Czochralski Silicon Growth Research Articles

Analyzing structure loss in Czochralski silicon growth: Root causes investigation through surface examination

A considerable proportion of the grown Czochralski Si ingots are remelted due to the generation of dislocations or the so-called structure loss. The assessment of the failed ingots is a crucial step toward achieving higher yield. Nonetheless, characterizing Si ingots poses a challenge attributed to their inherent high brittleness and the elevated concentration of dislocations, further complicating the cutting process. In this work, we utilize a non-destructive method to categorize the failed ingots and reveal the root causes of this failure. This study is performed on roughly 80 industrial monocrystalline silicon ingots that are grown for solar cell applications. Most of these ingots have experienced structure loss during the body growth. Analyzing the surface features reveals major categories of the structure loss ingots. Approximately, 66% of the examined ingots seem to be linked with temperature fluctuations, specifically a sudden drop in the melt temperature, and contamination by foreign particles. It is found that the primary causes can be categorized into four major groups: melt contamination, thermal fluctuations, melt vibration, and variations in growth rate. The primary root causes are identified within a fishbone diagram.

Extended investigation of an abrupt crystal diameter change during Czochralski silicon growth with transverse magnetic field

An investigation about the phenomenon of an abrupt diameter deviation during Czochralski crystal growth, a characteristic when using a transverse magnet, has been carried out both experimentally and computationally. 300-mm silicon crystals have been pulled under certain conditions and the diameter deviations have been recorded in these processes. Three-dimensional calculations of the melt flow have been performed using CGSim Flow Module 3D, accounting for distribution of the actual non-uniform magnetic field, to accurately simulate the heat transfer and melt flow for selected growth stages along the entire process. The sudden change of melt temperature near the triple point that leads to the diameter deviation, is attributed to the evolution of melt flow pattern, which can be altered by positioning the magnet at a different height. The discovery of such melt flow behavior proposes an effective solution to eventually eliminate the abrupt diameter deviation during body growth. The visualization of the melt flow transformation by 3-D simulation offers another adjustability to the process of modern industrial crystal growth with transverse magnet. The mechanism of how the magnet position impacts the melt flow is also discussed.

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.

Model experiments for melt flow in Czochralski growth of silicon

The melt flow plays a key role in the Czochralski (Cz) growth of silicon crystals, and in-situ measurement data are crucial for efficient process development. We present new low-temperature model experiments and numerical simulations for Cz type melt flow studies. A novel cylindrical setup is equipped with a traveling magnetic field (TMF), and with an advanced ultrasound (US) based measurement technique for 2D flow imaging. The setup has been designed for comprehensive flow measurements in a GaInSn melt under well-defined thermal and TMF forcing conditions to generate as exact as possible experimental data to validate flow simulations. The applied numerical models combine time-dependent 3D flow calculations under adjusted heat flux boundary conditions with a 2D treatment of the Lorentz force. The dependence of the buoyant flow on the boundary conditions as well as the interaction between the buoyant flow and a symmetric TMF-forced flow are studied in detail. Special attention is paid to the investigation of flow transitions between symmetric toroidal and non-symmetric roll-like structures. In terms of the dimensionless Grashof (Gr) and magnetic forcing (F) numbers, such transitions are found to occur at around Gr = 3 × 107 and for F < Gr. The results are compared with recent studies in the literature, and a concept to transfer experimental and numerical flow modeling to real Cz growth of silicon is briefly outlined. The observed flow structures may significantly influence the convective heat and mass transport in Cz growth.

Physically-based, lumped-parameter models for the prediction of oxygen concentration during Czochralski growth of silicon crystals

Lumped-parameter models are derived from boundary layer and other physical arguments to describe oxygen concentration levels during the Czochralski (CZ) growth of silicon. These models are assessed against predictions from a detailed, high-fidelity 2D-3D numerical simulation of the entire CZ puller, whose solutions are realistic but require intense computational effort. Comparisons of predictions show that the lumped-parameter model captures the correct trends of melt oxygen levels influenced by melt height, crucible rotation, and crystal rotation. A simple fitting of coefficients provides reasonably good quantitative predictions by the lumped-parameter model, and its near-instantaneous computations make it an interesting candidate for real-time growth optimization and control. Possible model improvements and extensions are discussed.

