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Fast prediction of fluid flow and thermal fields during the growth of bulk silicon single crystals by the ‘Vertical Magnetic Field Applied Czochralski (VMCz) Method’ was successfully achieved by the application of Physics Informed Neural Networks (PINNs) without any answer-labeled training data generated by a numerical simulation. The PINNs’ results are in good agreement with those of the numerical simulation. The prediction time by PINNs was significantly reduced; to less than 0.1 seconds compared with about 30 minutes required by the numerical simulation. Moreover, being mesh-free techniques, PINNs do not require mesh reconstruction to accommodate the change in the growth melt volume during growth. This shows that PINNs have great potential, as real-time simulation techniques, for future applications in various areas.

In the process of preparing silicon single crystal, the Czochralski method has problems such as multiple mechanism assumptions, unclear boundary conditions under multiple field couplings, interlaced and mutual influence of physical and chemical changes, which makes it impossible to establish an accurate mechanism model for silicon single crystal growth process control. To solve this problem, based on a large amount of crystal growth data in the single crystal furnace pulling workshop, this paper analyzes the characteristic parameters related to crystal diameter based on the maximum information coefficient (MIC) algorithm proposed by the mutual information theory. Then, based on the nonlinear autoregressive with exogeneous inputs (NARX) dynamic neural network, a multi-input, and single-output equal-diameter phase crystal diameter prediction model was established, the diameter prediction was also performed for the three single crystal furnace pulling data, and the average mean square error value of the prediction is 0.000774. Finally, the prediction model of crystal diameter in the equal diameter stage established based on the NARX dynamic neural network is compared with the prediction model of crystal diameter in the equal diameter stage established based on the back propagation (BP) neural network. The results of the comparative analysis verified the superiority of the NARX dynamic neural network model for predicting the crystal diameter in the isodiametric stage. The results show the NARX dynamic neural network provides a more accurate identification model for the control of crystal diameter. [ABSTRACT FROM AUTHOR]

The effect of radiation of a nanosecond ultraviolet laser ( λ = 355 nm, pulse duration 10 ns, pulse energy up to 8 mJ, pulse repetition rate – up to 100 Hz) on a silicon single crystal has been investigated by methods of the optical profilometry and scanning electron microscopy. At an energy density of ≥ 1,2 J/сm^2, formation of the plasma torch and crater was observed. At an energy density of ≥ 0,2 J/сm^2, pockets of microbreakdown appeared on processing defects, and traces of uncontrolled surface uplift were recorded. Irradiation with a scanning laser beam at an energy density of 0,2 J/сm^2 forms microcraters on a surface with a size of several microns. With an increase in the energy density, the size of the microbreakdowns increased, and at an energy density ≥ 0,7 J/сm^2, the impact of the scanning beam forms a continuous damage zone.

In the vision-based shape control system of silicon single crystal (SSC) growth, shape parameters are used as the control variables to make the grown SSC approximate to a perfect cylinder. A highlight halo at the junction of the solid crystal and the liquid crysta is a distinctive feature that reflects the current shape of SSC, and the edge of the captured halo is an elliptic arc that consistently changes with the shape of the halo. To estimate the shape parameters through the elliptic arc, we propose a two-side (TS) constraint method to fit the elliptic arc. Firstly, the error correction parameter is introduced into the second-order polynomial model to make the model more robust in the case of noise disturbing, and the resultant non-convex TS constraint model is constructed. Then, two weighted functions, which give the data out of TS constraint a small weight coefficient to resist the large level noise disturbing, are brought into the TS constraint optimization problem tactfully. Simulation and real SSC data examples show that the proposed method can obtain the elliptic arc parameters effectively.

To evaluate and improve the accuracy of the ther-modynamic equation of state for sea-water (TEOS-10), there are pressing needs for precise density measurements for stan-dard sea-water samples. In the present study, a hydrostatic weighing apparatus using a silicon single-crystal sinker was developed. The relative expanded uncertainty of the density measurement is 1.4 ppm which is the highest among the exist-ing density measurement equipment. The validity of the den-sity measurement was checked by measuring n-tridecane and pure water. Measurement results for standard sea-water sam-ples are discussed in this paper.

