54570987
Relationship between Dislocation Density and Oxygen Concentration in Silicon Crystals during Directional Solidification
This paper reports the relationship between oxygen concentration and dislocation multiplication in silicon crystals during directional solidification using numerical analysis. Based on the Alexander–Haasen–Sumino model, this analysis involved oxygen diffusion from the bulk to dislocation cores during crystal growth and annealing processes in a furnace. The results showed that the dislocation density mainly increased during cooling process, rather than crystal growth, when the effect of oxygen diffusion to dislocation cores was ignored. On the contrary, the dislocation density increased during both crystal growth and cooling processes when the effect of interstitial oxygen diffusion was considered. At a dislocation density larger than 1.0 × 105 cm−2, the interstitial oxygen concentration in bulk decreased due to the diffusion process, if interstitial oxygen atoms were between dislocations, whereas the concentration at dislocation cores increases.
137107910
Deformation behavior of silicon
Dynamic processes of individual dislocations in Si, such as generation, motion, and multiplication, are reviewed on the basis of direct observations by means of X-ray topography and transmission electron microscopy. The characteristics in the reaction of oxygen impurities with dislocations are clarified by real time observations with these techniques. Immobilization of dislocations due to the reaction is demonstrated. Stress-strain behavior of Si in the yield deformation is described in detail. It is sensitive to the deformation temperature, strain rate, and also to the density of dislocations initially contained in the crystal. Though the yield behavior of Si crystals free from dislocations is not influenced by oxygen impurities contained, that of dislocated crystals is affected significantly by these impurities. All of these characteristics in the yield deformation of Si are shown to be successfully described with a model that takes into account the dynamic processes of individual dislocations revealed by the direct observations.
135619355
In situ X-ray topographic study of the dislocation mobility in high-purity and impurity-doped silicon crystals
Abstract An in situ X-ray topographic technique using a high-power X-ray generator has been used to study the dislocation mobility at elevated temperatures in the stress range 1·2-40 MN m−2 for pure and impurity-doped silicon crystals. The variation of velocity with stress for both 60° and screw dislocations in high-purity crystal is linear throughout the whole stress range investigated, the activation energies for motion being independent of stress. No previously published theoretical models are able to account for the measured velocities quantitatively. Effects of impurities, such as oxygen, carbon, nitrogen, phosphorus and boron, are investigated in detail. Generally, the impurities bring about a deviation from linearity of the variation of velocity with stress under low stresses. Dislocations originally moving in impure crystals are immobilized when the stress becomes lower than a critical value. These phenomena are interpreted in terms of the development of an impurity atmosphere around slowly moving...
97905743
On the locking of dislocations by oxygen in silicon
Abstract Locking of dislocations by oxygen atoms in Czochralski silicon has been investigated both experimentally and theoretically. Experiments were performed at annealing temperatures between 700 and 850°C for different annealing times and different oxygen concentrations. These showed five distinct regimes for the unlocking stress as a function of annealing time. First the unlocking stress increases almost linearly with time and then saturates. The saturation stress, the time needed to reach saturation and the duration of saturation depend on the annealing conditions and oxygen content. Following the saturation a rapid increase and a second saturation of the unlocking stress with increasing annealing time were observed. Finally after long anneals the locking effect is much reduced. From the temperature dependence of the first saturation stress the interaction energy between an oxygen atom and a dislocation has been deduced and it is shown that the change in entropy when an oxygen atom is trapped at a dislocation is significant. The transport of oxygen to dislocations has also been investigated by solving the diffusion equation numerically. For these calculations both trapping and emission of oxygen atoms from the dislocation core have been considered.
97952343
On the dislocation-oxygen interactions in Czochralski-grown Si: oxygen diffusion and binding at low temperatures
The interaction between oxygen atoms and dislocations in Czochralski-grown silicon has been studied experimentally. Measurements concerning the locking of dislocations by oxygen atoms have been carried out in the temperature range 450–850°C for different annealing times. Using samples with low oxygen content (2.6 × 1017 cm−3) it has been possible to investigate the nature of binding of oxygen atoms to dislocations for temperatures lower than 700°C for which diffusion of oxygen in silicon has well known 'anomalous' behaviour. It has been found that although the binding enthalpy for temperatures larger than 700°C agrees well with the previously published value, its value is different for lower temperatures. We measured the oxygen–dislocation binding enthalpy to be about 0.2 eV in the temperature range of 450–650°C.
