Silicon Crystal Growth Research Articles

Relationship between temperature gradient and growth rate during CZ silicon crystal growth

Temperature distribution in the growing crystal is the most important parameter that determines the grown-in-defects, growth rate, etc. There is a discussion either higher growth rate leads to larger thermal gradient or smaller thermal gradient. In this study, in order to make clear the reason of this discrepancy, the effects of growth rate on the shape of melt/crystal interface, and temperature distribution in growing crystal were investigated by numerical modeling. Firstly, as increasing the growth rate, the shape of melt/crystal interface becomes more concave. And temperature gradient along center axis on growing crystal increases as increasing the growth rate. On the other hand, temperature gradient along surface of growing crystal decreases as increasing the growth rate. To obtain higher growth rate, heat transfer should be enhanced. Along the center axis, heat transfer in vertical direction by heat conduction is dominant. Then concave interface shape and larger thermal gradient along center axis were obtained. In the periphery of grown crystal near the triple points, because of concave interface shape, heat transfer in radial direction, and radiative heat transfer from growing crystal become more important than heat transfer in vertical direction. Then smaller thermal gradient along the growing crystal surface was obtained. This surface temperature profile agrees well with Abe’s measurement results. It is cleared that higher growth rate leads to the higher heat transfer, and melt/crystal interface shape, and temperature distribution in growing crystal are determined by the balance of growth rate and heat transfer between heat conduction in vertical direction and heat conduction in radial direction combined with radiation heat transfer from crystal surface.

Optimizing CZ Silicon Crystal Growth: Algorithmic Approach for Defect Minimization

Optimizing CZ Silicon Crystal Growth: Algorithmic Approach for Defect Minimization

THERMAL SIMULATION OF THE CZOCHRALSKI PROCESS FOR SILICON CRYSTAL GROWTH USING FINITE ELEMENT MODELING APPROACH

This study investigates the thermal dynamics of the Czochralski (CZ) process for silicon crystal growth through numerical simulations. The simulation method of this study is based on finite element method (FEM) heat transfer simulation. The FEM simulation was performed using triangular mesh in half cross section of CZ system with real material properties. The analysis of heat transfer mechanisms includes conduction, convection, and radiation which reflect the impact of cooled argon convection on crystal growth. The simulations reveal that convection currents driven by cooled argon has a crucial role to promote uniform cooling which control crystal growth. This leads to enhanced mono-crystalline silicon ingot crystal quality and purity. Ultimately, insights gained from this study can inform optimization efforts in semiconductor manufacturing, facilitating advancements in electronic device fabrication.

Numerical modelling of melting front structures during floating zone silicon crystal growth

We propose a mathematical model of the thin molten silicon film to describe the quasi-steady shape of the inhomogeneous structures on the open melting front of polycrystalline feed rod during the floating zone process for single crystal silicon growth. As a result, precise shapes of the phase boundaries in a three-phase environment on a local scale were determined with the use of moving meshes. The presence of the local structures influences the heat transfer on the open melting front. Consequently, the global phase boundary model can be adjusted, resulting in improved agreement with the experimentally measured interface shape.

Influence of Thermal Conductivity and Emissivity of Heat Shield Surface Material on the Thermal Field of Czochralski Silicon Crystal Growth

Influence of Thermal Conductivity and Emissivity of Heat Shield Surface Material on the Thermal Field of Czochralski Silicon Crystal Growth

Effect of horizontal magnetic field position on oxygen distribution in CZ silicon crystal growth

The horizontal magnetic field-assisted Czochralski(CZ) method is gaining significant popularity in the semiconductor industry for producing 200 mm semiconductor-grade silicon wafers. In this study, the impact of the horizontal magnetic field position on the oxygen content and radial uniformity of semiconductor-grade silicon crystals produced by the CZ method was investigated. Three-dimensional simulations were conducted using finite element software to calculate the melt convection and oxygen content before and after adjustment of the magnetic field position, respectively. The simulations results predicted a decrease in the oxygen content of the crystals following the adjustment of the magnetic field position from 0 to 75 mm below the free surface, and this was experimentally verified. The velocity distribution of the free melt surface exhibits better uniformity when lowering the magnetic field position. The influence of the magnetic field position on the temperature distribution and Marangoni flow in the melt was investigated, and the result of oxygen concentration difference identified the adjustment of the magnetic field position promoted the greater Marangoni flow below the free melt surface, which promoted the volatilization of SiO gas and thus reduced the oxygen concentration in the silicon ingot. Therefore, adjusting the position of the magnetic field is an effective way to increase the Marangoni flow and to obtain semiconductor-grade silicon crystal with lower oxygen content and better oxygen radial homogeneity.

