Silicon Single Crystal Growth Research Articles

Effect of Crystal Rotation on Melt Convection and Resistivity Distribution in 200 mm Floating Zone Silicon Single Crystal Growth.

Floating silicon is particularly suitable for the production of power devices and detectors due to its high purity and high resistivity. However, when the crystal diameter increases to 200 mm, the inhomogeneous distribution of dopants in the radial direction of the crystal becomes an important factor affecting the quality of the crystal. In this paper, the melt flow and crystal interface dopant distribution of 200 mm floating zone silicon under different crystal rotation modes using 2D axisymmetric models was calculated. In the simulation, the crystal rotates unidirectionally clockwise or alternates between clockwise and counterclockwise rotations and is compared with the corresponding experimental results. The results of alternate rotation show a significant improvement in the distribution of resistivity, which is explained from the perspective of melt flow, providing ideas for the industrial production of high-quality FZ silicon crystals.

Data-driven clustering learning modeling for semiconductor silicon single crystal growth process based on fuzzy C-means and DBN

Data-driven clustering learning modeling for semiconductor silicon single crystal growth process based on fuzzy C-means and DBN

Monitoring the operating state of crystal growth process based on digital twin model

The reliable assessment of the operational status during the silicon single crystal growth process is a prerequisite for ensuring system safety and improving crystal quality. However, in the actual silicon single crystal growth process, due to limitations in manpower, material resources, financial resources, and current technical methods, the establishment of monitoring models is still in its infancy. To address this issue, this paper proposes a hybrid deep belief network (HDBN) algorithm aided by the digital twin (DT) model to achieve real-time monitoring of equipment operational status. Firstly, this study constructs the DT model based on the basic principles of crystal growth, mainly to achieve high-precision simulation of the actual silicon single crystal growth process and generate abnormal data for the equipment. This operation can expand the sample set, enhance the diversity and coverage of data, and effectively solve the problem of insufficient sample size. Secondly, this study uses the variational mode decomposition (VMD) algorithm to decompose the dataset composed of obtained abnormal and normal data, and constructs sub-deep belief network (DBN) for the decomposed subsequences to capture deep feature information at different frequencies of the data. Subsequently, based on the concept of ensemble learning, the outputs of each sub-DBN network are used as inputs to construct the overall DBN network, achieving monitoring of the equipment operational status. Through the combination of VMD decomposition and DBN networks, this algorithm can better capture the frequency characteristics and time-domain features of the signal, enhancing monitoring accuracy. Experimental results show that this algorithm can accurately identify abnormal equipment states, effectively improve monitoring performance, and is of significant importance for the optimization and control of the semiconductor-grade silicon single crystal growth process, contributing to increased production efficiency and product quality.

Adversarial Robustness Enhancement for Deep Learning-Based Soft Sensors: An Adversarial Training Strategy Using Historical Gradients and Domain Adaptation.

Despite their high prediction accuracy, deep learning-based soft sensor (DLSS) models face challenges related to adversarial robustness against malicious adversarial attacks, which hinder their widespread deployment and safe application. Although adversarial training is the primary method for enhancing adversarial robustness, existing adversarial-training-based defense methods often struggle with accurately estimating transfer gradients and avoiding adversarial robust overfitting. To address these issues, we propose a novel adversarial training approach, namely domain-adaptive adversarial training (DAAT). DAAT comprises two stages: historical gradient-based adversarial attack (HGAA) and domain-adaptive training. In the first stage, HGAA incorporates historical gradient information into the iterative process of generating adversarial samples. It considers gradient similarity between iterative steps to stabilize the updating direction, resulting in improved transfer gradient estimation and stronger adversarial samples. In the second stage, a soft sensor domain-adaptive training model is developed to learn common features from adversarial and original samples through domain-adaptive training, thereby avoiding excessive leaning toward either side and enhancing the adversarial robustness of DLSS without robust overfitting. To demonstrate the effectiveness of DAAT, a DLSS model for crystal quality variables in silicon single-crystal growth manufacturing processes is used as a case study. Through DAAT, the DLSS achieves a balance between defense against adversarial samples and prediction accuracy on normal samples to some extent, offering an effective approach for enhancing the adversarial robustness of DLSS.