With the rapid development of photovoltaic industry, the quality requirement of silicon single crystal is increasing. Czochralski is the main method to produce single crystal silicon. The production scale of single crystal silicon can be enlarged by increasing the height of the sub-chamber in the single crystal furnace. Due to the large increase in the height of the sub- chamber and the distance between the centroid of the single crystal furnace lifting head and the rotating axis of the single crystal furnace, the overall stability of the single crystal furnace is greatly affected and the production quality of the single crystal silicon is reduced. In order to solve this problem, a reliable mechanical analysis model of single crystal furnace was established, and the dynamic response of the whole single crystal furnace was analyzed by numerical simulation method. The law of motion and the maximum swing amplitude of the bottom end of tungsten wire rope were calculated when the height of the sub-chamber was increased, which provides a basis for improving the design. The numerical simulation analysis shows that the large eccentricity of the lifting head is the main reason for the shaking of the single crystal furnace lifting system. For this reason, it is proposed to add a centroid adjustment device to the lifting head, and the control system is adjusted to ensure that the mass center of the lifting head is on the rotation axis to reduce the swing of the lifting system. [ABSTRACT FROM AUTHOR]

When a dynamic crack front travels through material heterogeneities, elastic waves are emitted, which perturb the crack and change the morphology of the fracture surface. For asperity-free crystalline materials, crack propagation along preferential cleavage planes is expected to present a smooth crack front and form a mirror-like fracture surface. Surprisingly, we show here that in single crystalline silicon without material asperities, the crack front presents a local kink during high-speed crack propagation. Meanwhile, local oscillations of the crack front, which can move along the crack front, emerge at the front kink position and generate periodic fracture surface corrugations. They grow from angstrom amplitude to a few hundred nanometers and propagate with a long lifetime at a frequency-dependent speed, while keeping a scale-independent shape. In particular, the local front oscillations collide in a particle-like manner rather than proceeding with a linear superposition upon interaction, which presents the characteristic of solitary waves. We propose that such a propagating mode of the crack front, which results from the fracture energy fluctuation at a critical crack speed in the silicon crystal, can be considered as nonlinear elastic waves that we call "corrugation waves.". [ABSTRACT FROM AUTHOR]

In the process of silicon single-crystal growth, the detection of melt level is an important step to ensure that the grown silicon single crystal is of high quality. Since there exist many mechanical motions, chemical interactions, thermal convection, and so on, it is extremely difficult to obtain the noise statistics of the liquid-level data. To attain a high-accuracy detection of liquid level with unknown noise statistics, we present an extended set-membership-based particle filter (PF). The key points are as follows. We construct a nonlinear state-space model for liquid-level detection system based on the kinematic principle and laser triangulation measurement principle and cast the detection problem of the liquid level into a state estimation problem. Based on this model, we use the extended set-membership estimation theory to generate an ellipsoid set that contains the true value of the liquid-level state. To overcome the difficulty of drawing particles under the case of unknown statistics noise, we draw particles from a Gaussian distribution in the obtained ellipsoidal set. In order to resample particles when the measurement noise statistic is unknown, we introduce a cost function to obtain the weights of the particles, and the ultimate estimation of liquid level is calculated by the weighted particles after the resampling procedure. Comparing with the extended Kalman PF (EPF) and the cost-reference PF (CRPF), the proposed algorithm has higher estimation accuracy. Some simulation and experiment results are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A new control structure with constant pulling speed for growing high-quality crystal in the Czochralski (CZ) method is presented in this brief. In this control structure, the pulling speed is not involved in the controlling of crystal diameter and only the temperature is used as the control quantity. Due to the time delay and the nonlinearity relationship are commonly involved between the temperature and crystal diameter, which make the diameter control difficult and complicated, a generalized predictive controller (GPC) based on the stacked sparse autoencoder (SSAE) is proposed under the new control structure. The time delay is obtained by using the correlation identification algorithm, the input order and output order are determined by the Lipchitz quotients algorithm, and the prediction model is trained by SSAE. Combining the SSAE with the nonlinear GPC algorithm, the control law of the temperature is calculated for diameter control. The simulation result verifies the correctness of the proposed control algorithm. The experimental result indicates that the new control structure with constant pulling speed is more conducive to growing high-quality crystal, avoiding the fluctuation of pulling speed. The proposed SSAE-based GPC algorithm can accurately track the reference diameter. The studies in this brief provide a feasible strategy for growing large size and high-quality crystal in the CZ method. [ABSTRACT FROM AUTHOR]

