Czochralski Research Articles

Multi-Task Learning With Latent Variation Decomposition for Multivariate Responses in a Manufacturing Network

Modeling the relationships between the quality response variables and process settings or in situ sensing variables is a fundamental problem in quality engineering. Such relationships are important for product quality prediction, process monitoring, and optimization. Data collected from a single system often only carry limited information, making modeling one system at a time challenging. Multi-task learning (MTL) jointly models similar-but-non-identical systems and utilizes the similarities among systems for better performance. However, existing MTL becomes much less effective if important variables are missing or unmeasurable in the underlying process (latent variables). More importantly, commonly shared latent variables across systems often reflect important process patterns/behaviors, deserving more investigations. We proposed an MTL framework for multivariate or profile responses by explicitly decomposing the variation among systems into explainable variation and latent variation. Specifically, the explainable variation is from variables observed in data, while the latent variation is from the latent basis functions automatically generated from model residuals. The proposed method improves the prediction accuracy and interpretability of modeling. The simulation and a case study in a silicon ingot manufacturing network demonstrate that the proposed method can improve the quality modeling performance and recover critical process knowledge for silicon ingot manufacturing based on Czochralski (CZ) process. Note to Practitioners—This research is motivated by quality modeling of a semiconductor manufacturing network consisting of multiple furnaces (systems) producing silicon ingots. An accurate quality model in manufacturing is essential for downstream tasks such as process monitoring and optimization. As data collected from a single system often only carry limited information, aggregating data from multiple systems in quality modeling can significantly improve the performance. However, different systems in a network are often similar-but-non-identical to each other due to different degradation statuses, usage history, product receipts. As a result, data from different systems are heterogeneous, making combining all data for modeling inappropriate. Multi-task learning (MTL) solves this problem and recovers the similar-but-non-identical nature of systems. However, existing MTL is much less effective if important latent factors/variables are missing or unmeasurable in the underlying process. More importantly, such latent factors can reflect important process patterns/behaviors. This work improves the MTL framework by explicitly explaining the unexplained variations using the latent factors automatically generated from model residuals. The simulation and the case study in a silicon ingot manufacturing network demonstrate that the proposed method improves the quality modeling performance and recovers critical process knowledge for silicon ingot manufacturing based on Czochralski (CZ) process.

Novel laser crystal Nd3+: Ca(Y, Gd)AlO4: A promising candidate for laser operation beyond 1.37 µm

A novel laser crystal Nd: CaGd0.1Y0.9AlO4 (Nd3+: Ca(Y, Gd)AlO4) crystal has been successfully grown by Czochralski (CZ) method. With the introduction of Gd3+ ions, this crystal has a more disorder structure than that of the Nd: CaYAlO4 (Nd: CYA). The full width at half-maximum (FWHM) of the π polarization emission spectra at around 1365 nm for the Nd3+: Ca(Y, Gd)AlO4 crystal was 53 nm, which is larger than that of Nd: CYA (35 nm) crystals, provided clear evidence for the more disorder structure. Moreover, its wide absorption spectral was maintained compared to the Nd: CYA crystal. At the same time, the effective dual-wavelength continuous-wave laser operation at 1358.4 nm and 1374 nm was realized of the as-grown crystal for the first time. These results suggest that the Nd3+: Ca(Y, Gd)AlO4 crystal is a promising disordered laser host for solid laser operation at the wavelength longer than 1370 nm in the range of 1.3–1.4 µm.

