Finite element analysis of dislocation density during bulk single crystal growth (effect of doping atoms in InP single crystal)

A computer code for simulation of dislocation density in a bulk single crystal during liquid encapsulated Czochralski (LEC) or Czochralski (CZ) growth process. In this computer code, the shape of crystal–melt interface and the temperature in a crystal at an arbitrary time were determined by linear interpolation of the results that were discretely obtained by heat conduction analysis of a CZ single crystal growth system. A dislocation kinetics model called Haasen–Sumino model was used as a constitutive equation. In this model, creep strain rate is related to dislocation density, and this model extended to multiaxial stress state was incorporated into a finite element elastic creep analysis program for axisymmetric bodies. Dislocation density simulations were performed using this computer code for InP bulk single crystals with about 8″ in diameter. In the analysis, the effect of dopant atoms on the dislocation density was examined. In the case of a low doped InP single crystal, dislocations are distributed in the whole of the crystal. On the other hand, in the case of a highly doped InP single crystal, dislocations are localized at both the central and peripheral regions of the crystal.     

晶格畸变检测仪研究碳化硅晶片中位错缺陷分布

利用晶格畸变检测仪研究了SiC晶片位错分布情况,通过对熔融KOH腐蚀后的SiC晶片进行全片或局部扫描,从而得到完整SiC晶片或局部区域的位错分布.与LEXT OLS40003D激光共聚焦显微镜扫描腐蚀图进行比较,晶格畸变检测仪扫描腐蚀图可以将晶片上位错腐蚀坑信息完全呈现出来,且根据腐蚀坑呈现的颜色及尺寸大小,可以分辨出...     

Dislocations and dislocation reduction in space grown GaSb

The behaviour of dislocations in GaSb crystals grown in space both from a stoichiometric melt (floating zone method, FZ) and a Bi solution (floating solution zone, FSZ) respectively, is studied. Predominantly straight 60° dislocations with Burgers vectors of the type b = a/2 <110> in (111) glide planes are identified. In the 20 mm long FZ single crystal the linear growing out of the dislocations is observed which reduces the dislocation density in the centre of the crystal to values below 300 cm^–2. The Bi incorporation in the FSZ crystal results in a misfit between seed and grown crystal and in a network of misfit dislocations at the interface. Thermocapillary convection during growth as well as the surface tension may be the reasons for the presence of curved dislocations and the higher dislocation density within a 1 – 2 mm border region at the edges of both of the crystals. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Specific features of the formation of dislocation structure in gallium arsenide single crystals obtained by the Czochralski method

The influence of the deviation of seed orientation from the [100] direction on the formation of a dislocation structure of gallium arsenide single crystals grown by the Czochralski method has been revealed. The intensive multiplication of dislocations and formation of a block structure occur at deviation by an angle of more than 3° in the region that is radially shifted to one of crystal sides. The linear density of dislocations in the walls changes from 1 × 10⁴ cm^–1 in low-angle boundaries to 6 × 10⁴ cm^–1 in subboundaries.     

An In-situ Investigation of the Creep Mechanisms of Aluminium at Intermediate Temperatures

In-situ deformation experiments are performed at 150 °C and 200 °C after a macroscopic creep test in polycrystalline aluminium. The significant microscopie events which take place during the constant strain rate stage of creep are subboundary migration and destruction, dislocation multiplication, interaction of individual dislocations with the three dimensional network inside the cells and with the subboundaries. The observations are discussed in terms of different models interpreting the measured activation energy and area.     

Propagation behavior of threading dislocations during physical vapor transport growth of silicon carbide (SiC) single crystals

The dislocation formation and propagation processes in physical vapor transport (PVT) grown 4H silicon carbide (4H–SiC) single crystals have been investigated using defect selective etching and transmission electron microscopy (TEM). It was found that while the growth initiation process generally increased the density of threading dislocations in the grown crystal, for certain areas of the crystal, threading dislocations were terminated at the growth initiation. Foreign polytype inclusions also introduced a high density of dislocations at the polytype boundary. In the polytype-transformed areas of the crystal, almost no medium size hexagonal etch pits due to threading screw dislocations were observed, indicating that the foreign polytype inclusions had ceased the propagation of threading screw dislocations. Based on these results, we argued the formation and propagation of the threading dislocations in PVT grown SiC crystals, and proposed the dislocation conversion process as a plausible cause of the density reduction of threading dislocations during the PVT growth of SiC single crystals.     

