Cz Growth Research Articles

Investigation of Doping Processes to Achieve Highly Doped Czochralski Germanium Ingots

Highly doped germanium (HD-Ge) is a promising material for mid-infrared detectors, bio-sensors, and other devices. Bulk crystals with a doping concentration higher than 1018 cm−3 would be desirable for such device fabrication technologies. Hence, an effective method needs to be developed to dope germanium (Ge) ingots in the Czochralski (Cz) growth process. In this study, a total of 5 ingots were grown by the Cz technique: two undoped Ge ingots as a reference and three doped ingots with 1018, 1019 , and 1020 atoms/cm3 respectively. To obtain a uniform p-type doping concentration along the crystal, co-doping of boron-gallium (B-Ga) via the Ge feed material was also attempted. Both B and Ga are p-type dopants, but with a large difference in their segregation behavior (contrary segregation profile) in Ge, and hence it is expected that the incorporation of dopants in the crystal would be uniform along the crystal length. The distribution of the dopants followed the Scheil-predicted profile. The etch pit density maps of the grown crystals showed an average dislocation density in the order of 105 cm−2. No increase in the overall etch pit count was observed with increasing dopant concentration in the crystal. The grown highly doped Ge crystals have a good structural quality as confirmed by x-ray diffraction rocking curve measurements.

Particularities of the thermal and oxygen concentration instabilities in a Czochralski process for solar silicon growth

A previous presented numerical model was used to study the time behavior particularities of temperature and oxygen concentration in a Czochralski (Cz) growth process of 200 mm diameter silicon single crystals for photovoltaic applications. First, some important model issues have been addressed: the dependence of the numerical results on the refinement level of the grid and on the model for oxygen equilibrium concentration at the melt-crucible interface. Then a parametrical study have been performed to study how the pulling rate and the rotation rate of the crucible influence the fluctuations of temperature and oxygen concentration near the crystallization interface. The numerical simulations have revealed that the temperature oscillations are closer to a normal distribution than the oxygen concentration, which is closer to a skewed left distribution.Both the increase of crucible rotation rate and pull speed has an effect of “pushing to the left”: the histogram of temperature fluctuations tends from a skewed right distribution to a normal distribution with the increase of the pull speed and crucible rotation values while the oxygen concentration is more skewed to the left. As a general conclusion, the numerical simulations have shown that the oxygen concentration is more sensitive to the crucible rotation than the temperature field, while the pull speed has a stronger effect on temperature oscillations than on the oxygen concentration oscillations.

Long-Term Stability of Novel Crucible Systems for the Growth of Oxygen-Free Czochralski Silicon Crystals

The replacement of the silica glass crucible by oxygen-free crucible materials in silicon Czochralski (Cz) growth technology could be a key factor to obtaining Cz silicon, with extremely low oxygen contamination < 1 × 1017 at/cm3 required for power electronic applications. So far, isostatic pressed graphite or nitrogen-bonded silicon nitride (NSN) crucible material, in combination with a chemical vapor deposited silicon nitride (CVD-Si3N4) surface coating, could be identified as promising materials by first short-term experiments. However, for the evaluation of their potential for industrial scale Cz growth application, the knowledge about the long-term behavior of these crucible setups is mandatory. For that purpose, the different materials were brought in contact with silicon melt up to 60 h to investigate the infiltration and dissolution behavior. The chosen graphite, as well as the pore-sealed NSN material, revealed a subordinated infiltration-depth of ≤1 mm and dissolution of ≤275 µm by the silicon melt, so they basically fulfilled the general safety requirements for Cz application. Further, the highly pure and dense CVD Si3N4 crucible coating showed no measurable infiltration as well as minor dissolution of ≤50 µm and may further acts as a nucleation site for nitrogen-based precipitates. Consequently, these novel crucible systems have a high potential to withstand the stresses during industrial Cz growth considering that more research on the process side relating to the particle transport in the silicon melt is needed.