Effect of seed orientations on crystallographic texture control in faceted Al2O3/YAG eutectic ceramic during directional solidification

Crystallographic texture control is a major challenge in directionally solidified multiphase eutectic ceramics with complex faceted growth characteristics. In this study, the Czochralski (CZ) technique is proposed to prepare eutectic single crystal ceramic with large size (Φ 30 mm × 125 mm). A highly oriented and unique texture of Al2O3/Y3Al5O12 (YAG) eutectic ceramic is formed via the 〈112¯0〉 Al2O3 single crystal seed induction based on crystallographic orientation tailoring. The orientations of Al2O3/YAG eutectic are more strictly constrained by single crystal seed induction on the basis of the minimum interface energy principle, resulting in a defined single orientation relationship along the solidification direction. In particular, the single crystallographic orientation can be obtained in a short competitive solidification distance under the influence of epitaxial solidification from single crystal seed. Therefore, it has been confirmed that the orientations of 〈112¯0〉Al2O3 and 〈111〉 YAG are preferentially stabilized with the minimum under-cooling during directional solidification. Crystallographic orientation disturbances and instabilities due to polycrystalline crystal seed are avoided. Finally, the successful texture control inducted by 〈112¯0〉 Al2O3 single crystal seed can provide a promising orientation design pathway for faced oxide eutectic solidification.

Anisotropic alumina ceramics with isotropic optical properties

Excellent mechanical and isotropic optical properties are achieved simultaneously from fully dense polycrystalline advanced alumina ceramics with a hexagonal crystal structure, which are optically anisotropic. A small amount (240 ppm) of ZrO₂ additive is used to synthesize the transparent alumina ceramics with an average grain size of 0.7 µm, and locally detected optical distortion (birefringence) is extremely minimized, less than 20 nm/pass. Total transmittance (86%) of the alumina ceramics (thickness = 0.3 mm) in ultraviolet (UV) to infrared (IR) regions is similar to that of commercial <i>c</i>-axis sapphire single crystals produced by Czochralski (CZ) method, while the extinction ratio in the visible wavelength area is over 25 dB. Like glass and the <i>c</i>-axis sapphire single crystals, the alumina ceramics can clearly display texts and images on liquid crystal display (LCD) screens. A grain boundary phase of nano-sized Al₂O₃–ZrO₂ composition (amorphous) is formed at the grain boundary of the advanced alumina ceramics, which enhances four-point bending strength and fracture toughness (<i>K</i>_IC) simultaneously to 921 MPa and 6.8 MPa·m^0.5, respectively, and hence the mechanical properties are superior to those of the sapphire single crystals.

Defect generation behavior in Czochralski-grown ScAlMgO4 crystal using synchrotron X-ray topography

Synchrotron X-ray topography was employed to characterize the defect structure and investigate the defect generation process in Czochralski (CZ)-grown ScAlMgO4 (SAM) crystals. In the X-ray topographs of the <2¯ 0 2 0>, <2¯ 0 2 22>, and 0 0 0 24 diffractions of a SAM(0 0 0 1) in-plane wafer, straight- and stream-type dislocations were analyzed using the extinction rule. These dislocations were ascertained to have both <1¯1¯ 2 0> and <0 0 0 1> components of the Burgers vector. A SAM(0 1¯ 1 0) cross-section wafer was then observed by X-ray topography to investigate the generation process of the defect structure. Straight-type dislocations along [1¯ 0 1 0], [0 1 1¯ 0], and [1 1¯ 0 0] were generated at the early-growth stage, to release accumulated large thermal strain derived from the solid–liquid phase change. Dislocation-free regions and low-dislocation density regions, including stream- and edge-type dislocations, appeared in the late-growth stage. The weak contrast of the growth-striation in the late-growth stage indicates the reduction in strain. The reduced strain is considered to have generated dislocation-free and low-dislocation density regions. The dislocation structure in SAM reflected the behavior of the thermal strain during the CZ-growth.