The effects on heat and oxygen transport of different heat shield and sidewall insulation designs during continuous Czochralski silicon crystal growth

Numerical work has been done to optimize the hot zone for the continuous Czochralski growth of 8-inch diameter silicon crystals using a double-crucible system. Thicker insulation layers on a high-heel-shaped heat shield and the sidewall insulation led to a reduction in the heater power of more than 40%, a decrease in the oxygen content, and a significant flattening of the growth interface. This design also allowed a stronger argon gas flow near the outer free melt surface and the quartz crucible wall, which prevented the generation of an argon gas vortex in this area. Stronger flow of argon gas would assist in moving more SiO gas and dust out of the chamber. However, the reduction in the outer melt temperature compared to the original design could slow down the melting of the silicon granules.

Adjustment of oxygen transport phenomena for Czochralski silicon crystal growth

During silicon crystal growth, oxygen, a well-known major impurity, affects the final silicon wafer's mechanical and electrical properties. This study focused on regulation of discharge of different concentrations of oxygen from the quartz crucible into the silicon melt while considering the crucible angular speed and the friction at the melt–crucible interface. The three-dimensional transient governing equations for heat transfer, fluid flow, and impurity transportation in the Czochralski (CZ) puller were solved numerically. The oxygen solvation equation representing the crucible to silicon melt was modified to evaluate the accuracy of oxygen concentration calculations during the CZ process. Experimental measurements using the Fourier-transform infrared (FTIR) technique were used to confirm the simulation results. The results demonstrate that the crucible angular speed affects the oxygen concentration near the crucible wall and therefore in the silicon ingot. The proposed modifications for evaluating oxygen concentration offer a more comprehensive understanding of the oxygen dynamics during the CZ crystal growth.

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.

Multi-label oxide classification in float-zone silicon crystal growth using transfer learning and asymmetric loss

AbstractFloat-Zone (FZ) crystal growth process allows for producing higher purity silicon crystal with much lower concentrations of impurities, in particular low oxygen content. Nevertheless, the FZ process occasionally faces the problem of small contamination from oxidation. This can come in the form of a thin oxide layer that may form on un-melted polysilicon surface. The appearance of the oxide layer indicates degraded machine performance and the need for machine maintenance. Therefore, oxide investigation is important for improving both the FZ process and FZ machines, and the first step is oxide recognition. In this study, we characterized oxide into mainly three varieties, according to their surface texture characteristics, which are: (i) spot (ii) shadow and (iii) ghost curtain. We leveraged FZ images captured from the vision system integrated on the FZ machine to establish an oxide dataset. Targeted for data imbalance problem in our dataset, a method based on transfer learning and asymmetric loss for multi-label oxide classification is presented in this work. The results showed that the pre-trained model and the asymmetric loss used for training outperformed the baseline models and improved the classification performance. Furthermore, this study deeply investigated the effectiveness of the components of asymmetric loss. Finally, Gradient-weighted Class Activation Mapping (Grad-CAM) was employed to explain decision process of the models in order to adopt them in the industry.

Reduction of oxygen concentration in 300 mm diameter n-type Czochralski silicon crystal growth using an optimized heating zone with dual side-heaters

In this study, the modified heating zone structure for 300 mm diameter Cz-Si crystal growth with dual side-heaters has been proposed. Based on it, 300 mm diameter n-type RCz-Si crystals with the oxygen concentration of 9.5–10.5 ppma were obtained.

Study on power consumption and heat transfer paths in Czochralski silicon crystal growth based on global 3D numerical simulation

Power consumption is a significant part of the cost for growing silicon crystal by Czochralski (CZ) method, and reducing power consumption is a key technical concern, especially for photovoltaic industry....

A Critical Review of The Process and Challenges of Silicon Crystal Growth for Photovoltaic Applications

AbstractCrystalline silicon (c‐Si) solar cells have been accepted as the only environmentally and economically acceptable alternative source to fossil fuels. The majority of commercially available solar cells of all Photovoltaic (PV) cells produced worldwide, are made of crystalline silicon. Due to their excellent price/performance ratio and their demonstrated ecological durability, crystalline silicon wafers are by far the most common absorber material used in the production of solar cells and modules today. These wafers are primarily made using either a directional solidification that produces large‐grained multi‐crystalline (mc‐Si) wafers with a greater defect density or a solar‐optimized Czochralski (Cz) growing method that produces crystalline silicon with low defect density (c‐Si). The grown crystalline wafer contains foreign atoms that enhance the wire saw damage, reduce the minority carrier lifetime as a result get the minimum conversion efficiency of the solar cells. The current review illustrates how the elements of the furnace system affect impurity production and distribution of the developed silicon ingot and how the growth process affects the chemical reaction. Additionally, it covers the outcomes of simulations and experiments conducted on the growing process of c‐Si and mc‐Si ingots and recommends the most appropriate processing parameters, geometrical system, and argon gas flow rate.

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.