73586541
Constitutive modeling of intrinsic and oxygen-contaminated silicon monocrystals in easy glide
We generalize in this work the constitutive model for silicon crystals of Alexander and Haasen. Strain-rate and temperature dependency of the mechanical behavior of intrinsic crystals are correctly accounted for into stage I of hardening. We show that the steady-state of deformation in stage I is very well reproduced in a wide range of temperature and strain rate. The case of extrinsic crystals containing high levels of dissolved oxygen is examined. The introduction of an effective density of mobile dislocations dependent on the unlocking stress created by oxygen atoms gathered at the dislocation cores is combined to an alteration of the dislocation multiplication rate, due to pinning of the dislocation line by oxygen atoms. This increases the upper yield stress with the bulk oxygen concentration in agreement with experimental observations. The fraction of effectively mobile dislocations is found to decay exponentially with the unlocking stress. Finally, the influence of oxygen migration back onto the dis...
96044547
Relationship between the locations of activated dislocations and the cooling flux direction in monocrystalline‐like silicon grown in the [001] and [111] directions
To effectively control dislocations of monocrystalline-like silicon grown in the [001] and [111] directions, the relationship between the locations of activated dislocations and the cooling flux direction was studied numerically from the perspective of activation of slip systems. The cooling flux direction was shown to have a significant effect on the activation of slip systems. The radial flux and axial flux activate different slip systems at different locations in the crystal. The relationship between the flux direction and the activation of slip systems in the [001] and [111] growth directions has been revealed. The results provide theoretical support for reducing dislocations inside a crystal or in the part of the crystal where dislocations can cause the most damage, by intentionally controlling the flux direction during the crystal growth process.
102628720
Effect of oxygen on dislocation multiplication in silicon crystals
Abstract This paper aims to clarify the effect of oxygen on dislocation multiplication in silicon single crystals grown by the Czochralski and floating zone methods using numerical analysis. The analysis is based on the Alexander–Haasen–Sumino model and involves oxygen diffusion from the bulk to the dislocation cores during the annealing process in a furnace. The results show that after the annealing process, the dislocation density in silicon single crystals decreases as a function of oxygen concentration. This decrease can be explained by considering the unlocking stress caused by interstitial oxygen atoms. When the oxygen concentration is 7.5 × 1017 cm−3, the total stress is about 2 MPa and the unlocking stress is less than 1 MPa. As the oxygen concentration increases, the unlocking stress also increases; however, the dislocation velocity decreases.
101306092
Anisotropic Thermal Stress Simulation with Complex Crystal–Melt Interface Evolution for Seeded Growth of Monocrystalline Silicon
To simulate the anisotropic thermal stress with complex crystal–melt interface evolution by the fixed-grid method during seeded growth of monocrystalline silicon, a new method that can solve the global stress field involving the crystal and melt regions without a requisite of accurate locations of the interface was proposed. The melt is regarded as a kind of hypothetical solid material that has isotropic material properties. Free boundary conditions along the crystal–melt interface are implicitly satisfied with all of the stress components inside the melt region being close to zero compared to those inside the crystal region. Therefore, regardless of the complexity of the interface shape, the stress field can be easily analyzed by a simple solver and a set of simple fixed grids even for extremely complex interface evolution. Results of numerical simulations in the isotropic, [001], and [111] growths show good consistence with other numerical and experimental results.