Data-Driven and Mechanism-Based Hybrid Model for Semiconductor Silicon Monocrystalline Quality Prediction in the Czochralski Process

The Czochralski (CZ) process is the core technology for producing semiconductor silicon monocrystalline (SMC), and it is a complex batch process. However, the crystal growth rate and crystal diameter, which are key quality indicators, are difficult to detect directly online, and the offline calculation process lags seriously, which easily causes blind crystal quality control. Therefore, this paper proposes a data-driven and mechanism-based hybrid model for semiconductor SMC quality variables prediction in the CZ process. Firstly, a data-driven model JITL-SAE-ELM based on just-in-time learning (JITL) fine-tuning strategy is proposed. This model is used to solve the nonlinear and time-varying relationship of the energy transfer process in the CZ process that cannot be accurately described by traditional mechanism models. Here, the SAE-ELM model integrates a stacked autoencoder (SAE) and an extreme learning machine (ELM), which are used to deeply capture the nonlinear and time-varying features of process data. Secondly, according to the hydrodynamics and geometric behavior, a crystal pulling dynamic mechanism model based on the crystal growth mechanism is constructed, which avoids the complicated heat transfer link. Further, considering the unmodeled dynamics caused by model parameter uncertainty during the combination of the energy transfer model and crystal pulling dynamic mechanism model, a crystal diameter compensation model SAE-ELM was developed to improve the prediction accuracy of the CZ process hybrid model. Finally, an industrial data experiment based on a CZ monocrystal furnace illustrates the proposed method.

Preparation of large Cu3Sn single crystal by Czochralski method

Cu3Sn was recently predicted to host topological Dirac fermions, but related research is still in its infancy. The growth of large and high-quality Cu3Sn single crystals is, therefore, highly desired to investigate the possible topological properties. In this work, we report the single crystal growth of Cu3Sn by Czochralski (CZ) method. Crystal structure, chemical composition, and transport properties of Cu3Sn single crystals were analyzed to verify the crystal quality. Notably, compared to the mm-sized crystals from a molten Sn flux, the cm-sized crystals obtained by the CZ method are free from contamination from flux materials, paving the way for the follow-up works.

Floating Particles in the Melt during the Growth of β-Ga2O3 Single Crystals Using the Czochralski Method

Floating particles often appear during the Czochralski (CZ) growth of β-Ga2O3 in the Ir crucible, thereby impeding the seeding process. Identifying the floating nanoparticles and then inhibiting or removing them is critical for growing high-quality β-Ga2O3 single crystals. We grew β-Ga2O3 crystals containing floating particles using the CZ method. It is indicated that the floating particles were composed of Ir with a face-centered cubic (fcc) structure. In addition, the β-Ga2O3/Ir interface was comprehensively characterized, showing sharp and straight configuration on the whole with small fluctuations at the nanoscale. Combined with density functional theory (DFT) calculation, we found that Ir-O bonding was responsible for stabilizing the interface. Accordingly, the atomic configuration of the interface with the stablest structure, including the relaxed one, was determined. Based on the formation mechanism of the floating particles, we propose three effective strategies, including blowing sufficient oxygen into the bottom of the Ir crucible, coating a protective layer on its inwall and equipping a mechanical arm for inhibiting or removing them.

Projected Cost of Gallium Oxide Wafers from Edge-Defined Film-Fed Crystal Growth

Gallium oxide (Ga2O3) is an emerging ultra-wide bandgap semiconductor that has unique properties ideal for high-power, high-temperature, optoelectronic, and sensing applications and has piqued interest over the last decade. It has the potential to be technologically and economically superior to commercially available wide bandgap semiconductor materials, such as silicon carbide and gallium nitride, because its wider bandgap enables increased breakdown voltages and lower on-state resistances, and its ability to be grown from melt enable cost-competitive economics. In this study, we present a techno-economic analysis that projects the cost of 6″ β-Ga2O3 wafers fabricated from crystals grown via edge-defined film-fed growth (EFG). At a manufacturing volume of 5000 wafers per month, we predict a unit cost of $320 for a 6″ EFG grown β-Ga2O3 epi-wafer. We determine that, when calculated using 2021 iridium crucible costs, EFG has a 2× cost advantage compared to previously reported epi-wafers grown via the Czochralski (CZ) method. We further identify key cost parameters for 6″ β-Ga2O3 epi-wafers and present cost-sensitivity analysis of their impact on the final cost.

