Dislocation Density In Crystals Research Articles

Growing indium antimonide single crystals with a diameter of 100 mm by the modified Chochralsky method

At present, all over the world there is a tendency to increase the diameters of single crystals of both elementary semiconductors and semiconductor compounds. There are reports indicating the use of single crystals of III-V semiconductors with a diameter of four to six inches. So far, indium antimonide single crystals up to 75 mm in diameter have been obtained in Russia.Indium antimonide is the element base of the broadest field of solid-state electronics — optoelectronics. On its basis, linear and matrix photodetectors are manufactured, operating in the spectral wavelength range of 3-5 microns, which are used as a viewing element in thermal imaging systems.In this work, we selected the thermal growth conditions and obtained indium antimonide single crystals 100 mm in diameter in the crystallographic direction [100]. The solution of this problem has made it possible to significantly increase the yield of suitable photodetectors.Single crystals 100 mm in diameter were grown by the Czochralski method in a two-stage process. The design of the graphite heating unit was enlarged and matched to a working crucible with a diameter of 150 millimeters and a load of 4.5-5 kg.The Van der Pauw method was used to measure the electrical properties of the obtained single crystals, which corresponded to the standard parameters of undoped indium antimonide. Using an optical microscope, the etching pits were counted using the 9-field method. The dislocation density in crystals with a diameter of 100 mm was ≤ 100 cm-2 and corresponded to the values ​for crystals of 50 mm.

Degenerate Structure of Transformation Twins and Estimation of Dislocation Density in Martensite Crystals

In the dynamic theory of martensitic transformations, the wave mechanism of controlling martensite crystal growth is determined by the superposition of wave beams of quasi-longitudinal (or longitudinal) waves carrying the “tensile–compression” deformation in the orthogonal directions. The wave beam formation is considered to be a result of the formation of excited (vibrational) states. The existence of transformation twins is interpreted as a result of a matched propagation with respect to long-wave (l waves) and short-wave (s waves) shifts. The matching condition is analyzed for the γ–α martensitic transformation in iron-base alloys. It is shown for the first time that the transition to a degenerate twin structure with the allowance for the medium discreteness enables one to estimate the dislocation density in crystals with habit {557}, which agrees with that observed experimentally.

Вырожденная структура двойников превращения и оценка плотности дислокаций мартенситных кристаллов

Abstract In the dynamic theory of martensitic transformations, the wave mechanism of controlling martensite crystal growth is determined by the superposition of wave beams of quasi-longitudinal (or longitudinal) waves carrying the “tensile–compression” deformation in the orthogonal directions. The wave beam formation is considered to be a result of the formation of excited (vibrational) states. The existence of transformation twins is interpreted as a result of a matched propagation with respect to long-wave ( l waves) and short-wave ( s waves) shifts. The matching condition is analyzed for the γ–α martensitic transformation in iron-base alloys. It is shown for the first time that the transition to a degenerate twin structure with the allowance for the medium discreteness enables one to estimate the dislocation density in crystals with habit {557}, which agrees with that observed experimentally.

Effect of Crystallization Front Shape on the Dislocation Density in Germanium Single Crystals

The effect of crystallization front shape on the dislocation density in Ge single crystals with a diameter of 100 mm, grown by the Czochralski method, has been studied. The dislocation density in crystals with a convex crystallization front is found to be considerably higher. The average dislocation density in experimental ingots with deviation of crystallization front shape from flat in the range from –1.5 to +1.5 mm increases from 75 to 1000 cm–2 and from 75 to 700 cm–2 in the cases of convex and concave fronts, respectively. Minimum dislocation densities are observed for a flat or slightly concave front.

Analysis of microstructural evolution properties based on laser shock peening

Laser shock peening changes the microstructure of a metal surface and causes the severe plastic deformation. This paper studied the changes in the crystal dislocation density and grain size of the microstructure after laser shock peening. The finite element method was used to calculate the deformation of the LY2 aluminum after the laser shock peening under the different number of impact times. Through a subroutine programming, the microstructure prediction programming was embedded into the finite element model to analyze the dislocation density and grain size of the metal. Based on the simulation of the metal microstructure deformation under different laser impact times, it was found that with the increase of the impact times, the growth rate of the plastic deformation layer and the severe plastic deformation layer decreased. At the same time, the grain size refinement rate gradually declined. When the impact times exceeds four, the depth of the severe plastic deformation layer and the grain size have almost no change.

Formal derivation and existence result of an approximate model on dislocation densities

AbstractIn this work, we are interested in a mathematical problem arising from the dynamics of dislocation densities in crystals. The model, originally developed by Groma, Czikor, and Zaiser in [], is a coupled singular parabolic system that describes the motion of dislocations in a bounded crystal, taking into account the short‐range interactions and the effect of exterior stresses. We show the derivation and the short time existence and uniqueness of a regular solution in a Hölder space using a fixed point argument and a particular comparison principle.

