Silicon Single Crystal Growth Research Articles

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.

Numerical Investigation of Effect of Temperature Profile Imposed on the Crucible Surface on Oxygen Incorporated at the Crystal Melt Interface for 450 mm Diameter Silicon Single Crystal Growth in Presence of CUSP Magnetic Field Using Czochralski Technique

Numerical investigation has been carried out to study the effect of thermal boundary condition on turbulent melt flow and oxygen transfer inside a crucible used to grow 450 mm diameter silicon single crystal using Czochralski method. Two types of thermal boundary conditions, namely, isothermal crucible surface and experimentally measured temperatures on the crucible surface have been imposed on the crucible wall and crucible bottom. Melt motion owing to buoyancy, surface tension variation at the free melt surface as well as crystal and crucible rotation has been considered. Effect of CUSP magnetic field has also been investigated. Melt having aspect ratio of 1 and 0.5, representing high and moderate level of melt inside the crucible have been considered. K-epsilon turbulent model with low Reynolds number formulation has been used for turbulence modelling. Melt motion governed by natural convection, Marangoni convection and crystal as well as crucible rotation shows higher oxygen concentration at melt crystal interface for aspect ratio of 1, when experimental temperature profile is imposed at the crucible wall. For melt aspect ratio of 0.5, natural convection and Marangoni convection dependent melt show higher oxygen concentration for isothermal crucible wall boundary condition. Marangoni convection in absence of rotation of crystal and crucible leads to low oxygen concentration zone near the crystal outer surface, the size of which is larger for melt aspect ratio of 0.5. Maximum turbulent viscosity values for aspect ratio of 1, in case of experimental temperature at the crucible are higher compared to isothermal case, which is just the opposite of the trend for aspect ratio of 0.5. Imposing a CUSP magnetic field leads to similar distribution of turbulent viscosity for both types of thermal boundary conditions, irrespective of the type of thermal boundary condition. Oxygen concentration at the melt crystal interface is found to be higher in presence of CUSP magnetic field. Value of maximum turbulent viscosity for the two boundary condition are similar for melt aspect ratio of 1.0. Crucible surface temperature profile for aspect ratio of 1, on actual melt aspect ratio of 0.5 predicts lower oxygen concentration at melt crystal interface. Values and distribution of turbulent viscosity is however the same for both temperature profiles.

Elliptic Arc Fitting for the Shape Control System of Silicon Single Crystal Growth

In the vision-based shape control system of silicon single crystal (SSC) growth, shape parameters are used as the control variables to make the grown SSC approximate to a perfect cylinder. A highlight halo at the junction of the solid crystal and the liquid crysta is a distinctive feature that reflects the current shape of SSC, and the edge of the captured halo is an elliptic arc that consistently changes with the shape of the halo. To estimate the shape parameters through the elliptic arc, we propose a two-side (TS) constraint method to fit the elliptic arc. Firstly, the error correction parameter is introduced into the second-order polynomial model to make the model more robust in the case of noise disturbing, and the resultant non-convex TS constraint model is constructed. Then, two weighted functions, which give the data out of TS constraint a small weight coefficient to resist the large level noise disturbing, are brought into the TS constraint optimization problem tactfully. Simulation and real SSC data examples show that the proposed method can obtain the elliptic arc parameters effectively.

Operational Semantics of Annotated Reflex Programs

Reflex is a process-oriented language that provides a design of easy-to-maintain control software for programmable logic controllers. The language has been successfully used in a several reliability critical control systems, e. g. control software for a silicon single crystal growth furnace and electronic equipment control system. Currently, the main goal of the Reflex language project is to develop formal verification methods for Reflex programs in order to guarantee increased reliability of the software created on its basis. The paper presents the formal operational semantics of Reflex programs extended by annotations describing the formal specification of software requirements as a necessary basis for the application of such methods. A brief overview of the Reflex language is given and a simple example of its use – a control program for a hand dryer – is provided. The concepts of environment and variables shared with the environment are defined that allows to disengage from specific input/output ports. Types of annotations that specify restrictions on the values of the variables at program launch, restrictions on the environment (in particular, on the control object), invariants of the control cycle, pre- and postconditions of external functions used in Reflex programs are defined. Annotated Reflex also uses standard annotations assume, assert and havoc. The operational semantics of the annotated Reflex programs uses the global clock as well as the local clocks of separate processes, the time of which is measured in the number of iterations of the control cycle, to simulate time constraints on the execution of processes at certain states. It stores a complete history of changes of the values of shared variables for a more precise description of the time properties of the program and its environment. Semantics takes into account the infinity of the program execution cycle, the logic of process transition management from state to state and the interaction of processes with each other and with the environment. Extending the formal operational semantics of the Reflex language to annotations simplifies the proof of the correctness of the transformation approach to deductive verification of Reflex programs developed by the authors, transforming an annotated Reflex program to an annotated program in a very limited subset of the C language, by reducing a complex proof of preserving the truth of program requirements during the transformation to a simpler proof of equivalence of the original and the resulting annotated programs with respect to their operational semantics.

Particle Filter With Unknown Statistics to Estimate Liquid Level in the Silicon Single-Crystal Growth

In the process of silicon single-crystal growth, the detection of melt level is an important step to ensure that the grown silicon single crystal is of high quality. Since there exist many mechanical motions, chemical interactions, thermal convection, and so on, it is extremely difficult to obtain the noise statistics of the liquid-level data. To attain a high-accuracy detection of liquid level with unknown noise statistics, we present an extended set-membership-based particle filter (PF). The key points are as follows. We construct a nonlinear state-space model for liquid-level detection system based on the kinematic principle and laser triangulation measurement principle and cast the detection problem of the liquid level into a state estimation problem. Based on this model, we use the extended set-membership estimation theory to generate an ellipsoid set that contains the true value of the liquid-level state. To overcome the difficulty of drawing particles under the case of unknown statistics noise, we draw particles from a Gaussian distribution in the obtained ellipsoidal set. In order to resample particles when the measurement noise statistic is unknown, we introduce a cost function to obtain the weights of the particles, and the ultimate estimation of liquid level is calculated by the weighted particles after the resampling procedure. Comparing with the extended Kalman PF (EPF) and the cost-reference PF (CRPF), the proposed algorithm has higher estimation accuracy. Some simulation and experiment results are presented to illustrate the effectiveness of the proposed method.