Measuring the end-face of silicon boules using mid-infrared laser scanning

Laser scanning is investigated to measure the deflection of the crystal–melt interface during Czochralski-growth of silicon.

Advanced Ellipse Fitting Algorithm Based on ADMM and Hybrid BFGS Method

Quick and accurate ellipse detection is essential for computer vision, automatic manufacturing, and other fields. In order to obtain more accurate ellipse parameters, the least-squares support vector regression is employed to establish the objective function and further convert the ellipse fitting problem into an optimization problem. This article proposes a hybrid BFGS algorithm integrated with an alternating direction method of multipliers (ADMM) to reduce the number of iterations and improve the algorithm convergence speed. The effectiveness and accuracy of the proposed algorithm are then verified in a series of numerical simulations by using the actual data of crystal images taken by charge-coupled device (CCD) cameras within the Czochralski silicon growth. Finally, the effectiveness is verified by comparing Hough transform (HT), maximum correntropy criterion (MCC), sparsity-based method (SBM), and other methods.

Numerical method for thermal donors formation simulation during silicon Czochralski growth

Various upgrades of the Czochralski (Cz) growth process are currently being investigated in order to increase throughput and reduce production cost of high efficiency silicon-based solar cells. However, as-grown thermal donors (TD) in Cz silicon can significantly reduce the conversion efficiency of such solar cells. An accurate simulation tool is therefore required to investigate and optimize TD formation during crystal growth. A numerical method combining thermo-hydraulic simulations and a kinetic TD formation model was improved by the implementation of a more appropriate TD formation model, identified through a benchmark of the different models available in the literature. Three different Cz growth processes were investigated both numerically and experimentally. Numerical results are in remarkable agreement with TD concentrations measured along the three ingots by the OxyMap technique developed at CEA. The simulations were then used to detect when TD were formed during Cz processes. The reliability of the method was also assessed through sensitivity analyses, highlighting the critical importance of the input interstitial oxygen concentration. These results show that accurate estimates of axial TD concentration profiles can be obtained and so for very different Cz processes, supporting the robustness of the developed method and its relevance to process optimization and furnace design to reduce TD concentrations.

Investigation of gas bubble growth in fused silica crucibles for silicon Czochralski crystal growth

Abstract Gas bubbles in crucibles for Czochralski (Cz) silicon growth are both necessary and detrimental: In the outer, bubble-containing (BC) layer of the crucible, they are required for mechanical stability, while in the inner, bubble-free (BF) layer, bubbles can cause the release of particles from the crucible into the melt which may disrupt the single-crystalline growth. In this work, a vacuum bake-out test (VBT) procedure was set up for unused crucible parts and a microscopic characterization routine was developed to systematically investigate bubble formation and growth. Longer process time, higher temperature, and lower atmospheric pressure lead to an increased bubble growth in both, the BC and BF layer. During the VBT, no new bubbles form in the BF layer, while existing bubbles grow. The comparison to experimental data from crucibles used in an industrial Cz process indicates that VBTs can simulate this process. This allows the prediction of the gas-bubble formation in Cz crucibles using a cost-effective and less time-consuming analyzation method.

Transient global modeling for the pulling process of Czochralski silicon crystal growth. II. Investigation on segregation of oxygen and carbon

Abstract We conducted the transient global simulations for the crystal pulling process of Czochralski silicon (CZ-Si) growth with the cusp-shaped magnetic field (CMF). The generation, transport, and segregation of oxygen (O) were considered for the crystal growing process. Further, the incorporation, accumulation, and segregation of carbon (C) were also predicted based on our previous studies on CZ-Si growth. The distributions of O and C at the growth interface were dynamically predicted for the diameter pulling stages, and their segregations were plotted as a function of solidified fraction and crystal length. The O level and uniformities at the growth interface exhibit a strong correlation with the depth of melt in the crucible and the flow structures inside the melt. The comparisons of different CMFs indicated that adjustments of the zero-Gauss plane (ZGP) have the potential to optimize the O segregation into the pulling crystal from the level, axial, and radial uniformities. Further, the C concentration increased with the increase in the crystal length because of the continuous contamination and the lower segregation coefficient. Hence, the developed dynamic global model also has applications in the segregation prediction of other dopants and impurities in the CZ-Si growing process.