Electrical, optical, and mechanical properties of modified Czochralski grown organic 4-nitrobenzaldehyde single crystal

Growing large crystals of organic compounds with low melting points is a challenge but it was resolved by suitable modifications of the Czochralski (CZ) technique in the present study. A nonlinear optical single crystal of 4-nitrobenzaldehyde (4-NB) with a cylindrical shape, length of 2.5 cm, and diameter of 3 mm was successfully grown using an inexpensive modified CZ crystal growth technique at a temperature of 106 °C. The crystal structure and lattice parameters of the as-grown crystal were determined by single crystal and powder X-ray diffraction analyses. Intermolecular interactions were studied in the 4-NB crystal based on the Hirshfeld surface and two-dimensional fingerprint plot. The presence of various functional groups in the as-grown crystal was confirmed by Fourier transform infrared spectroscopy and nuclear magnetic resonance (1H and 13C) spectroscopy. The thermal behavior of the 4-NB crystal was analyzed by thermogravimetric analysis and differential thermal analysis. High transparency (75%) with an optical band gap of 3.34 eV and lower cut-off of 370 nm were confirmed by ultraviolet–visible–near infrared spectroscopy. The temperature-dependent dielectric behavior was determined for the 4-NB crystal at a constant frequency of 5 kHz. The mechanical properties of the 4-NB single crystal were analyzed based on the Vickers microhardness and void analysis, which confirmed the soft nature of the crystal. The modified CZ technique allowed us to obtain disk-shaped organic 4-NB crystals for use in optical applications.

Development and validation of a thermal simulation for the Czochralski crystal growth process using model experiments

The Czochralski (CZ) process is one of the most important techniques for the production of bulk single crystals. Various numerical models for CZ growth furnaces exist, however, a review of the recent literature demonstrates that their validation is often questionable due to missing in-situ measurement data. In this work, a new 2D open-source thermal CZ growth model is introduced, verified with analytical solutions, and validated using dedicated model experiments with tin and hence easy access for the required measurements. A three-step procedure is applied to identify critical modeling parameters, make adjustments of these parameters, and evaluate the resulting modeling accuracy. Gas and melt convection, modeled with heat transfer coefficients and an effective heat conductivity, are found to be crucial and are adjusted using experimental data. Comparison of measured temperatures in the crucible shows good agreement, with deviations of max. 0.3 / 1.3 K under natural / forced convection. The model is able to predict the influence of crystal pull velocity and melt temperature on crystal diameter qualitatively.

The CNN Deep Learning-Based Melting Process Prediction of Czochralski Monocrystalline Silicon

To solve seeding failures due to the misjudgment caused by manual observation in the traditional melting process of Czochralski (CZ) monocrystalline silicon, a method for predicting the melting progress of CZ monocrystalline silicon based on Convolutional Neural Network (CNN) deep learning was proposed. The deep learning method and image classification of the melting process were combined. By taking CNN as the research object, the AlexNet network-based melting classification model was constructed. Meanwhile, the comparative analysis was performed by adjusting the number of AlexNet network convolution layers and the size of the convolution kernel. After several experiments, a CNN-based melting stage classification model was finally determined. Simulation results showed that the model could achieve higher accuracy when predicting the melting process. This paper focuses on the key technical issues such as polycrystalline silicon melting and temperature predication in the growth process of the monocrystalline silicon, and predicts the melting process of silicon materials, which lays the foundation for the quality improvement of monocrystalline silicon growth process in the semiconductor field.

Effects of High-Pressure Hydrogen Gas Exposure on the Residual Stress Fields and Cracks around Vickers Indentations