Effects of the Crystal Diameter on the Dislocation Density in KCl Crystals Grown by the Czochralski Method

The dependence of dislocation density on the crystal diameter of the Czochralski grown KCl crystals (both pure and Sr doped) was investigated by the method of the etch pit and X-ray topograph. (1) The dislocation density drastically decreased with the decrease in diameter (D) for small D (D < 2 mm, Fig. 2). (2) The dislocation density in the Sr doped crystal was lower than that of pure component in the diameter examined. (3) Many helical dislocations and dislocation loops were observed in the thin crystals (D ∼ 0.5 mm) of the pure KCl and Sr doped one, respectively, by X-ray projection topography. These results were discussed in connection with the dislocation generation mechanisms due to thermal stresses or supersaturated point defects.     

Analysis of X‐ray extinction in crystals with inhomogeniously distributed dislocations

The secondary extinction theory of Zachariasen for mosaic crystals as well as the formalism of Becker&Coppens have been used for substructure analysis (lattice disorientations, block size, density of excess dislocations, etc.) in crystals with inhomogeniously distributed dislocations in the Bragg case of diffraction geometry. In the case of large crystals D_S ≫ Λ_hkl the mean total density ρ_D of randomly distributed dislocations was also estimated taking into account additionally the primary X‐ ray extinction treatment. In this connection two cases are considered: I) pure secondary extinction related to arrangement of dislocation walls and II) mixed extinction in crystals with large subgrains related to randomly distributed dislocations and arrangement of dislocation walls. In order to check the considerations, the experimental and calculated data were compared for Be (model I) and Cu (model II) single crystals. The weakly distorted single crystals of Be and Cu were experimentally investigated in the Bragg case of diffraction geometry using Cu Kα₁ radiation by means of double crystal diffractometer. A new experimental procedure was proposed. Using alternative technique for substructure analysis (for instance EBSD) the reliability of analysis based on extinction phenomenon in weakly distorted single crystals has been checked. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The influence of the mode of hardness increase on the dislocation mobility of the crystal with NaCl lattice

The influence of the three types of hardening (1 – radiation hardening; 2 – the hardening in lowering of temperature; 3 – the hardening in the series of KCl-NaCl-NaF-LiF-MgO crystals) on the length of dislocation rosettes arms is investigated. This length characterizes the dislocation ensemble mobility in the nonuniform stress field. It is shown that the change of microhardness and that of mobility of dislocations correlate well while introducing the radiation damage. In contrast to it the microhardness rise does not cause marked decrease of the length of rosettes arms in the other two cases. The conclusion is made that the length of rosettes arms depends not only upon the value of crystal hardness but also upon the mode of origin of this value. On the (001) plane of the crystals under investigation it is found that the length of dislocation rosettes arms depends on the indentor orientation. A possible explanation of this phenomenon is proposed.     

Helical dislocations produced by low temperature thermocycling in a Ti–Al Alloy

By transmission electron microscopy (TEM), the structural state of a Ti–Al alloy subjected to low temperature thermocycling from 300 to 77 K has been investigated. As the result of this observation, helical dislocations were revealed with the density 10⁹ cm⁻³. These were generated mainly by grain boundaries or subboundaries. Their formation is thought to be associated with thermomechanical stresses arising during thermocycling. Thermomechanical stresses at the interface of neighbouring grains, estimated with making allowance for the anisotropy of the linear expansion coefficient, appeared to be about 7 kg/mm². It is assumed that helical dislocation formation is one of the ways in which local internal stresses are relieved.     

TEM and X-ray investigations of defect structure of PbSnTe crystal

The Pb_0.8Sn_0.2Te single crystal grown by the Bridgman technique was examined by X-ray and TEM methods. The X-ray reflection topography revealed that the PbSnTe crystal consisted of monocrystallinic blocks with linear dimensions of 1–5 mm separated by low angle boundaries of tilt-twist character. “As grown” defects observed by TEM method have been identified as single perfect dislocations and dislocation pairs. A mean density of dislocations inside the crystal blocks was no more than 10³ cm⁻². Except “as grown” defects rows of mobile dislocations were observed. All of dislocations lines were characterized by the same type of Burgers vector, i.e. b = 1/2a〈110〉.     

Plastische Verformung von Siliziumeinkristallen unterschiedlicher Ausgangsversetzungsdichte im Streckgrenzenbereich

Floating-zoned Silicon crystals orientated for single slip both dislocation-free and with grown-in dislocations (EPD₀ = 6,5 · 10⁴ cm⁻²) were dynamically deformed in compression in the temperature range 1120 … 1300 K up to the lower yield point. The dislocation structure of plastically deformed crystals (T = 1138 K; a₀ = 1,45 · 10⁻⁴ s⁻¹) was examined by etching and high-voltage electron microscopy. The crystals exhibit essential differences in deformation behaviour and in the resulting dislocation structure. Typical for the dislocation-free basic material are (i) an inhomogeneous deformation in the range of the upper yield point (ii) a greater portion of sessile lomer dislocations at the lower yield point in relation to the crystal with grown-in dislocations. The measured stresses were related to those values calculated from structure data by employing plasticity theory of diamond-like semiconductors.     