Melt convection and temperature distribution in 300 mm Czochralski crystal growth with transverse magnetic field

Two-dimensional (2D) and Three-dimensional (3D) simulation solutions of the melt flow and heat transfer in the industrial scale 300 mm diameter single silicon Czochralski (Cz) growth with a transverse magnetic field were presented. The flow structure of the melt is no longer rotationally symmetric when the crystal and crucible rotate. The complex flow pattern is investigated, and simulation results show that the current caused by crystal rotation has a strong impact on melt convection beneath the interface. In addition, the mechanism through which the current influences melt flow is clarified. A special flow near the interface caused by Lorenz force is reported. All these results indicate the crystal conductivity cannot be neglected in simulation.

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.

Single-crystal growth of triphenylphosphine using the Czochralski method

The Czochralski (Cz) method for organic materials with a low melting point was used to fabricate single-crystal growth apparatus, and the single crystals of triphenylphosphine were successfully grown. The unit cell parameters and orientations of the grown crystals were determined through X-ray diffractometry. Further, the necking process was also introduced into the crystal growth by controlling the melt temperature during the Cz growth. The necking was effective in suppressing crack propagation from the seed crystal. Moreover, using the grown single crystals as the seed crystal allowed to control the crystal orientation of these crystals.

A modified hypothesis of Reynolds stress tensor modeling for mixed turbulent convection in crystal growth

Within implicit large eddy simulation, we have provided unsteady 3D numerical study of turbulent melt convection during 100 mm diameter Si Cz growth, using refined time step and material properties. Comparison of calculated and measured time-averaged temperature profiles along the melt/crucible interface has demonstrated advantages of using updated material properties. Reference data on the spatial distributions of the turbulent stress tensor and heat fluxes in the melt have been obtained and used for validation of the conventional and modified hypothesis of Reynolds stress tensor modeling. Contrary to the conventional Boussinesq assumption of isotropic turbulent viscosity, our modified hypothesis has reproduced qualitative and quantitative details of reference Reynolds stress tensor distributions, including the boundary layer anisotropy due to the wall and free surface effects, mean velocity shear effect, and the buoyancy contribution to enhance vertical velocity fluctuations. Using our modified hypothesis and generalized Reynolds analogy for turbulent heat transport modeling, it become feasible to reproduce quantitatively the distributions of the turbulent heat flux, shear and buoyancy production terms of the kinetic energy transport equation, which is the necessary basis for further turbulence model development.

Optical Properties of Bulk Silicon Germanium in the Near Infrared Evaluated By Spectroscopic Ellipsometry

Background and ObjectivesSilicon germanium (SiGe) is expected to be applied to optical devices such as infrared sensors because of its narrower band gap than Si. For this purpose, it is very important to understand the optical properties in the infrared region of SiGe. Although there have been many reports on the optical properties of SiGe [1], there are few reports on the optical properties in the near infrared region. Since the optical properties must be modulated by the applied strain, we believe that bulk SiGe is the most appropriate sample to obtain the original optical properties of SiGe without the effect of strain. In this study, we evaluated the optical properties of bulk SiGe including the infrared region by using spectroscopic ellipsometry.ExperimentsThe samples were bulk SiGe with 16% Ge composition fabricated by Czochralski (Cz) method [2], and bulk SiGe with 32, 45 and 90% Ge composition fabricated by Traveling Liquidus Zone (TLZ) method [3]. All of these samples were confirmed to be single crystals by X-ray diffraction (XRD) and electron backscattered pattern. In addition, we confirmed that the SiGe samples are strain-free by XRD and Raman spectroscopy. The spectroscopic ellipsometry measurements were performed with an incident angle of 60°, a 70 W xenon lamp as the light source, and a wavelength range of 200 to 1600 nm for the light source.Results and DiscusssionFigure 1 shows the (a) refractive index and (b) extinction coefficient of bulk SiGe with 16% Ge composition in conjunction with those of pure Si, pure Ge. Fig. 1(a), it can be confirmed that the refractive index of bulk SiGe (16%) has an anomalous increase from around 1100 nm. On the other hand, Fig. 1(b) indicates that the extinction coefficient does not show such an anomalous change. These behavior was also observed for other bulk SiGe samples. Since this increase was observed in both Cz and TLZ growth methods, it is not considered to originate from the fabrication method. The value at 1100 nm where the anomalous increase is observed, is close to the Si band gap of 1.1 eV. The characteristics are Si like before the increase, while it is Ge like after the increase. Therefore, the refractive index of Ge seems to become dominant after the Si band gap. Since the effect of free carrier absorption is expected to occur at longer wavelengths, this anomalous increase should not be due to the free carrier absorption but some unique phenomena for SiGe alloy. We believe that this unique phenomena in the refractive index of bulk SiGe is an important finding for the application of SiGe in optical devices.[1]. J. Humlicek, M. Garriga, M. I. Alonso, and M. Cardona, J. Appl. Phys. 65, 2827 (1989).[2]. I. Yonenaga, J.Cryst. Growth 275, 91 (2005).[3]. K. Kinoshita et al., Jpn. J. Appl. Phys. 54, 04DH03 (2015). Figure 1