In silicon single crystal micro-electrical discharge machining (Micro-EDM), the plasma channel and workpiece temperature field directly affect the machined parts. For Si single crystal, with short single discharge time and small inter-electrode gap, the temperature cannot be easily measured directly. Based on the theory of energy conservation and heat conduction, combined with Micro-EDM process, in this paper, thermodynamic analysis of plasma in Micro-EDM process is conducted, and a plasma temperature distribution model considering latent heat of fusion is established. Adopting Gaussian distribution heat flux boundary condition and the temperature field distribution of the workpiece surface is simulated by FLUENT. The relationship between material removal rate (MRR) and surface roughness (SR) corresponding to temperature distribution under different peak current and pulse width conditions is analyzed. The results show that plasma temperature has a positive correlation with peak current and pulse width. The increase of peak current and pulse width within the processing parameter range leads to the increase of MRR and SR. The experimental results verify the correctness of the model. [ABSTRACT FROM AUTHOR]

The results of experiments on the impact of fast helium ions (Ei ~ 100 keV) and helium plasma (v ~ 2 × 107 cm/s) on a silicon single crystal plate in the Vikhr plasma focus (PF) installation with radiation power density in the range of q ≈ 106–107 W/cm2 are presented. It is shown that, at low values of q = 106–1011 W/cm2, the damageability of silicon is due to its surface sputtering mainly in the zone of mechanical defects, while with more intense irradiation (108< q ≤ 1011 W/cm2) the processes of melting and evaporation of the surface layer occur with the formation of structural defects in the form of waves, flows, bubbles, craters and microcracks. The specific nature of damage of the Si plate at high power density and a large number of pulsed beam-plasma impacts (q ≥ 109 W/cm2, N = 50) is described. It is associated with the formation of a brittle fine-crystalline surface layer, which is easily separated from the base material and disintegrates in the form of a powder of particles of micron and nanoscale size. This result is a consequence of the action of thermal stresses in combination with the implantation of helium ions into the material as well as the possible influence of shock waves generated in the Si target during hard irradiation regimes. The presence of copper, carbon, and nitrogen on the silicon surface after its beam-plasma treatment, as well as an increase in the electrical resistivity on the irradiated side and backside of the plate, is noted. The results obtained are discussed taking into account the features of the experiments in the PF setup. [ABSTRACT FROM AUTHOR]

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To improve the accuracy and speed of detecting crystal shape during the growth of Czochralski silicon single crystals, a straight line detection method is proposed based on the multiple signal classification (MUSIC) algorithm. First, in order to obtain multi-snapshot signals to meet the MUSIC algorithm requirements, we add multiple sets of zero-mean Gaussian noise. These sets of noise obey the same distribution (i.e., zero-mean Gaussian). This supports the generation of multiple images, which are converted into multi-snapshot signals of a virtual sensor array. These multi-snapshot signals are used to construct a far-field model; the tilt angle estimation problem of a straight line is transformed into a search problem, which seeks the direction of arrival in the virtual input sources. Finally, a near-field model is constructed, and the estimated potential offsets corresponding to the tilt angles are calculated to determine the parameters of the straight line. The simulation and engineering experiments show that the proposed method can accurately and quickly detect the tilt angle and the offset of the straight line, and is superior to existing methods. [ABSTRACT FROM AUTHOR]