Simulation of thermal-fluid coupling in silicon single crystal growth based on gradient normalized physics-informed neural network

The thermal-fluid coupling phenomenon of silicon melt is significant in the growth process of silicon single crystals. Complex convection affects the temperature and concentration distribution of the silicon melt. Therefore, establishing and solving the thermal-fluid coupling model of silicon melts is crucial to optimizing the crystal growth process and improving crystal quality. Traditional numerical simulation methods have limitations in regard to optimization, control, and real-time monitoring. Physics-Informed Neural Network (PINN) does not require model discretization, after training, it can make predictions quickly, showing potential for industrial applications. However, when solving practical industrial coupling models, PINN often struggles to converge due to large parameter values and significant gaps between solution variables. Moreover, solving the thermal-fluid coupling model with PINN can be treated as a multitask problem, where the gradients of different equations interfere with each other, leading to gradient confusion, slow convergence, or even divergence. Therefore, this paper proposes a gradient normalized PINN (GNPINN) for solving the thermal-fluid coupling model of silicon melt. GNPINN balances the contribution of each task, ensuring a more equitable training speed between different tasks to stabilize the training process of the coupling model. This paper considers the thermal-fluid coupling model of silicon melt under different rotation conditions. GNPINN can accurately and comprehensively capture the complex temperature, velocity, and pressure distribution of silicon melt compared with other methods. Additionally, the experimental results uncover the flow and heat transfer properties of silicon melt, validating the effectiveness and industrial applicability of GNPINN.

A Soft Measurement Method for the Tail Diameter in the Growing Process of Czochralski Silicon Single Crystals

In the Czochralski silicon single crystal growth process, the tail diameter is a key parameter that cannot be directly measured. In this paper, we propose a real-time soft measurement method that combines a deep belief network (DBN) and a support vector regression (SVR) network based on system identification to accurately predict the crystal diameter. The main steps of the proposed method are as follows: First, we address the delay problem of the effects of the temperature and crystal pulling speed on the tail diameter growth by using a back propagation (BP) neural network based on the mean impact value (MIV) method to determine the optimal delay time. Second, we construct a prediction model of the tail diameter by using the DBN network with the temperature and crystal pulling speed as input variables in the crystal growth process. Third, we improve the DBN network by using the SVR network to enhance its linear regression capability. We also employ the ant colony optimization (ACO) algorithm to obtain the optimal parameters of the SVR network. Finally, we compare the performance of the DBN-ACO-SVR network based on system identification with the DBN and SVR networks, and the results show that our method can effectively deal with the delay problem and achieve the accurate prediction of the tail diameter in the Czochralski silicon single crystal growth process.

Research on Classification Algorithm of Silicon Single-Crystal Growth Temperature Gradient Trend Based on Multi-Level Feature Fusion.

In the process of silicon single-crystal preparation, the timely identification and adjustment of abnormal conditions are crucial. Failure to promptly detect and resolve issues may result in a substandard silicon crystal product quality or even crystal pulling failure. Therefore, the early identification of abnormal furnace conditions is essential for ensuring the preparation of perfect silicon single crystals. Additionally, since the thermal field is the fundamental driving force for stable crystal growth and the primary assurance of crystal quality, this paper proposes a silicon single-crystal growth temperature gradient trend classification algorithm based on multi-level feature fusion. The aim is to accurately identify temperature gradient changes during silicon crystal growth, in order to promptly react to early growth failures and ensure the stable growth of high-quality silicon single crystals to meet industrial production requirements. The algorithm first divides the temperature gradient trend into reasonable categories based on expert knowledge and qualitative analysis methods. Then, it fuses the original features of actual production data, shallow features extracted based on statistical information, and deep features extracted through deep learning. During the fusion process, the algorithm considers the impact of different features on the target variable and calculates mutual information based on the difference between information entropy and conditional entropy, ultimately using mutual information for feature weighting. Subsequently, the fused multi-level feature vectors and their corresponding trend labels are input into a Deep Belief Network (DBN) model to capture process dynamics and classify trend changes. Finally, the experimental results demonstrate that the proposed algorithm can effectively predict the changing trend of thermal field temperature gradients. The introduction of this algorithm will help improve the accuracy of fault trend prediction in silicon single-crystal preparation, thereby minimizing product quality issues and production interruptions caused by abnormal conditions.