3D unsteady and steady modeling of heat and mass transfer during Cz Si crystal growth with a horizontal magnetic field

A combined LES/RANS approach is applied to modeling Czochralski (Cz) Si growth with a strong horizontal magnetic field stabilizing the melt flow. A model furnace geometry with a cylindrical crucible is considered, which can be suggested for benchmarking Cz Si melt convection of industrial scale. Grid resolution in boundary layers is carefully adjusted and the 4th approximation order for diffusion terms is shown to provide sufficient computation accuracy even with comparatively rough grids. The computed flow structure, temperature distribution on the melt free surface, and RMS temperature fluctuations of the melt are in good agreement with published experimental data and modeling results for industrial furnaces. The effect of the crystal rotation rate on the interface shape and oxygen incorporation into the crystal is analyzed. Due to high thermal conductivity (or low Pr number) of the melt, the unsteady oscillations do not exert a significant effect on the temperature and heat flux distribution in the melt, which allows quite accurate predictions of the interface shape, even neglecting the flow unsteadiness. In contrast, due to a low diffusivity (or high Sc number) of atomic oxygen in the melt, the unsteady oscillations quite significantly affect its transport through the melt and incorporation into the crystal, which results in remarkable overestimation of the oxygen concentration without consideration of unsteady melt flow evolution. The formulation of the LES/RANS approach used in the benchmark problem was verified on experimental data for an industrial furnace for Magnetic Cz (MCz) growth of 300 mm silicon crystals.

Facet growth and geometry of the growth ridge during dynamic Czochralski processes

The facet length and growth ridge geometry during Cz growth processes are analyzed both experimentally and theoretically. The experimental analysis is conducted based on the novel approach of measuring the growth ridge geometry by means of optical profilometry. A simple theoretical model is presented that describes the variations of the facet length and of the growth ridge extension. The origin of growth ridge asymmetry is explained as a result of crystal rotation and the relation between diffusive and convective heat transfer. An approach to extract the temperature gradient at the crystal surface above the interface is proposed. All theoretical deliberations are supported by experimental results.

Inverse response behaviour in the bright ring radius measurement of the Czochralski process I: Investigation

This is the first part of a two-article series that deals with the investigation of the anomalous behaviour in the radius measurement signal of the Czochralski (Cz) process and its mitigation in a feedback control system. The inverse or anomalous behaviour is indeed a measurement signal response, which initially is opposite to that of the expected response. This is a crucial and limiting factor in feedback control system design. The paper presents the development of a rigorous 3D ray-tracing method to investigate the inverse response behaviour in the measurement signal. The results of this study provide an insight into the dynamic behaviour of the Cz growth process. It can serve as a guideline for achieving effective crystal radius control, which is addressed in the second part of this article series.

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.

Effects of crystal-crucible iso-rotation and a balanced/unbalanced cusp magnetic field on the heat, flow, and oxygen transport in a Czochralski silicon melt

