in space satellites, with superior conversion efficiency, on-orbit lifetime, and reliability compared to traditional silicon-based cells. With the mass deployment of low-Earth orbit constellations and commercial spaceflight, 4-inch substrates are no longer sufficient to meet the demands for significant weight reduction, cost reduction, and high power output in solar cell arrays. High-quality 6-inch germanium substrates have become the next-generation standard.

[0003] Dislocations and resistivity inhomogeneity are the core defects that limit wafer performance. Firstly, when the dislocation density is ≥5×10⁻⁶... 4 At a density of cm⁻², dislocation lines penetrate the active region, forming non-radiative recombination centers. Minority carrier lifetime drops from milliseconds to tens of nanoseconds, dark current increases by an order of magnitude, and lattice mismatch, leakage current paths, and microcracks are induced, causing a decrease in photoelectric conversion efficiency of more than 3% abs. When the solid-liquid interface convexity is >8 mm, it leads to a resistivity radial / axial dispersion of ±25%, causing series-parallel resistance mismatch in single-cell cells, reducing the fill factor by 2–3% abs, and accelerating electrode diffusion due to localized overheating, directly jeopardizing on-orbit reliability. Therefore, achieving EPD ≤3×10³ cm⁻² and resistivity non-uniformity ≤±5% is a crucial performance threshold that high-quality 6-inch germanium single crystals must overcome.

[0004] Existing publicly available technologies CN116905089B and CN120199370A only provide a temperature control framework for indium phosphide based on big data or sensor networks. Its thermal field structure, material properties, and defect formation mechanism are significantly different from those of germanium single crystals. The thermal field and single crystal growth process parameters of various metal single crystals are different, and the corresponding temperature control requirements are different. In addition, the temperature control of germanium single crystals requires the establishment of a closed loop of three stages: a corresponding temperature control benchmark, a temperature control calibration criterion, and automatic temperature fitting. The temperature control technologies involved in the above-mentioned publicly available literature have drawbacks such as passivity and bias in terms of temperature control input values ​​and prediction. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes an adaptive fuzzy temperature control method for the growth of large-diameter, low-defect, and highly uniform germanium single crystals.

[0006] The method includes the following steps: S1, 6-inch germanium single crystal thermal field simulation and unsteady single crystal growth simulation: By using thermal field simulation and unsteady single crystal growth simulation software, after completing the calibration of the thermal field simulation model through the steps of establishing a 6-inch germanium single crystal furnace model, finite cell analysis, material property matching and boundary condition setting, the unsteady single crystal growth simulation is used to identify whether there are thermal field weak points. S2, Local thermal field optimization of 6-inch germanium single crystal: For weak points in the thermal field, materials with excellent thermal insulation coefficient or thermal conductivity are used to insulate or conduct heat to the local area. S3, Establishment of a large-diameter, low-defect, and highly uniform germanium single crystal growth model: Collect temperature data for the growth of at least 30 sets of 6-inch germanium single crystal samples. The technical specifications of the germanium single crystal samples must simultaneously meet the requirement of an average dislocation density ≤ 50 cm⁻¹. -2 The standards include resistivity non-uniformity ≤6% and single crystal length ≥100mm. The temperature data for the growth of germanium single crystal samples include temperature distribution data, expected value and standard deviation of each temperature measurement point, and statistical calculations to obtain the growth temperature and cooling rate model of germanium single crystal. S4, Adaptive Fuzzy PID Algorithm and Adaptive Fuzzy PID Control: During the growth of a 6-inch germanium single crystal, actual temperature data is collected and combined with a model of germanium single crystal growth temperature and cooling rate to form temperature deviation e and temperature deviation change rate ec or cooling rate deviation ve and temperature change rate vec as input quantities; the proportional gain K of the PID is adjusted by the fuzzy control rule base and fuzzy algorithm. P Integral gain K I Differential gain K D Online adjustments are made by continuously monitoring the values ​​of temperature deviation e and temperature deviation change rate ec in real time through the fuzzy relationship between them, thereby improving the control effect of the temperature control system and achieving the control target of temperature deviation e and temperature deviation change rate ec on the parameters.

[0007] Based on the germanium single crystal growth temperature controlled by the adaptive fuzzy PID algorithm, we continuously collect growth temperature data of germanium single crystal samples with lower dislocations, higher uniformity, and longer single crystals, and continuously iterate the germanium single crystal growth temperature and cooling rate model to improve the accuracy of the model.