93887191
Oxygen diffusion and thermal donor formation in silicon
The information available on the diffusion of oxygen and on the formation of thermal donors in silicon is critically reviewed. In this context the effects of intrinsic point defects on the diffusion-controlled growth of oxygen precipitates is investigated in some detail. Seemingly contradictory experimental results on the diffusivity of oxygen in silicon at temperatures around 400° C are explained in terms offast-diffusing gas-like molecular oxygen in silicon. The concept of molecular oxygen is also invoked in a newly suggested model of thermal donor formation in silicon. The diffusivity of molecular oxygen in silicon is estimated to be around 10−9cm2s−1 at 450° C, almost nine orders of magnitude higher than the diffusivity of atomic oxygen in interstitial position.
55636311
Numerical Analysis of the Dislocation Density in Multicrystalline Silicon for Solar Cells by the Vertical Bridgman Process
We studied the effects of cooling process on the generation of dislocations in multicrystalline silicon grown by the vertical Bridgman process. From the temperature field obtained by a global model, the stress relaxation and multiplication of dislocations were calculated using the Haasen-Alexander-Sumino model. It was found that the multiplication of dislocations is higher in fast cooling processes. It was confirmed that residual stress is low at high temperatures because the movement of the dislocations relaxes the thermal strain, while the residual stress increases with decreasing temperature, because of reduced motion of dislocations and formation of a strain field at lower temperatures.
93352959
An analysis of temperature distribution near the melt–crystal interface in silicon Czochralski growth with a transverse magnetic field
A three-dimensional (3D) global analysis was carried out numerically for a small silicon Czochralski furnace in a transverse magnetic field to clarify temperature distribution near a melt–crystal interface. The melt–crystal interface shape and the axial temperature gradients in solid and liquid near the interface were calculated as functions of the magnetic field intensity and the pulling rate of a crystal. It was found that the axial temperature gradient in the crystal increases with increase in the crystal-pulling rate and that in the melt decreases near the interface. With increase in intensity of the magnetic field, the axial temperature gradients in both crystal and melt increase. The influence of melt convection becomes smaller with increase in either the magnetic field intensity or the crystal-pulling rate. The melt–crystal interface moves upward with increase in either the ratio between crystal-pulling rate and temperature gradient in the crystal or the intensity of the applied magnetic field.
99274448
Numerical analysis of the relation between dislocation density and residual strain in silicon ingots used in solar cells
Abstract We have developed a three dimensional Haasen-Alexander-Sumino model to investigate the distribution of dislocation density and residual strain in Si crystals and compared the calculation results with experimental data performed in mono-like and multicrystalline silicon ingots. The results show that the residual strain in a multicrystal is lower than in a mono-like crystal, whereas the dislocation density in the multicrystal is higher than that in the mono-like crystal. This phenomenon is due to the relation between dislocation density and residual strain caused by the difference of activated slip systems in a mono-like crystal and a multicrystal.
96983435
Relationship between oxygen impurity distribution in multicrystalline solar cell silicon and the use of top and side heaters during manufacture
Abstract The relationship between the oxygen impurity distribution in multicrystalline silicon and the use of top and/or side heaters in an unidirectional solidification process was investigated by numerical analysis. It was found that the oxygen concentration in the melt for the side heating system is lower than that for only the top heating system. This occurs because of the difference in flow direction of the melt near the crucible wall. The melt flows upward near the crucible wall when the side heating system is used. Oxygen is therefore dissolved from the silica crucible wall and is transported easily to the melt surface, where it evaporates.
97341485
Dynamic simulation of temperature and iron distributions in a casting process for crystalline silicon solar cells with a global model
The casting method is a key method for large-scale production of multi-crystalline silicon for use in highly efficient solar cells in the photovoltaic industry. Since the efficiency of solar cells depends on the quality of the multi-crystalline silicon, it is important to optimize the casting process to control temperature and iron distributions in a silicon ingot. We developed a new transient global model for the casting process and carried out simulations to study the temperature and iron distributions in a silicon ingot during solidification. Conductive heat transfer and radiative heat exchange in a casting furnace and convective heat transfer in the melt in a crucible are coupled to each other. These heat exchanges were solved iteratively by a finite-volume method in a transient way. Time-dependent distributions of iron and temperature in a silicon ingot during the casting process were numerically studied.