Antistructure disorder and its relation to dislocations in III–V semiconductors

Intimate relationship between antistructure defects and dislocations occurs in GaAs which manifests itself as: (i) appearing of spatial correlation between grown-in dislocations and the EL2 defects (component of the latter are As_Ga antisites), (ii) similar suppression of the concentration of EL2 and dislocation density due to the doping with donor impurities, (iii) generation of As_Ga antisites during the plastic deformation of a crystal. Al these effects can be understood in terms of the dislocation-mediated generation of As_Ga antisites via absorption of As_i interstitials at dislocation jogs. Large anion (cation) precipitates appearing at dislocations are pointed out to be important for both antisite and dislocation generation under certain conditions.     

Lattice strain and misfit dislocations in GaAs-GaAlAsP heterojunctions

The lattice strain and misfit dislocations in a GaAs-GaAlAsP heterojunction were examined. The change in lattice strain with the composition ratio or the position of the crystal was measured, and it was found that some of the misfit dislocations introduced in the heterojunction were edge-type dislocations. The critical thickness of the epitaxial layer for the generation of misfit dislocations was also measured. The critical differential strain between the atomic layers was on the order of several angstroms. The distribution of lattice strain was analyzed by a two-dimensional simple cubic lattice model, and the distribution of differential strain was examined.     

The X-ray topographic investigation of defect distribution in dendritic silicon crystals along their cross section

Using the modified method of limited X-ray topographs the distribution of defects along the silicon dendritic thickness was investigated. It is found that there are two dislocation sources in the given crystals, one of which acts near the surface and generates the loop-shaped dislocations in the centre of the sample. The other source located in the interior parts of the crystal creates the edge defect pilings.     

Untersuchungen zur Neubildung von Versetzungen bei der tiegelfreien Züchtung von Silizium-Einkristallen

During the crucible free growing of dislocation free silicon monocrystals frequently spontaneous generations of new dislocations are observed which cannot be attributed to perceptible reasons. By means of X-ray topographic and metallographic methods it is tried to localize the origin of these dislocation generations in the crystal. Their generation in areas of the crystal surface permits to suppose the existence of a temperature stress mechanism, which releases the generation of new dislocations in the plastic regions of the just formed crystal in consequence of high shocks of stress.     

The defect structure of ammonium sulphate single crystals

The defect structure of larger ammonium sulphate crystals, grown from aqueous solutions, has been studied by means of X-ray diffraction topography after Lang's method. Several types of dislocations were identified. Moreover it was found that no relationship exists between growth rate and dislocation density, which implies that crystal growth proceeds via two-dimensional nucleation. No difference was found in the defect structure of crystals grown from pure water solutions and from aqueous solutions with 10 – 20% glycerine as additive: In both cases neither growth bands nor sector boundaries were found. On the other hand, crystals grown in aqueous solutions contaminated with Mn²⁺ and Fe³⁺ revealed growth bands and for Fe³⁺ a mosaic-like structure.     

Efficiency of dislocations as sinks of radiation defects in fcc copper crystal

The sink efficiency of perfect dislocations for self-point defects (interstitials and vacancies) in fcc copper crystal has been calculated by the kinetic Monte Carlo method in a temperature range of 293–1000 K and a range of dislocation densities from 1.3 × 10¹² to 3.0 × 10¹⁴ m^?2. Screw, mixed, and edge dislocations with a Burgers vector 1/2<110> in different slip systems are analyzed. The interaction energies of self-point defects with dislocations are calculated using the anisotropic theory of elasticity. Analytical expressions are proposed for the dependences of the calculated values of dislocation sink efficiency on temperature and dislocation density.     

Extended defects in III-V semiconductor compounds

A new class of defects characterized by inherent non-exponential capture and emission processes was observed. A theory – based on the potential barrier model – is proposed to describe the measured DLTS and capacitance transient data. It is argued that these defects are related to dislocations or dislocation generated lattice defects.     

Plastic bend in a growing crystal

In case of nonlinear axial temperature distribution the relaxation of thermoelastic stresses results in the plastic bend of the growing crystal, i. e. in the generation of a residual lattice curvature equal to ϱ b . Based on results from Billig and from Indenbom the author presents estimations of dislocation densities (ϱ) (i. e. residual lattice curvature) taking into account an elastic limit differing from zero. It is shown that sign and value of the residual lattice curvature may be effectively used as criteria pointing out how thermal conditions should be changed for abtaining more perfect crystals. This approach application allowed to grow larger KCl single crystals (300 mm in diameter more than 100 kg by weight) with better structure perfection (specific subboundaries surface 2—3 cm²/cm³, mean subgrain dimension 0.6—1 cm, mean mutual disorientation of subgrains of not more than 6′).