Дослідження розподілу кисню по довжині монокристалів кремнію, легованих компонентами з різним типом провідності

The purpose of the article is the study of convective flows and their influence on the growth of single crystals of silicon by the Czochralsky method from a large melt, which contributes to the emergence of non-stationary convection. Therefore, simulation of convection for the growth of silicon single crystals is an important step in the development of conditions for the growth of perfect single crystals. Silicon substrates are used to manufacture more than 90% of semiconductor devices and solar cells. A special role in the development of electronics is played by monocrystalline silicon, which is used for the manufacture of semiconductor devices and integrated microcircuits. The main requirements for the development of technology for the production of silicon substrates is an increase in quality at a decrease in cost. Promising technologies of 10-nm size and 3D-transistor structures significantly increase the requirements for uniformity of distribution of components, including layering in silicon single crystals. For the mathematical modeling of convective flows, melt flows were considered for a cylindrical crucible with a radius of 150 mm at a melt height of up to 40 mm. Such parameters ensure stationary convection in molten silicon. Methods of reducing stratification have been studied and developed for more than 50 years, but have not yet found a definitive solution. This method of single crystal growth is the most controlled and allows to influence the convective flows in the silicon melt below the phase interface with ultrasonic waves in the megahertz range. The effectiveness of using ultrasound in the extraction of semiconductor single crystals depends on the creation of special conditions for introducing them into the melt. 
 Reducing the influence of oxygen on the electrophysical properties of silicon single crystals is an intractable problem of silicon technology. One of the ways to solve this problem is alloying with an isomorphic impurity, for example, tin. The development of a method of doping single crystals of silicon with tin requires determination of its concentration in the liquid and solid phases

APPLICATION OF CARBON-CARBON COMPOSITE MATERIALS FOR THE MANUFACTURE OF HIGH-TEMPERATURE HEATERS OF HEAT EXCHANGERS WITH AUTOMATIC TEMPERATURE CONTROL


 The article justifies the use of high-temperature heaters made of carbon-carbon composite material (CCCM) for the thermal unit of a silicon single crystal growth chamber. The conducted analysis confirms that the electrical properties of composite materials, specifically their specific resistance, allow for the creation of heating elements for high-temperature vacuum furnaces or furnaces operating in inert atmospheres at temperatures up to 2200°C.
 The use of heaters made from carbon-carbon composite material eliminates the main drawback of graphite heaters - uncontrolled energy dissipation during resistive heating due to the presence of transient electrical resistance at the junctions of graphite plates, and ensures a more uniform temperature field throughout the chamber volume. The capabilities in terms of the maximum permissible temperature of such a CCCM heater exceed the working temperature by more than two times, which also positively affects the service life.
 The modes of thermal processes occurring during crystal growth are determined by the technological process depending on the composition of the raw material and require high uniformity of heating in the working zone, high precision, and stability of the heater's temperature control. For precise temperature regulation, it is proposed to additionally measure the integral temperature in the chamber indirectly, which is based on measuring the electrical current passing through the heater, which is in thermodynamic equilibrium with the object. Thus, the heater is considered as a system susceptible to various thermal influences that determine the heat transfer process and the temperature change within the chamber and in the zone of the thermal unit's bricks.
 An improved structural diagram of a step-type extremal control system is proposed for automatic temperature control of a high-temperature heater using modern power electronics, sensors, microprocessors. To ensure speed and accuracy in temperature control, the pulse-phase control method implemented with modern specialized thermoregulator with PID-regulation was applied.
 Experimental tests conducted on the «Redmet-30» installation under factory conditions confirm the energy efficiency of using high-temperature heaters made of CCCM.