• Melt flow pattern is varied by crystal-crucible rotation rates and magnetic ratios. • CMF insignificantly affects oxygen content at low crystal iso-rotation rates. • Iso-rotating crystal faster than crucible enhances oxygen content under a CMF. • Iso-rotating crystal faster than crucible increases the uniformity of oxygen content under a CMF. The effects of using a balanced/unbalanced cusp magnetic field (CMF) along with crystal-crucible counter-/iso-rotation on the heat, flow, and oxygen distributions during Czochralski (Cz) growth of an 8-inch silicon crystal are numerically investigated. One counter-rotation example is compared to iso-rotation cases. In both rotation modes, the vertical flow in the central melt region is strengthened while the buoyancy-driven melt flow is weakened under a cusp field. The CMF has a stronger effect on the oxygen content when there is a large difference in rotation rate between the crystal and the crucible (n S − n C ). This is because a higher value of (n S − n C ) induces stronger melt convection and hence, the Lorentz force has a more significant effect on a fast melt flow than a slow one. Although diffusion significantly influences oxygen transport in the melt at low crystal iso-rotation rates, different flow patterns and local melt velocities induced by different crystal iso-rotation speeds will modify the oxygen distribution. There is a slight change in the oxygen content at a low ingot iso-rotation rate with a CMF. In cases of iso-rotation, the radial oxygen content is enhanced more by an unbalanced CMF than a balanced one. Greater uniformity of the radial oxygen concentration is achieved applying iso-rotation with n S > n C under a CMF.

Effect of crucible and crystal rotations on the solute distribution in large size sapphire crystals during Czochralski growth

In this study, the flow, temperature and solute concentration fields in the melt during the CZ growth process are numerically investigated. The results show that the magnitude and distribution of the solute concentration in the melt is strongly affected by the convective flow and thermal distribution. The maximum solute concentration always occurs at the crucible sidewall where the maximum temperature in the melt is found and the solute concentration at the crystal-melt interface increases from the triple point to the centerline. Heat transport from the side crucible wall towards the crystal-melt interface is enhanced by the crucible rotation. The level of the solute concentration inside the melt is reduced due to the lowering of the maximum temperature at the crucible wall. As a consequence, the distribution of the solute concentration along the crystal-melt interface becomes smaller and more uniform as the crucible rotation rate increases. However, after the crucible rotation rate becomes large enough, the maximum solute concentration and the solute concentration along the crystal-melt interface start to increase. Heat transport inside the melt is also affected by the crystal rotation. The centrifugal force induced by the crystal rotation generates a vortex below the crystal-melt interface. This vortex gets larger and stronger as the crystal rotation rate increases. In the smaller crystal rotation rate regime, this vortex is very small, suppressing the solute concentration at the crystal-melt interface. Therefore, the solute concentration along the crystal-melt interface becomes less when the crystal rotation rate is higher, although there is an increase in the maximum solute concentration in the melt due to the higher maximum temperature. In the higher crystal rotation rate regime, there is a reduction in the convexity of the crystal-melt interface due to enhancement of heat transport from the bottom wall of the crucible by vortex motion under the crystal-melt interface. Therefore, there is a switch to an increase in the transport of solute impurities into the crystal-melt interface. Hence, the solute concentration along the crystal-melt interface increases as the crystal rotation rate increases. However, with a further increase in the crystal rotation rate, as the shape of the crystal-melt interface changes becoming concave towards the melt, the solute concentration along the crystal-melt interface decreases because the maximum temperature is significantly reduced. In this study, both counter- and iso-rotations are considered. The results of a comparison of the cases of iso- and counter- crystal rotation show that the lowest and most uniform solute distribution along the crystal-melt interface is achieved when there is no crystal rotation and the crucible rotation rate is fixed at 1 rpm. In other words, the lowest and most uniform solute concentration can be achieved with the only crucible rotation.

Experimental and numerical effects of active afterheater addition on the growth of langatate (La3Ga5.5Ta0.5O14) crystals by the Czochralski method

Experimental and numerical study on afterheater addition during Cz growth of LGT which resulted in a defect-free crystal with high stability and reproducibility.

Quality of n-Type Czochralski Silicon Crystals for Solar Cells Grown from the Melt in Liquinert Crucibles

For the application to advanced high-performance solar cells, we have developed n-type CZ monocrystalline silicon crystals whose lifetime values are almost equal to those of MCZ silicon. We analyzed this point in detail, using the Shockley-Read-Hall model. In our growth, liquinert silica crucibles having non-wettable properties for molten silicon were employed in a conventional CZ puller. The improved lifetime is likely due to reduced carbon impurity. The CZ growth technique with liquinert crucibles brings a novel approach to the new CZ technique because it can supply higher-quality silicon compared to silicon grown by conventional CZ technique.