[0008] Specifically, the method for identifying whether there are weak points in the thermal field in S1 is as follows: observe the temperature gradient legend of the thermal field simulation model, and judge the weak points in the thermal field by the magnitude of the axial temperature gradient and the radial temperature gradient.

[0009] Specifically, the method for localized heat preservation or heat conduction in S2 is as follows: the quartz tube capping area is located in the high-temperature zone of the thermal field and is insulated with fiber blankets; silicon carbide or graphite is used as a heat-conducting material in the crucible cone and is attached to the crucible cone for uniform heat conduction.

[0010] Specifically, the adaptive fuzzy PID algorithm in S4 is as follows: ; Where u(t) is the output of the control system; The error of the controlled object at time t; The rate of change of the error of the controlled object at time t; k P k I k D These are proportional gain, integral gain, and derivative gain. Adjust K online P K I K D : k P =K´ P +∆K P k I =K´ I +∆K I k D =K´ D +∆K D Where, ∆K P ∆K I ∆K D These correspond to the online changes in proportional gain, integral gain, and derivative gain, respectively.

[0011] The proportional gain enhances the system's responsiveness and rapidly adjusts system errors; the integral gain gradually eliminates steady-state errors; and the derivative gain predicts the trend of system error changes in advance, thereby eliminating errors and suppressing oscillations generated during regulation. Compared to conventional PID algorithms, the adaptive fuzzy PID algorithm incorporates fuzzy control logic, resulting in higher stability, flexibility, and robustness. It is particularly effective for controlled objects with significant time-varying and nonlinear characteristics. Furthermore, incremental adjustments to the PID parameters based on the input parameters enhance the adaptive performance of the PID controller, enabling online adjustment of PID parameters to suit different operating environments and higher control precision requirements.

[0012] Specifically, the adaptive fuzzy PID control in S4 is as follows: Temperature error e and temperature error rate ec are selected as the input variables of the adaptive fuzzy PID controller, with K... P K I K D Online variation of the three parameters ∆K P ∆K I ∆KD As the output variable of the adaptive fuzzy PID controller; define e and ec as fuzzy linguistic variables E and EC, respectively, with the basic universe of discourse [-6, 6]; ∆K P ∆K I ∆K D The corresponding fuzzy linguistic variable is K. P K I K D The basic universe of discourse is the same as that of its fuzzy linguistic variables, which are [0.64, 1.2], [8, 12], and [2, 3], respectively; the quantization factors of the input variables e(t) and ∆e(t) are obtained as follows: ; Output variable ∆K P ∆K I ∆K D The scaling factors are as follows:

[0013] Based on the characteristics of the single-crystal temperature control system and the above requirements, a high-resolution triangular membership function is selected. Therefore, the input and output variables of the adaptive fuzzy PID algorithm are selected as 7 linguistic variables: NB (negative large), NM (negative medium), NS (negative small), ZO (zero), PS (positive small), PM (positive medium), and PB (positive large).

[0014] PID control is characterized by its simple structure, convenient design, and strong stability. However, its control effect is poor under conditions of nonlinearity, time-varying factors, and numerous disturbances, making it difficult to meet practical control requirements.

[0015] The beneficial effects of this invention are as follows: 1) Based on thermal field simulation and unsteady single crystal growth simulation, the weak points of the thermal field physical structure are identified in a targeted manner, and the thermal field structure is systematically optimized and verified; for the common cone region of PBN crucible, the thermal field can be quickly optimized by adding heat insulation or thermal conductive materials, which is simple to operate and easy to implement; 2) By establishing a model of germanium single crystal growth temperature and cooling rate, key control parameters in the single crystal growth process are identified, and fuzzy control rules for temperature or cooling rate are formulated. Fuzzy algorithms are then used to control the three parameters K of the PID controller. P K I K DOnline adjustments were made, enabling real-time monitoring of key single crystal growth parameters, namely actual temperature or cooling rate, and model parameters. Combined with automatic deviation fitting and correction control, the influence of uncontrollable factors such as thermal field attenuation between different single crystal furnaces and different batches during production scheduling was avoided, improving the controllability of the thermal field and single crystal growth. The deviation range of growth temperature or cooling rate during germanium single crystal growth was controlled, enabling repeatable growth of large-diameter, low-defect, and highly uniform germanium single crystals, which has extremely high practical value and economic benefits. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the process of the adaptive fuzzy temperature control method for the growth of large-diameter, low-defect, and highly uniform germanium single crystals according to the present invention.