Graphical abstract For nanosecond laser irradiation, after melting happens the redistribution of nanosecond laser energy lead to shock effect into the high temperature base materials. The influence factors, including base material temperature, laser intensity, and crystal orientation, on the dynamic response of silicon single crystal are investigated. Highlights • The thermal-mechanical interaction during nanosecond laser ablation was studied. • Laser induced shock effect is not only studied by MDS, but also theoretically studied, and good agreement can be found. • It directly investigated the mechanism of dynamic response of silicon single crystal during laser ablation. • The physical foundations of laser induced damages are investigated. Abstract The dynamic behaviors of silicon single crystal under nanosecond laser irradiation are investigated. To comprehensively study the dynamic behaviors of silicon single crystal under laser irradiation, the effects of laser intensity, temperature, and crystal orientation are directly studied using molecular dynamics simulations. The relevant physical backgrounds are learned under the help of Rankine-Hugoniot theory. It shows the amplitude of laser induced shock wave will increase with the increase of laser intensity. The shock velocity can be greatly affected by lattice orientation, temperature and the amplitude of shock wave. With the increase of shock pressure and temperature, laser induced damages, including virtual melting, pre-melting, shear belt become severe. And laser induced damages inversely result in shock attenuation. It also can be found that damages grow along the 〈1 1 1〉 crystal planes, due to the concentration of dislocation belt along these planes. Our work sheds insight into the dynamic behaviors of silicon single crystal under the irradiation of nanosecond laser. [ABSTRACT FROM AUTHOR]

Stress perturbations and material defects can significantly affect the fracture initiation and propagation behaviors in brittle materials. In this work, we show that (110)[110] cleavage in silicon deflects onto (111) plane in the presence of contact stresses. The deflection is however not permanent as the crack returns to the (110) plane after a certain length of propagation, even in the case where the crack velocity is up to 78% of the Rayleigh wave speed. The recovery behavior indicates that the (110)[110] cleavage is invariably prevailing when perpendicular to the maximum stress. Following this indication, it can be concluded that the observed (110)[110]–(111) deflection in previous literature is more likely driven by the external disturbance rather than the crack velocity induced toughness evolution. We also highlight that the extra energy for the (110) recovery is minimized at the expense of a large propagation distance upon the plane switch. [ABSTRACT FROM AUTHOR]

The uniformity of the lattice spacing of silicon crystals was evaluated by the self-referenced lattice comparator with a resolution of 3 × 10−9. Lattice strain measurements were performed for the sample 10.5 cut from 28Si ingot (Avo28), which was used to determine the Avogadro constant. The mapping results for samples 4.R1, XINT, and 9.R1 performed in the previous works have also been re-evaluated. The 4.R1 in the seed side of the ingot and the XINT in the middle of the ingot have small distribution of lattice spacing. The standard deviations of the lattice spacing distribution for the 4.R1 and XINT were 4.8 × 10−9 and 5.5 ×10−9, respectively. In contrast, the 9.R1 and the 10.5 samples cut from the tail side of the ingot have a larger distribution of lattice spacing. These lattice spacing distributions in the ingot are consistent with the impurity distribution in the ingot. [ABSTRACT FROM AUTHOR]

In this article, we report special fracture initiation behavior of (110) cleavage in silicon single crystal. It is found that the static energy release rate always exceeds the material toughness upon crack initiation. According to high-speed imaging measurements and fractographies, it is found that the crack has an important initial velocity, i.e. up to 3000 m/s, and then reaches the steady-state propagation regime very quickly. The experimentally revealed initial crack velocity is in good agreement with estimation from the energy flux at crack initiation. [ABSTRACT FROM AUTHOR]