Transient global modeling for the pulling process of Czochralski silicon crystal growth. I. Principles, formulation, and implementation of the model

Abstract A transient global model for the crystal pulling process was developed for magnetic-field-applied Czochralski silicon (CZ-Si) growth. Heat transfer by solid conduction, melt convection, and diffuse gray radiation is taken into account for the crystal, melt, and other components in the furnace. The mesh adaption and view factor updating for the dynamic pulling process were realized by the structured grid deformations for different domains. By imposing the thermal boundary conditions in the vicinity of the triple point, the inverse control by the virtual proportional integral derivative controller and heat flux is acceptable for the transient global simulation of the pulling process in CZ-Si crystal growth. The applied cusp-shaped magnetic field (CMF) suppressed the turbulent melt flow and stabilized the heat and mass transport. CMF with different zero-Gauss-plane locations resulted in different flow patterns, which could affect the impurity transport during the pulling process. This developed transient global model can be applied for the segregation predictions of impurities (oxygen and carbon) and dopants in the CZ-Si growing process.

Model Experiments for Flow Phenomena in Crystal Growth

AbstractThe concept of a physical model experiment is introduced and discussed in the context of melt and gas flows in bulk crystal growth processes. Such experiments allow one to "extract" selected physical phenomena from the full complexity of a real crystal growth process and “transfer” them to material systems with an easier access for experimental measurements. Model experiments for the main techniques of melt growth are summarized in a literature review, and the applicability of the results to real crystal growth systems is analyzed. Recent examples of model experiments for melt and gas flows in Czochralski growth of silicon are used to demonstrate the state of the art and show the potential of such experiments to improve the understanding of complex multi‐physical multi‐scale phenomena occurring in every crystal growth process.

Time-dependent behavior of melt flow in the industrial scale silicon Czochralski growth with a transverse magnetic field

The time-dependent behavior of the silicon melt flow in the industrial scaled 300-mm diameter silicon Czochralski growth with a transverse magnetic field was investigated by both the experiment and numerical simulation. The measured temperatures at multiple positions in the melt showed oscillation with the same period but different amplitudes. The calculated results by the fully three-dimensional numerical simulation represented the measurement results and provided a qualitative explanation to this phenomenon. The periodic change of melt flow pattern occurred via the generating, descending, and vanishing of the cold plume. This behavior was driven by the buoyancy, which was similar to the flow under the non-magnetic field reported by Ozoe and Sung.

Qualitative Characterization of Solute Boundary Layer in Industrial Czochralski Growth of Silicon

The effective viscosity (μeff) has a crucial turbulent effect in the fluid flow. In this work, μeff is proposed and applied to the Burton, Prim, and Slichter (BPS) and Ostrogorsky-Muller (OM) analytical models to estimate the solute boundary layer in Czochralski (CZ) growth of silicon. A series of numerical simulations for CZ silicon growth are performed, with different crystal rotation rates (ranging from 1 to 50 rpm), in order to obtain different convective flow regimes. The results revealed 3.6% as the average predicted error (where, μeff was employed as an input) for the boundary layer thickness between the modified models. Furthermore, the modified OM model was also verified to describe the radial distribution of solute boundary layer, and to demonstrate the capturing efficiency of the characteristic points at melt/crystal interface. Aiming at practical purposes, Gr/Re2 was proposed as a criterion to obtain the weak lateral segregation of impurities in the crystal growth process.

Fully three dimensional numerical analysis of industrial scale silicon Czochralski growth with a transverse magnetic field

Fully three dimensional (3D) numerical simulation model of the heat and mass transfer in the silicon (Si) Czochralski growth with a transverse magnetic field (MCZ) was developed. Time transient calculation of heat and mass transfer in the industrial scale crystal growth of 300mm diameter was performed under the quasi steady state assumption. The model predicts the completely asymmetrically 3D melt flow and off-centered temperature distributions, different from the previous works. The temperature distribution measured experimentally by thermocouples, beneath the melt surface along the azimuthal direction, was almost the same as the model prediction, providing a strong support for the 3D simulation model.