Numerical study of continuous Czochralski (CCz) silicon single crystal growth in a double-side heater

The effect of heater power control on heat, flow, and oxygen transport for the CCz growth of 8-inch diameter silicon crystal in a triple-crucible was numerically studied. Three different designs of a double-side heater at different power ratios of the lower and upper side heaters (PRSD = 0.25, 1, and 4) were compared with the case of a single-side heater. For the cases considered in the present work, a design in which the upper side heater was shorter than the lower one at PRSD = 0.25 could be a good choice for improving the crystal quality and CCz growth. This was shown by the reductions in the crystal-melt interface deflection and oxygen content and the increase in the melt temperature in the feeding zone. In this case, reducing the interface deflection and crucible bottom wall temperature could enhance the pulling speed. However, the power consumption in this condition was higher than that in the single-side heater case. Achieving a lower heater power was feasible with a higher PRSD value. However, it was important to note that the oxygen content would be higher, and the melt temperature in the outer melt significantly dropped.

Electrophysical parameters of p-i-n photodiodes, irradiated with 60Co γ-quanta

The results of studies of changes in the electrical parameters of p-i-n photodiodes manufactured on monocrystalline silicon wafers of p-type conductivity orientation (100) with ρ = 1000 Ohm cm, when irradiated with γ-quanta from a 60Co source, are presented. It has been established that as a result of irradiation of p-i-n photodiodes with doses up to 2·1015 quanta/cm2, the reverse dark current increases by more than an order of magnitude. However, the shape of the curve of the dependence of the current on the applied reverse voltage of irradiated p-i-n photodiodes does not change qualitatively, as for the original devices there are three regions with different dependences of current on voltage: sublinear, superlinear and linear, due to different mechanisms of generation-recombination processes in the depletion region of the p-n junction. The main reason for the increase in the reverse current of p-i-n photodiodes as a result of irradiation with γ-quanta is the formation of generation-recombination centers of radiation origin due to the condensation of primary radiation defects (vacancies and/or self-interstitial atoms) on technological residual structural defects formed during the growth of silicon single crystals, and during subsequent high-temperature treatments during the formation of devices.

Node-Loss Detection Methods for CZ Silicon Single Crystal Based on Multimodal Data Fusion

Monocrystalline silicon is an important raw material in the semiconductor and photovoltaic industries. In the Czochralski (CZ) method of growing monocrystalline silicon, various factors may cause node loss and lead to the failure of crystal growth. Currently, there is no efficient method to detect the node loss of monocrystalline silicon at industrial sites. Therefore, this paper proposed a monocrystalline silicon node-loss detection method based on multimodal data fusion. The aim was to explore a new data-driven approach for the study of monocrystalline silicon growth. This article first collected the diameter, temperature, and pulling speed signals as well as two-dimensional images of the meniscus. Later, the continuous wavelet transform was used to preprocess the one-dimensional signals. Finally, convolutional neural networks and attention mechanisms were used to analyze and recognize the features of multimodal data. In the article, a convolutional neural network based on an improved channel attention mechanism (ICAM-CNN) for one-dimensional signal fusion as well as a multimodal fusion network (MMFN) for multimodal data fusion was proposed, which could automatically detect node loss in the CZ silicon single-crystal growth process. The experimental results showed that the proposed methods effectively detected node-loss defects in the growth process of monocrystalline silicon with high accuracy, robustness, and real-time performance. The methods could provide effective technical support to improve efficiency and quality control in the CZ silicon single-crystal growth process.

Simulation of thermoelastic coupling in silicon single crystal growth based on alternate two-stage physics-informed neural network

This paper proposes a alternate physics-informed neural network (PINN) with a two-stage training strategy to solve the thermoelastic coupling in the growth of Czochralski silicon single crystal. Particularly, neural networks with a two-stage training strategy are established for solving partial differential equations in the thermoelastic coupling model. At present, PINN still faces challenges in solving coupling models. Especially for the imbalance between and within equations in the coupling model. To solve this problem, this paper splits the model into two independent systems with their coupling term exchanged in the alternating iteration. Then, the imbalance inside a single solution of the coupling model is solved by the proposed two-stage training strategy, and the imbalance between solutions is avoided by alternative iterations. Experimental results show that the proposed alternate two-stage PINN (ATPINN) can accurately simulate the temperature and displacement in the thermoelastic coupling model. Compared with the finite element results, the error of temperature prediction and displacement prediction is acceptable. The numerical results demonstrate the feasibility and performance of the ATPINN. Furthermore, ATPINN can be extended to any type of coupling model, especially for coupling models with large differences in the magnitudes of the loss functions. The codes developed in this manuscript are publicy available at https://github.com/callmedrcom/ATPINN.