Twenty years crystal growth of solar silicon: My serendipity journey

The past two decades have been a transformative era for solar silicon crystal growth, especially in the competition between multi-crystalline silicon (Multi-Si) and mono-crystalline silicon (Mono-Si). As a critical sector of the solar photovoltaic (PV) industry, the demand for this crucial material has surged exponentially, expanding over a thousand-fold. This remarkable increase has led to an accumulative deployment of silicon solar panels, which now approach a striking terawatt (TW), capturing over 95 % of the global PV market share. Furthermore, the rapid advancements in crystal growth technology during this period have set an unprecedented historical benchmark. This paper reviewed our early effort in the hot-zone design of Czochralski (CZ) solar silicon and then discussed its recent advancements. In between, the small-grain high-performance multi-crystalline silicon (HPM-Si), which we proposed, and the mono-like silicon (ML-Si) were briefly introduced. Because of the much better ingot quality and growth yield, HPM-Si became the mainstream until 2018. Its market share peaked at more than 70 % in 2017 but slid down quickly and was replaced by CZ silicon due to the emergence of diamond wire sawing (DWS); the CZ silicon was easier to cut, and its kerf loss was much less. Since then, the CZ ingot size has also started to increase quickly. The wafer size increased from 156 mm × 156 mm (M0) to 217 mm × 217 mm (M12+) in a few recent years; the increase in wafer area was almost doubled. Nowadays, the market share of CZ mono-Si is over 80 %.

Effects of different crucible shapes on heat and oxygen transport during continuous Czochralski silicon crystal growth

The effects of different quartz crucible geometries on continuous Czochralski growth of 8-inch silicon crystals in a double-crucible system are investigated. The numerical results show that a design in which the bottom and the side walls of the crucible are flat lowers the oxygen content, saves energy, and weakens the melt flow turbulence. Moreover, the lowest von Mises thermal stress in the crucible system was obtained with this crucible design. The flat crucible side wall reduces heat loss from the outer melt surface, facilitating heat transfer from the side heater into the melt. The differences in crucible geometry change the temperature distribution and flow pattern in the outer melt but have an insignificant effect on the deflection of the crystal-melt interface.

Control of the Thermal Field of S/L Interface Front and Crystal Growth of Mono-Like Crystalline Silicon Assisted by Direct Current

Control of the Thermal Field of S/L Interface Front and Crystal Growth of Mono-Like Crystalline Silicon Assisted by Direct Current

Fast Prediction of Transport Structures in the Melt by Physics Informed Neural Networks during ‘VMCz’ Crystal Growth of Silicon

Fast Prediction of Transport Structures in the Melt by Physics Informed Neural Networks during ‘VMCz’ Crystal Growth of Silicon

Evaluation of numerical simulation of constitutional supercooling during heavily Boron-Doped silicon crystal growth using Cz method

Using the Czochralski (Cz) method, it has been established that heavily doped silicon (Si) single crystals with impurities such as boron (B) can negatively impact the quality of grown crystals due to morphological instabilities such as cellular growth caused by constitutional supercooling for doping higher than 1 × 1019 cm−3. To produce high-quality heavily doped Si single crystals, constitutional supercooling must be prevented during growth. In this study, we used a three-dimensional numerical simulation to predict constitutional supercooling during the growth of heavily B-doped Cz-Si single crystals, considering the transport of B in the melt and the segregation effect. We compared the numerically predicted constitutional supercooling region with experimental data to assess its accuracy and found that the cellular growth region observed in the experiment was in good agreement with the region of constitutional supercooling predicted by the simulation. Moreover, we considered the effects of different pulling rates and crystal lengths during the growth process on constitutional supercooling, and the limitations of numerical modelling.

Effects of Induced Current in Crystals on the Melt Flow and the Melt–Crystal Interface during Industrial 300 mm Czochralski Silicon Crystal Growth under a Transverse Magnetic Field

Due to the high magnetic field intensity during industrial 300 mm silicon crystal growth, typically up to 0.3 T, the crystal’s rotation under this transverse magnetic field (TMF) induces a current that is strong enough to impact both the melt flow and the melt/crystal interface (m/c interface) shape. This paper investigates the influence of TMF-induced current in crystals on the melt flow, temperature distribution, and interface shape through the conduction of three sets of 3D simulations that vary in the electrical conductivity of crystals, TMF intensities, and crystal rotation rates. Combined with experiments, the accuracy of the model has been validated, and a reasonable electrical conductivity of the crystal has been predicted. The study findings reveal a shift in the driving force of forced convection from centrifugal to Lorentz force when the induced current in crystal is augmented. This alteration affects the melt flow and the m/c interface shape. Notably, this study serves as a significant complement to the conventional model, which overlooks the induced current in crystals, enhancing the accuracy and comprehensiveness of the simulation outcomes to provide a robust theoretical underpinning for industrial production.