Scale up aspects of directional solidification and Czochralski silicon growth processes in traveling magnetic fields

We performed 3D simulations of directional solidification (DS) and Czochralski (Cz) silicon growth processes in traveling magnetic fields (TMFs) and verified them with the experimental data that were available. Particularly, we studied silicon DS growth in real G1, G2 and G5 size setups and Cz growth in 6″ and 24″ crucibles in furnaces provided with KRISTMAG® heater magnet modules (HMMs). TMFs were used for a solid/liquid interface shaping and for a melt stirring. Based on our simulation findings, we discussed scale up challenges and proposed a method for safe upscaling. The method related all present driving forces using dimensionless numbers: Grashof (Gr), Stephan (Ste), Reynolds (Re), Shielding (S) and magnetic forcing number (F).

Analysis of the effect of symmetric/asymmetric CUSP magnetic fields on melt/crystal interface during Czochralski silicon growth

With the use of 300mm silicon wafers for industrial semiconductor device manufacturing, the Czochralski (Cz) crystal growth process has to be optimized to achieve higher quality and productivity. Numerical studies based on 2D global thermal models combined with 3D simulation of melt convection are widely used today to save time and money in the process development. Melt convection in large scale Cz Si growth is controlled by a CUSP or transversal magnetic field (MF) to suppress the melt turbulence. MF can be optimized to meet necessary characteristics of the growing crystal, in terms of point defects, as MF affects the melt/crystal interface geometry and allows adjustment of the pulling rate.Among the different knobs associated with the CUSP magnetic field, the nature of its configuration, going from symmetric to asymmetric, is also reported to be an important tool for the control of crystallization front. Using a 3D unsteady model of the CGSim software, we have studied these effects and compared with several experimental results. In addition, physical mechanisms behind these observations are explored through a detailed modeling analysis of the effect of an asymmetric CUSP MF on convection features governing the heat transport in the silicon melt.

(Invited) Growth of Czochralski Silicon Crystals with Ultralow Carbon Concentrations for High-Power Insulated-Gate Bipolar Transistor Devices

The effects of the argon gas flow in a Czochralski (CZ) silicon growth furnace and the evaporation of carbon monoxide (CO) from the silicon melt on the carbon concentration in 8-inch CZ silicon crystals were studied by evaluating the carbon concentrations in the crystals using photoluminescence spectroscopy. Preventing silicon monoxide from flowing through the side of the heater and the graphite susceptor and preventing back-diffusion of CO from the top of the graphite susceptor effectively reduced carbon contamination during CZ silicon growth. In addition, CO was evaporated from the melt by increasing the gas flow rate above the melt surface. Owing to the effects of CO evaporation from the melt, 8-inch CZ silicon crystals were grown with a carbon concentration considerably lower than that in floating-zone silicon.

Growth Dynamics of Single Void during Czochralski Silicon Crystal Growth Using Phase-Field Modeling

To investigate the growth dynamics of the single void during Czochralski silicon growth as well as capture the basic features of the diffusion-controlled dynamic mechanisms, a phase field method has been developed. The free energy of the system involving the chemical free energy and the gradient energy is presented. Numerical tests were performed to examine the capability of this model, and the results show that: the void grows due to the absorption of vacancies in the matrix, which essentially reduces the free energy of the system; with the growth of the void, there forms vacancy concentration gradient towards the void in the matrix; the increase of initial vacancy concentration contributes to a larger void size and growth rate.

Three-dimensional numerical simulation of flow, thermal and oxygen distributions for a Czochralski silicon growth with in a transverse magnetic field

A three-dimensional numerical simulation has been performed to understand the motion of the melt flow and thermal field during the Czochralski silicon single crystal growth process under the influence of a transverse magnetic field. With the application of a transverse magnetic field, the velocity, temperature and oxygen concentration fields in the melt become three-dimensional and asymmetric. Stronger downward flow motion is formed under the melt-crystal interface which can prevent the movement of oxygen impurities towards the melt-crystal interface. This may explain why the presence of a transverse magnetic field decreases the oxygen concentration level along the melt–crystal interface. The uniformity of the oxygen concentration at the melt–crystal interface is also improved when the magnetic field is applied. There is an increase in either the crystal diameter or the crucible rotation rate, and the oxygen concentration level becomes greater. The uniformity of oxygen concentration is better for higher crystal diameters.