Effects of high-pressure hydrogen gas exposure on the residual stress fields and cracks around the Vickers indentations introduced into {100} silicon wafers were investigated. Square chip test pieces (10 × 10 × 0.6 mm3) were cut out from a mirror-finished (001) silicon wafer that was sliced from a large crystal (diameter 300 mm, resistivity 15 Ωcm) grown using the Czochralski (CZ) method. Vickers indentations were introduced on the (001) Si wafer surface. Loads of indentations were 0.98 N and 1.96 N, and the holding time was 30 s. Upon indentation, not only was a large internal stress field formed around the indent, but small cracks were also initiated along the {110} planes from the four corners of the indent. A laser Raman microscope was used to measure the residual stress distribution before and after the hydrogen gas exposure, with four hydrogen gas pressures (from 10 to 100 MPa) applied at 270 °C for 24 h. Crack growth occurred after the hydrogen gas exposure. The crack growth ratio increased up to a hydrogen gas pressure of 35 MPa, with increasing gas pressure. However, for the hydrogen pressures above 35 MPa, the crack growth ratio was saturated, and the upper limit of the crack growth ratio was approximately 9%. Furthermore, it was found that the hydrogen gas exposure caused the compressive residual stress around the indentation to decrease. The results suggest that hydrogen may reduce the residual stress field around the crack, which is related to one of the causes of hydrogen embrittlement.

Model experiments for Czochralski crystal growth processes using inductive and resistive heating

The Czochralski (CZ) growth technique is widely applied in crystal growth, using both induction and resistance heaters. In this work, a novel model experiment platform with comprehensive in-situ measurement capability is introduced. Growth experiments with the model material tin applying both heating concepts are performed and analyzed, e.g., in terms of the maximum achievable crystal diameter. Strong asymmetries in the magnetic field of the induction heater are measured and temperature distribution on the resistance heater is found to be non-uniform. Furthermore, significant losses are observed in the power supplies of the resistance heater. The heating efficiency of both concepts is compared considering different insulation geometries. The obtained results show the capability of model experiments for design optimization and will provide valuable input for further validation of numerical simulations.

Growth, spectral properties, and laser demonstration of Yb3+ doped K5Bi(WO4)0.22(MoO4)3.78 crystal

A novel 15at. % Yb3+ ion doped K5Bi(WO4)0.22(MoO4)3.78(Yb: KBWM) crystal with a disordered structure is successfully grown by Czochralski (CZ) method. The crystal growth, structure, optical properties, and laser performance were investigated. With the introduction of the (WO4)2- anionic group, not only maintains the crystal structure of K5Bi(MoO4)4, but also results in a non-uniform broadening of the spectra. The absorption cross-section is 2.5 × 10−20 cm2 at 975 nm. The stimulated emission cross-section is 1.2 × 10−20 cm2 at 1014 nm, with a full width at half maximum (FWHM) of 47.2 nm. The fluorescence lifetime is 730.6 μs. Furthermore, continuous wave laser operations are achieved in Yb: KBWM crystal with different output coupler transmissions. Slope efficiency as high as 11.8% with respect to the pump power and an output power of 59.6 mW were achieved with a laser diode-pumped Yb: KBWM laser. The results show that the anion group modified crystal Yb: KBWM may be used in solid-state tunable and ultra-fast lasers.

Photodarkening and dopant segregation in Cu-doped β-Ga2O3 Czochralski single crystals

β-Ga2O3 has demonstrated insulating properties with Mg, Fe, and Zn acceptor doping. Here we investigate Cu doping (0.25 at.%) in bulk Czochralski (CZ) and vertical gradient freeze (VGF) β-Ga2O3, with significant Cu incorporation, even with the expected Cu evaporation. Representative crystals were assessed for orientation, purity, optical, and electrical properties. The solubility and electronic behavior of Cu dopants are consistent with measured concentrations of 1 × 1018–1 × 1019 atoms/cm3 and electrical measurements that show high resistivities of 109–1010 Ω∙cm. Segregation and precipitation of Cu species in part of the VGF material was determined to be Cu2O by analysis with Raman spectroscopy, photoluminescence microscopy, energy-dispersive X-ray spectroscopy, and laser ablation inductively coupled plasma mass spectrometry. With sufficient Cu concentration, β-Ga2O3 crystals excited with deep ultraviolet light photodarken rapidly and exhibit decreased resistivity. This darkened state remains at room temperature for several days before decaying.

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.