Lattice Boltzmann Modeling of the Dissolution Process of Silicon into Germanium using a Simplified Crystal Growth Technique

Numerical simulations were carried out to explain the behavior exhibited in experimental work on the dissolution process of silicon into a germanium melt. The experimental work utilized a material configuration similar to that used in the Liquid Phase Diffusion (LPD) and Melt-Replenishment Czochralski (Cz) growth systems. The numerical simulations were carried out under the assumption of 2D. The mathematical model equations were developed using Lattice Boltzmann Method (namely the BGK approximation was adopted). Measured concentration profiles and dissolution height from the samples processed with and without the application of magnetic field show that the amount of silicon transported into the melt is slightly higher in the samples processed under magnetic field, and there is a difference in dissolution interface shape indicating a change in flow structure. This change in flow structure was predicted by the present LB model. In the absence of magnetic field a flat stable interface is observed. In the presence of an applied field, however, the dissolution interface remains flat in the center but curves back into the source material near the edge of the wall. This indicates a far higher dissolution rate at the edge of the silicon source.

Numerical study on the effect of temperature oscillations on the crystallization front shape during Czochralski growth of gadolinium gallium garnet crystal

Time-dependent, finite volume method calculations of momentum and heat transfer were carried out to investigate the correlation between oscillatory convection and the crystallization front dynamics during the Czochralski (Cz) growth of an oxide material. The present modeling allows us to illustrate the modification of the interface shape during the time period of oscillation of the flow manifesting as the formation of a cold plume beneath the phase boundary. It was shown that the instability mechanism is associated with an irreversible dramatic change in the interface shape, which occurs at a critical Reynolds number significantly lower than that is predicted by the quasi-stationary global model analysis of the Cz growth system. The baroclinic term which appears in the vorticity equation in a rotating stratified fluid is used to describe the numerical results of the model. The properties of the thermal waves were studied in the monitoring points located nearby the interface. The waves are regular but not in fact vertically correlated as observed in the case of baroclinic waves. The Rayleigh–Benard dynamics is suggested to be the predominant mechanism even though the instability is primarily baroclinic.

Effect of process parameters and crystal orientation on 3D anisotropic stress during CZ and FZ growth of silicon

Simulations of 3D anisotropic stress are carried out in <100> and <111> oriented Si crystals grown by FZ and CZ processes for different diameters, growth rates and process stages. Temperature dependent elastic constants and thermal expansion coefficients are used in the FE simulations. The von Mises stress at the triple point line is ~5–11% higher in <111> crystals compared to <100> crystals. The process parameters have a larger effect on the von Mises stress than the crystal orientation. Generally, the <111> crystal has a higher azimuthal variation of stress along the triple point line (~8%) than the <100> crystal (~2%). The presence of a crystal ridge increases the stress beside the ridge and decreases it on the ridge compared with the round crystal.

Correlation between steady-oscillatory flow transition and the interface inversion process during the Czochralski growth of semitransparent oxide crystal

In this paper, steady-oscillatory transition of the convective flow in a Czochralski (Cz) growth system was numerically studied. In this configuration, rapid variations in density across narrow region of the flow in the vicinity of the crystallization front leads to an unstable stratification of the flow in this region. Time-dependent, finite volume method calculation of the momentum and heat transport equations shows that an instability mechanism, giving rise to the formation of cold plumes beneath the phase boundary, might be associated with an irreversible change in the convexity of the front. Dynamics of the crystallization front was found to be correlated with the periodic oscillation of the flow. It was shown that the interface inversion process occurs at a critical Reynolds number significantly (∼25%) lower than that predicted by the steady-state Cz-oxide model analysis. Consistently, the time-averaged maximum value of stream function was found to be larger than its corresponding steady-state value. This indicates that the mechanism behind the oscillatory transition of the flow has a positive feedback on the intensity of forced convection flow. These numerical results were attributed to the baroclinic instability mechanism characterized by oscillations of a cold plume appearing at the crystal periphery and descending along the symmetry axis. The time period of oscillations was found to be considerably (30–40%) decreases and, simultaneously, the inclination angle of isopycnals increases (∼48%) at a critical rotation rate of the crystal for which the interface inversion occurs.