[0017] Figure 2 This is a schematic diagram of the thermal field simulation of germanium single crystal.

[0018] Figure 3 This is a schematic diagram of local thermal field optimization.

[0019] Figure 4 This is a schematic diagram of the adaptive fuzzy PID control principle. Detailed Implementation

[0020] To better illustrate the purpose, technical solution, and advantages of this invention, specific embodiments will be provided below to further explain the invention. The purpose of this explanation is to provide a more detailed understanding of the invention, not to limit it. Other embodiments obtained by those skilled in the art without inventive effort are all within the scope of protection of this invention.

[0021] Example 1: S1, 6-inch germanium single crystal thermal field simulation and unsteady single crystal growth simulation. A transient heat transfer model was established using the CGsim finite element method. The thermal field simulation and calibration were completed by calibrating the actual conditions and simulation conditions, such as geometric model, process parameters, physical property parameters, boundary conditions, and heater power. Furthermore, the unsteady single crystal growth thermal field simulation was carried out in conjunction with the single crystal growth process.

[0022] S2, 6-inch germanium single crystal local thermal field optimization: Simulation results show that there is a large temperature gradient and stress distribution in the cone region of the PBN crucible, requiring thermal field optimization in this region. A pre-fabricated silicon carbide thermal conductive fixing component is attached to the cone region of the PBN crucible to improve axial thermal conductivity. Figure 4 As shown.

[0023] S3: Establishment of a large-diameter, low-defect, and highly uniform germanium crystal growth model. Temperature data of 30 sets of 6-inch germanium single crystal samples were collected. The technical specifications of the germanium single crystal samples simultaneously meet the following requirements: average dislocation density ≤ 50 cm⁻¹. -2The standards include resistivity non-uniformity ≤6% and single crystal length ≥100 mm. The temperature data of the entire growth process of germanium single crystal sample, including temperature distribution, expected value and standard deviation of each temperature measurement point, are statistically calculated to obtain an ideal temperature or cooling rate single crystal growth model, and the cooling rate v(t) model is preferred.

[0024] S4: Adaptive Fuzzy PID Algorithm and Adaptive Fuzzy PID Control. During the growth of a 6-inch germanium single crystal, the real-time temperature or cooling rate of each measured temperature value and the temperature model or cooling rate model of the single crystal growth model form temperature deviation e and temperature deviation change rate ec, or cooling rate deviation ve and temperature change rate vec, which are used as input quantities. The rule base and fuzzy algorithm in the fuzzy controller adjust the three parameters K of the PID controller. P K I K D By making online adjustments and continuously monitoring the values ​​of ec and e in real time through the fuzzy relationship between ec and e, the control effect of the temperature control system can be improved, thereby achieving the control target of ec and e on the parameters.

[0025] Specifically, the temperature deviation and its rate of change are first divided into fuzzy subsets such as "negative large," "negative medium," "negative small," "zero," "positive small," "positive medium," and "positive large," and a control strategy encompassing 49 fuzzy rules (7×7) is formulated. When the temperature deviation is "positive large" and the rate of change is "positive small," the rule table outputs a large positive control quantity to quickly reduce the temperature; while when the deviation is close to zero, a smaller control quantity is used for fine-tuning to avoid temperature overshoot. In actual operation, the PLC collects temperature data from multiple temperature zones inside the furnace in real time through the analog input module, compares the data with the optimal value after A / D conversion, and calculates the temperature deviation and rate of change. Subsequently, the PLC performs fuzzification processing on the input variables according to the preset membership function and quickly matches the output value of the corresponding fuzzy rule. Finally, this value is used as a control signal to drive the actuator to adjust the power of the resistance wire.

[0026] S5: Iteration of the single crystal growth model. The single crystal controlled by the adaptive fuzzy algorithm will form a new temperature data cluster. Continuous iteration of the germanium single crystal growth temperature model or cooling rate model will improve the accuracy of the model.