Ga-doped Czochralski silicon with rear p-type polysilicon passivating contact for high-efficiency p-type solar cells

The use of Ga-doped Czochralski (CZ) silicon wafers in Passivated Emitter and Rear Cells (PERC) has been confirmed to have a prominent advantage in suppressing light-induced degradation (LID), which will attract considerable attention for the application of Ga-doped wafers in more efficient photovoltaic devices. In this work, we investigate the passivation quality and address the issue of LID in Ga-doped CZ Si wafers equipped with p-type polysilicon passivating contact that consists of an ultrathin SiO x and a heavily doped polysilicon. We also present the modeling results for solar cells using this type of contact. The experiments show that samples with Ga-doped CZ Si wafers have superior anti-LID properties when compared to the samples with B-doped wafers. An excellent passivation performance with a high implied open-circuit voltage ( iV oc ) of 705 mV and a low single-sided saturation current density ( J 0,s ) of 9 fA/cm 2 was achieved. Moreover, with the help of the numerical simulations, we predict that the p-type Ga-doped CZ Si solar cells with p-type polysilicon passivating contacts have the potential to achieve a high efficiency of 23.8%, an ~0.5% absolute efficiency improvement over that of PERC solar cells. The results demonstrated in this study suggest that Ga-doped CZ Si wafers combined with p-type polysilicon passivating contacts could resolve the LID issue while maintaining good passivation properties, providing a promising alternative for p-type solar cells in the photovoltaic industry. • The p-type TOPC on featuring Ga-doped CZ Si wafers achieved an excellent passivation quality with iV oc > 705 mV. • The passivation improvement sources of Ga-doped CZ Si-based structures were attributed to the suppression of B- and O-related defects. • Ga-doped TOPCon solar cells show the LID-free performance. • Simulation results show a comparable efficiency of 23.8% for Ga-doped TOPCon solar cells.

Model-Free Adaptive Iterative Learning Control Method for the Czochralski Silicon Monocrystalline Batch Process

Model-based control methods do not produce satisfactory control results with the batch process control of Czochralski (CZ) silicon monocrystalline with complex nonlinearity, large delay, and time-varying dynamics. Therefore, this paper proposes a data-driven model-free adaptive iterative learning control method (MFAILC) to achieve precision control of the batch process. Firstly, to improve the accuracy of the data-driven model, a novel deep learning model for crystal growth process is established by combining a stacked autoencoder (SAE) and a long short-term memory network (LSTM) to extract the working condition information and the dynamic timing features in process data. Traditional model-based control methods are limited by the difficulties in modeling and by the unmodeled dynamics. So, to overcome this problem, the heater controller and the crystal puller controller are designed, based on the iterative dynamic linearization technology, to ensure that the silicon monocrystalline batch manufacturing process always maintains precision control. Also, the discrete-time extended state observer (ESO) is introduced to compensate for the influence of disturbances, to improve the robustness of the control system. Finally, the efficacy of the proposed method is verified by applying it for the predictive modeling and batch control of thermal field temperature and crystal diameter during crystal growth.

Growth of nickel single crystals with a diameter of 8 in. using the Czochralski method

We grew large single crystals of metal nickel with a maximum diameter of 8 in. using the Czochralski (CZ) method. Characteristics of the metal material, namely, the seed elongation and intense cooling radiation at high temperatures during crystal growth, are the main challenges when growing ingots with large diameters. These problems were resolved by optimizing the parameters related to crystal growth, such as reduction of crucible and ingot rotation speed, and adjustment of shoulder formation angle of ingot shape. The produced ingots were confirmed to be single crystals by the Laue back-reflection method. Wafers were cut from single crystal ingots using a multi-wire saw with diamond abrasive grains. A smooth, mirror-like surface was obtained on the wafers by using an ordinary mechanical polishing method. The full width at half maximum values of the X-ray rocking curve of the metal nickel crystal surface significantly depends on the surface treatment method. It was found that ordinary mechanical mirror polishing introduces strain on the surface and non-uniformity of the crystal orientation.