The effect of the depths of two partitions on the heat, flow, and oxygen transport during the CCz growth of an 8-inch diameter silicon crystal is numerically investigated. A crucible in which two partitions are immersed in the silicon melt is so-called a triple-crucible. The different depths of two partitions change the effective wall surface area, which is the main source of oxygen at the growth interface, melt motion, and heat transfer within the crucible. The diffusion and convection of oxygen from the partitions and crucible wall towards the free surface and the crystal-melt (c-m) interface are also affected. The amount of oxygen that dissolves from the effective wall surface into the melt is proportional to the surface temperature and the surface area. The choice of at least one long partition will prevent the entry of unmelted granular silicon into the melt region under the c-m interface. Comparison of various cases shows that when the partition near the c-m interface is longer (90 mm) and the partition near the crucible sidewall is shorter (40 mm), the power consumption and the content of oxygen along the growth interface are lower. [ABSTRACT FROM AUTHOR]

Fracture mechanics at micro- and nano-scale has become a very attractive topic in the last years. However, the results are still few, mostly because of the lack of effective analytical tools and of the difficult to conduct experimental tests at those scales. In this study, the authors report preliminary analysis on the application of the Strain Energy Density (SED) method at nano-scale. In detail, starting from mechanical properties experimentally evaluated on small single crystal silicon cracked specimens, a first evaluation of the control volume due to a nano-size singular stress field is carried out. If the extension of the SED approach at micro- nano-scale is given in near future, an easy and fast tool to design against fatigue will be provided for micro- nano-devices such as MEMS and NEMS, resulting in a significant technological impact and providing an easy and fast tool to conduct static and fatigue assessment at micro- and nano-scale. [ABSTRACT FROM AUTHOR]

The homogeneity of the lattice spacing of silicon single crystals was investigated by a self-referenced lattice comparator. Strain measurements were performed on single crystals from an ^28 Si ingot (Avo28), which was used to determine the Avogadro constant. A swirl pattern was observed for sample 9.R1 cut from the tail side of the Avo28 ingot. The lattice spacing distribution of seed-side sample 4.R1 was smooth and homogeneous. The lattice spacing distribution was larger for the sample with higher impurities of carbon and oxygen. [ABSTRACT FROM PUBLISHER]

Ellipse fitting is widely applied in the fields of computer vision and automatic industry control, in which the procedure of ellipse fitting often follows the preprocessing step of edge detection in the original image. Therefore, the ellipse fitting method also depends on the accuracy of edge detection besides their own performance, especially due to the introduced outliers and edge point errors from edge detection which will cause severe performance degradation. In this paper, we develop a robust ellipse fitting method to alleviate the influence of outliers. The proposed algorithm solves ellipse parameters by linearly combining a subset of (“more accurate”) data points (formed from edge points) rather than all data points (which contain possible outliers). In addition, considering that squaring the fitting residuals can magnify the contributions of these extreme data points, our algorithm replaces it with the absolute residuals to reduce this influence. Moreover, the norm of data point errors is bounded, and the worst case performance optimization is formed to be robust against data point errors. The resulting mixed l1\--l2 optimization problem is further derived as a second-order cone programming one and solved by the computationally efficient interior-point methods. Note that the fitting approach developed in this paper specifically deals with the overdetermined system, whereas the current sparse representation theory is only applied to underdetermined systems. Therefore, the proposed algorithm can be looked upon as an extended application and development of the sparse representation theory. Some simulated and experimental examples are presented to illustrate the effectiveness of the proposed ellipse fitting approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper compares the physical and chemical properties of hydrogen-passivated Si(111) single crystalline surfaces prepared by two main chemical preparation procedures. The modified RCA cleaning is commonly used to prepare atomically flat stable surfaces that are easily identifiable spectroscopically and are the standard for chemical functionalization of silicon. On the other hand electronic properties of these surfaces are sometimes difficult to control. A much simpler silicon surface preparation procedure includes HF dipping for a short period of time. This procedure yields an atomically rough surface, whose chemical identity is not well-defined. However, the surfaces prepared by this approach often exhibit exceptionally attractive electronic properties as determined by long charge carrier lifetimes. This work utilizes infrared spectroscopy and X-ray photoelectron spectroscopy to investigate chemical modification of the surfaces prepared by these two different procedures with PCl5 (leading to surface chlorination) and with short- and long-alkyl-chain alkenes (1-decene and 1-octodecene, respectively) and follows the electronic properties of the starting surfaces produced by measuring charge-carrier lifetimes. [Copyright &y& Elsevier]