Simulation of the superconducting magnet for a silicon single crystal growth

The magnetic Czochralsky (MCz) technique is the most common and widely used approach to producing single crystal silicon. The magnetic field is applied to control the temperature fluctuations and suppress silicon melt convection. However, the magnetic field quality and manufacturing costs were mainly determined by the shape of the coils. In order to generate the transverse magnetic field, two pairs of coils are arranged around the crucible and face each other in opposite directions to construct the superconducting magnets system, which has an inner diameter of 1600 mm and an outer diameter of 2400 mm. The simulating results indicate the magnetic flux density (B) in the center of molten silicon is 0.4 T, and the magnetic field inhomogeneity in the X-Y plane is about 20%. The electrical power consumption and cooling capacity will be reduced. Furthermore, a smaller cryostat is required to hold the curve shape coils, which results in lower cost and lower weight of the superconducting magnet.

Impact of Marangoni effect of oxygen on solid–liquid interface shape during Czochralski silicon growth applied with transverse magnetic field

This study investigated the impact of the Marangoni effect of oxygen on the solid–liquid interface shape in the silicon single-crystal growth process by the transverse magnetic-field-applied Czochralski (Cz) method. To this end, the results of a 3D heat and mass transfer analysis were compared with the experimental results. The findings of the study revealed that the Marangoni effect of oxygen affected the solid–liquid interface shape predicted by the simulation. Moreover, with the introduction of this effect, both the solid–liquid interface shape and temperature distribution of the melt were found to be in good agreement with the experimental values.

Simulation of flow field in silicon single-crystal growth using physics-informed neural network with spatial information

Melt convection plays a crucial role in the growth of silicon single crystals. In particular, melt flow transfers mass and heat, and it may strongly affect the crystal growth conditions. Understanding and controlling convection remains a significant challenge in industrial crystal production. Currently, numerical methods such as the finite element method and the finite volume method are mainly used to simulate melt convection in the crystal growth process. However, these methods are not suitable for most applications with real-time requirements. Physics-informed neural networks (PINNs) have the advantages of fast calculation and wide application. They provide a new concept for the numerical solutions of nonlinear partial differential equations (PDEs). This paper proposes a PINN with spatial information to solve the silicon melt flow model, which does not depend on any simulation data. As the network depth (number of layers) increases, the derivative information in the PDE loss becomes weak, which reduces the expression of the original features in the loss function. Therefore, this study introduces spatial information into the hidden layer of the network, thereby enhancing the correlation between the network and the original input and improving the expression ability of the network. Specifically, silicon melt flow models under three rotating conditions are considered. Compared with other methods, the proposed algorithm can accurately capture regions with complex local morphology. The experimental results reveal the flow characteristics of the silicon melt and confirm the effectiveness of the proposed algorithm. All codes and data attached to this manuscript are publicly available on the following websites: https://github.com/callmedrcom/SIPINN.

Technology and thermomechanics in growing tubular silicon single crystals

The problem of growing high-resistance low-dislocation tubular silicon single crystals for non-planar manufacturing technologies of epitaxial p-n junctions and the production of new-generation power semiconductor devices is considered. The possibilities of Stepanov method for growing volumetric profiled crystalline products, the application of which is based on the use of shapers of various designs, are discussed. In particular, the shortcomings of shapers associated with the melt contamination by foreign particles and impurities are discussed. Therefore, the main attention is paid to the use of equipment that implements crystal growth from a melt without a shaper by Czochralski method. The processes of thermal mechanics are preliminary analyzed in relation to the existing and well-established process of growing polycrystalline highly dislocation silicon pipes of large diameter by Czochralski method for epitaxial reactors.It is noted that the growth of tubular low-dislocation small diameter silicon single crystals requires a significant modernization of the standard hot zone, which in this work is implemented for “REDMET-10” Czochralski furnace. By means of computer simulation, thermal mechanical processes are calculated for such a modernized Czochralski furnace. The parameters of grown tubular silicon single crystals are characterized, and their manufacturing suitability for power semiconductor devices using nonplanar technology is assessed.