Claims

1. An adaptive fuzzy temperature control method for the growth of large-diameter, low-defect, and highly uniform germanium single crystals, characterized in that... The method includes the following steps: S1, 6-inch germanium single crystal thermal field simulation and unsteady single crystal growth simulation: By using thermal field simulation and unsteady single crystal growth simulation software, after completing the calibration of the thermal field simulation model through the steps of establishing a 6-inch germanium single crystal furnace model, finite cell analysis, material property matching and boundary condition setting, the unsteady single crystal growth simulation is used to identify whether there are thermal field weak points. S2, Local thermal field optimization of 6-inch germanium single crystal: For weak points in the thermal field, materials with excellent thermal insulation coefficient or thermal conductivity are used to insulate or conduct heat to the local area. S3, Establishment of a large-diameter, low-defect, and highly uniform germanium single crystal growth model: Collect temperature data for the growth of at least 30 sets of 6-inch germanium single crystal samples. The technical specifications of the germanium single crystal samples must simultaneously meet the requirement of an average dislocation density ≤ 50 cm⁻¹. -2 The standards include resistivity non-uniformity ≤6% and single crystal length ≥100mm. The temperature data for the growth of germanium single crystal samples include temperature distribution data, expected value and standard deviation of each temperature measurement point, and statistical calculations to obtain the growth temperature and cooling rate model of germanium single crystal. S4, Adaptive Fuzzy PID Algorithm and Adaptive Fuzzy PID Control: During the growth of a 6-inch germanium single crystal, actual temperature data is collected and combined with a model of germanium single crystal growth temperature and cooling rate to form temperature deviation e and temperature deviation change rate ec or cooling rate deviation ve and temperature change rate vec as input quantities; the proportional gain K of the PID is adjusted by the fuzzy control rule base and fuzzy algorithm. P Integral gain K I Differential gain K D Online adjustments are made by continuously monitoring the values ​​of temperature deviation e and temperature deviation change rate ec in real time through the fuzzy relationship between them, thereby improving the control effect of the temperature control system and achieving the control target of temperature deviation e and temperature deviation change rate ec on the parameters.

2. An adaptive fuzzy temperature control method for the growth of large-diameter, low-defect, and highly uniform germanium single crystals, characterized in that... The method for identifying whether there are weak points in the thermal field in S1 is as follows: observe the temperature gradient legend of the thermal field simulation model, and judge the weak points by the magnitude of the axial temperature gradient and the radial temperature gradient.

3. An adaptive fuzzy temperature control method for the growth of large-diameter, low-defect, and highly uniform germanium single crystals, characterized in that... The method for localized heat preservation or heat conduction in S2 is as follows: the quartz tube capping area is located in the high-temperature zone of the thermal field and is insulated with fiber blankets; silicon carbide or graphite is used as a heat-conducting material in the crucible cone and is attached to the crucible cone for uniform heat conduction.

4. An adaptive fuzzy temperature control method for the growth of large-diameter, low-defect, and highly uniform germanium single crystals, characterized in that... The adaptive fuzzy PID algorithm in S4 is as follows: ； Where u(t) is the output of the control system; The error of the controlled object at time t; The rate of change of the error of the controlled object at time t; k P k I k D These are proportional gain, integral gain, and derivative gain. Adjust K online P K I K D : k P =K´ P +∆K P k I =K´ I +∆K I k D =K´ D +∆K D Where, ∆K P ∆K I ∆K D These correspond to the online changes in proportional gain, integral gain, and derivative gain, respectively.

5. An adaptive fuzzy temperature control method for the growth of large-diameter, low-defect, and highly uniform germanium single crystals, characterized in that... The adaptive fuzzy PID control in S4 is as follows: Temperature error e and temperature error rate ec are selected as the input variables of the adaptive fuzzy PID controller, with K... P K I K D Online variation of the three parameters ∆K P ∆K I ∆K D As the output variable of the adaptive fuzzy PID controller; define e and ec as fuzzy linguistic variables E and EC, respectively, with the basic universe of discourse [-6, 6]; ∆K P ∆K I ∆K D The corresponding fuzzy linguistic variable is K. P K I K D The basic universe of discourse is the same as that of its fuzzy linguistic variables, which are [0.64, 1.2], [8, 12], and [2, 3], respectively; the quantization factors of the input variables e(t) and ∆e(t) are obtained as follows: ； Output variable ∆K P ∆K I ∆K D The scaling factors are as follows: ； Based on the characteristics of the single-crystal temperature control system and the above requirements, a high-resolution triangular membership function is selected. Therefore, the input and output variables of the adaptive fuzzy PID algorithm are selected as 7 linguistic variables: NB (negative large), NM (negative medium), NS (negative small), ZO (zero), PS (positive small), PM (positive medium), and PB (positive large).

Images