In the diameter control system of silicon single crystal growth, the variation of the diameter of the aperture (i.e., a halo with high brightness, which appears at the junction of a solid crystal and a liquid solution) is consistent with the change in the diameter of the growing crystal. Therefore, the diameter of the aperture can be used as a control variable for adjusting the casting speed and temperature so that the grown silicon single crystal approximates to a perfect cylinder. It is obvious that the measured diameter of the current aperture plays an important role in the diameter control system of silicon single crystal growth. In fact, the obtained aperture image from a charge-coupled device camera is a halo of ellipses instead of circles. To estimate the diameter (or radius) of the elliptical aperture, we propose a Bayesian approach, in which a Bayesian model is derived to define a posterior distribution for the unknown parameters. This distribution is too complicated for analytical extraction of moments to sample directly. An efficient computational algorithm based on a Markov chain Monte Carlo method is derived to estimate the posterior distribution and draw samples from the distribution. Comparing with the classical Hough transform-based algorithm and the direct least-squares fitting method, the proposed algorithm has higher estimation accuracy. Some simulated and experimental examples are presented to illustrate the algorithm's effectiveness. [ABSTRACT FROM PUBLISHER]

Tip-enhanced Raman spectroscopy (TERS) has been used to obtain the Raman signal of surface species on silicon single crystal surfaces without the necessity for surface enhancement by addition of Ag nanoparticles. By illuminating the hydrogenterminated silicon surface covered with a droplet of 4-vinylpyridine with UV light, a 4-ethylpyridine modified silicon surface can be easily obtained. By bringing a scanning tunneling microscope (STM) Au tip with a nanoscale tip apex to a distance of ca. 1 nm from the modified silicon surface, enhanced Raman signals of the silicon phonon vibrations and the surface-bonded 4-ethylpyridine were obtained. The Raman enhancement factor was estimated to be close to 107. By comparing the surface-enhanced Raman scattering (SERS) signal obtained after surface enhancement with Ag nanoparticles and the TERS signal of the surface, the advantage of TERS over SERS for characterizing the surface species on substrates becomes apparent: TERS readily affords vibrational information about the system without disturbing it by surface enhancement. In this sense, TERS can be considered a truly non-invasive tool which is ideal for characterizing the actual surface species on substrates. [ABSTRACT FROM AUTHOR]

Abstract: Due to the lack of diffusion data of Li in solid silicon at room temperature, we decided to determine the diffusion coefficient of Li in solid silicon by the use of a bipolar cell system where a sheet of silicon sample is sandwiched as the bipolar electrode between two facing bipolar cell compartments. In both of the cell compartments counter and reference electrodes were mounted. In one of the cell compartments (Cell A), an electrolyte containing Li+ was filled, while the facing compartments (Cell B) was filled with an electrolyte containing Na+ instead of Li+, and a needle-like W/WOx electrode, which can sense the Li+ concentration, was mounted near the surface of the bipolar electrode. At first the potential of the bipolar electrode in Cell A was set at the natural potential, and the potential in Cell B was polarized at a sufficiently positive potential, then the potential in Cell A was set at a definite cathodic potential and the signal–time curve of the W/WOx electrode in Cell B was recorded. During the cathodic polarization in Cell A Li+ was incorporated in the bipolar electrode, migrating from the Cell A side to the Cell B side, and transferred to the electrolyte in Cell B compartment. As a result, the signal of the Li+ sensing electrode began to increase after a time delay which corresponds to the time for Li to migrate in the bipolar electrode from the Cell A side to the Cell B side. From the value of time delay we could calculate the diffusion coefficient by the use of a diffusion equation where a parameter of the thickness of the bipolar electrode is involved. The obtained value of the diffusion coefficient of the vacuum-deposited film was 10−9 cm2 s−1 independent of the polarization potential. In contrast, the silicon single crystal sample obtained by thinning the silicon single crystal wafer gave about 2×10−11 cm2 s−1. The larger value obtained with the vacuum-deposited film is attributed to the loose structure of the deposited film. [Copyright &y& Elsevier]