Multi-furnace optimization in silicon single crystal production plants by power load scheduling

The power consumption in the process of silicon single crystal growth is huge, so the power load must be limited to a specific range to ensure the safe and stable operation on the silicon single crystal furnace. This article establishes a two-objective mathematical model for the multi-furnace optimal scheduling problem in silicon single crystal production process. The first objective is to minimize the maximum completion time of silicon single crystal growth process on multi-furnaces, and the second objective is to minimize the maximum power consumption obtained by the multi-furnace operation together. A disturbed non-dominated sorting particle swarm optimization combined with genetic algorithm (DNSGPSO) is proposed to solve the multi-objective optimization problem. Through simulation analysis of actual growth data, the effectiveness of the proposed model and the superiority of the algorithm are verified.

Modeling and application of Czochralski silicon single crystal growth process using hybrid model of data-driven and mechanism-based methodologies

Czochralski (Cz) silicon single crystal growth process is a large delay, nonlinear dynamic time-varying system with complex physicochemical reactions, multi-field and multi-phase coupling, and its modeling and control has always been a problem in the automatic control field. In this paper, a hybrid modeling method based on the data-driven model and mechanism model is proposed, and applied to the Cz silicon crystal growth process modeling. Firstly, to simplify the model complexity and improve the model accuracy, the crystal growth process model is divided into the energy transfer model and a hydrodynamic and geometric model. Here, a Hammerstein–Wiener model based on a long short-term memory network (LSTM-Hammerstein–Wiener) is established for the energy transfer process with multiple heat transfer links and hysteresis effect. Further, a novel robust LSTM-Hammerstein–Wiener model is proposed by introducing the M-estimation method, which avoids the effect of the outliers on model robustness. Secondly, the proposed robust LSTM-Hammerstein–Wiener is combined with the hydrodynamic and geometric model to obtain the hybrid model between the heater power and the crystal diameter. Meanwhile, the crystal diameter error compensation model is established to reduce the unmodeled dynamics of the mechanism model, thereby improving the accuracy of the hybrid model. Besides, the proposed hybrid model is applied to the model-free adaptive control of silicon single crystal diameter. Finally, various data experiment results based on actual operating data verify the effectiveness of the proposed hybrid model.

An Intelligent Particle Filter With Adaptive M-H Resampling for Liquid-Level Estimation During Silicon Crystal Growth

During the growth of silicon single crystals, it is critical to detect the liquid level of the silicon melt to ensure their high-quality production. Because noise statistics are difficult to determine in measured values of the liquid level, a particle filter (PF) with unknown statistics has been presented to estimate the liquid level. However, this approach leads to inaccurate results due to sample impoverishment. To alleviate this problem, we propose an intelligent PF method with an adaptive Metropolis–Hastings (M-H) resampling strategy. To accomplish this, we first design an M-H resampling strategy with two proposed distributions to resample low-weight particles. These distributions randomly select high-weight particles for the Gaussian mutations or high-weight and low-weight particles for crossover operations, so as to promote the movement of low-weight particles to high-probability regions. We also construct a self-adaptive function to further improve the overall particle quality, which is used to calculate the selection probability of these two proposed distributions according to the proportion of low-weight particles in all of the particles. Finally, the liquid level is estimated according to the particles after the modified resampling strategy is applied. A comparative evaluation of the proposed method with the adaptive genetic particle filter (AGPF) and the firefly algorithm intelligence optimized particle filter (FAIOPF) is conducted. Some results of the simulation and the practical experiment are presented; they indicate the proposed method offers accuracy improvements in the liquid-level estimation during the silicon crystal growth. More specifically, compared with the AGPF and the FAIOPF, the mean absolute error (MAE) of the proposed method has been reduced by approximately 53.3% and 99.5%, respectively.