Abstract: A preliminary experiment for producing narrow-photon-energy cone-beam X-rays using a silicon single crystal is described. In order to produce low-photon-energy X-rays, a 100-μm-focus X-ray generator in conjunction with a (111) plane silicon crystal is employed. The X-ray generator consists of a main controller and a unit with a high-voltage circuit and a microfocus X-ray tube. The maximum tube voltage and current were 35kV and 0.50mA, respectively, and the X-ray intensity of the microfocus generator was 48.3μGy/s at 1.0m from the source with a tube voltage of 30kV and a current of 0.50mA. The effective photon energy is determined by Bragg''s angle, and the photon-energy width is regulated by the angle delta. Using this generator in conjunction with a computed radiography system, quasi-monochromatic radiography was performed using a cone beam with an effective energy of approximately 17keV. [Copyright &y& Elsevier]

Fracture toughness of silicon crystals has been investigated using indentation methods, and their surface energies have been calculated by molecular dynamics (MD). In order to determine the most preferential fracture plane at room temperature among the crystallographic planes containing the ⟨001⟩, ⟨110⟩ and ⟨111⟩ directions, a conical indenter was forced into (001), (110) and (111) silicon wafers at room temperature. Dominant {110}, {111} and {110} cracks were introduced from the indents on (001), (011) and (111) wafers, respectively. Fracture occurs most easily along {110}, {111} and {110} planes among the crystallographic planes containing the ⟨001⟩, ⟨011⟩ and ⟨111⟩ directions, respectively. A series of surface energies of those planes were calculated by MD to confirm the orientation dependence of fracture toughness. The surface energy of the {110} plane is the minimum of 1.50 Jm-2 among planes containing the ⟨001⟩ and ⟨111⟩ directions, respectively, and that of the {111} plane is the minimum of 1.19 Jm−2 among the planes containing the ⟨011⟩ direction. Fracture toughness of those planes was also derived from the calculated surface energies. It was shown that the K IC value of the {110} crack plane was the minimum among those for the planes containing the ⟨001⟩ and ⟨111⟩ directions, respectively, and that K IC value of the {111} crack plane was the minimum among those for the planes containing the ⟨011⟩ direction. These results are in good agreement with that obtained conical indentation. [ABSTRACT FROM AUTHOR]

Computer simulations of the dislocation density during Czochralski (CZ) single crystal growth were performed for silicon crystals with 8-inch or 10-inch diameter using a finite element computer code developed by the authors. In the computer code, a dislocation kinetics model called the Haasen-Sumino model was used for the constitutive equation of a crystal at elevated temperatures. The computer code provides the dislocation density distributions and stress distributions during the CZ growth process. In the simulations, two values for the Young’s modulus for the silicon single crystal were used in order to examine the effect of the Young’s modulus on the dislocation density. [ABSTRACT FROM AUTHOR]

When a dynamic crack front travels through material heterogeneities, elastic waves are emitted, which perturb the crack and change the morphology of the fracture surface. For asperity-free crystalline materials, crack propagation along preferential cleavage planes is expected to present a smooth crack front and form a mirror-like fracture surface. Surprisingly, we show here that in single crystalline silicon without material asperities, the crack front presents a local kink during high-speed crack propagation. Meanwhile, local oscillations of the crack front, which can move along the crack front, emerge at the front kink position and generate periodic fracture surface corrugations. They grow from angstrom amplitude to a few hundred nanometers and propagate with a long lifetime at a frequency-dependent speed, while keeping a scale-independent shape. In particular, the local front oscillations collide in a particle-like manner rather than proceeding with a linear superposition upon interaction, which presents the characteristic of solitary waves. We propose that such a propagating mode of the crack front, which results from the fracture energy fluctuation at a critical crack speed in the silicon crystal, can be considered as nonlinear elastic waves that we call "corrugation waves.", Competing Interests: The authors declare no competing interest.