Global BV solution for a non-local coupled system modeling the dynamics of dislocation densities

In this paper, we study a non-local coupled system arising in the modeling of the dynamics of dislocation densities in crystals. For this system, the global existence and uniqueness are available only for continuous viscosity solutions. In the present paper, we investigate the global time existence of this system by considering BV initial data. Based on a fundamental uniform BV estimate and the finite speed of propagation property of this system, we show, in a particular setting, the global existence of discontinuous viscosity solutions of this problem.

Numerical analysis of dislocation density and residual stress in a GaN single crystal during the cooling process

In this study, we investigate the influence of thermal stress on the dislocation density and residual stress in GaN single crystals by numerical analysis. The results show that the dislocation density increases, but the thermal stress does not decrease, and the residual stress increases throughout the cooling process. The reason for this phenomenon is that the dislocation density is higher at the periphery of the crystal and distribution of dislocation density in the crystal is inhomogeneous. Then, the increase of dislocation does not allow the thermal stress on the entire crystal to relax.

Defect-and-impurity state of type Ib diamond single crystals of cubic habit

Type Ib diamond single crystals of size to 5–6 mm and to 2.4 carats in weight have been grown at high pressures and temperatures. The defect-and-impurity state and dislocation structures of these crystals have been studied using the IR and optical microscopies as well as the method of the selective etching. To produce type Ib crystals of cubic habit has been made possible by the minimization of the growing temperature. Defect regions in the form of a cone with the basis 0.2–1.8 mm in diameter and 0.5–2.5 mm in height are contained by these crystals. The study of the cone-shaped defect regions using the selective etching showed that at the exposure on the faces the etching pits are of the tetragonal shape and the dislocation density in them exceeds the density of dislocations in crystals that were grown under the usual conditions by 70 to 100 times. The observed defect regions are formed in the course of the diamond crystals growth as the temperature decreases by ~ 30–35°C at the crystallization front because of the increasing heat sink in the direction of a seed crystal.

Shear banding and its contribution to texture evolution in rotated Goss orientations of BCC structured materials

Due to progressive deformation, the dislocation densities in crystals are accumulated and the resistance of grains to further deformation increases. Homogeneous deformation becomes energetically less favorable, which may result for some orientations in strain localization. In-grain shear banding, a typical kind of localized deformation in metals with BCC crystal structure, has been accounted for by the geometric softening of crystals. In this study, the occurrence of shear bands in rotated Goss ({110}<110>) orientations of Fe-Si steel is predicted by crystal plasticity simulations and validated by EBSD measurements. It was observed and confirmed by crystal plasticity modeling that such shear bands exhibit stable cube orientations The orientation evolution of crystals in shear bands and its impact on annealing texture of materials are also described.

X-ray extinction changes due to dislocations

A correct interpretation of the diffraction phenomenon in crystals with low dislocation content, for which the kinematical scattering theory does not yield any reasonable results, was carried out by X-ray extinction treatments. Different approaches to investigating the dislocation-induced X-ray extinction changes are reviewed and the applicability of the statistical dynamical theory to analysis of the substructure characteristics of crystals is discussed. A relationship between the scattering amplitudes and the dislocation density in crystals is established by using pair correlation functions. A procedure for determination of the substructure characteristics by means of measurements of the integrated intensities is proposed. The tests illustrate satisfactory agreement of the investigated approaches with experimental data.

Existence and uniqueness for a nonlinear parabolic/Hamilton–Jacobi coupled system describing the dynamics of dislocation densities

We study a mathematical model describing the dynamics of dislocation densities in crystals. This model is expressed as a 1D system of a parabolic equation and a first order Hamilton–Jacobi equation that are coupled together. We examine an associated Dirichlet boundary value problem. We prove the existence and uniqueness of a viscosity solution among those assuming a lower-bound on their gradient for all time including the initial time. Moreover, we show the existence of a viscosity solution when we have no such restriction on the initial data. We also state a result of existence and uniqueness of entropy solution for the initial value problem of the system obtained by spatial derivation. The uniqueness of this entropy solution holds in the class of bounded-from-below solutions. In order to prove our results on the bounded domain, we use an “extension and restriction” method, and we exploit a relation between scalar conservation laws and Hamilton–Jacobi equations, mainly to get our gradient estimates.

Well-Posedness Theory for a Nonconservative Burgers-Type System Arising in Dislocation Dynamics

In this work we study a system of nonconservative Burgers type in one space dimension, arising in modeling the dynamics of dislocation densities in crystals. Starting from physically relevant initial data that are of a special form, namely nondecreasing, periodic plus linear functions, we prove the global existence and uniqueness of a solution in $H^1_{loc}(\mathbb R\times[0,+\infty))$ that preserves the nature of the initial data. The approach is made by adding some viscosity to the system, obtaining energy estimates, and passing to the limit for vanishing viscosity. A comparison principle is shown for this system as well as an application in the case of the classical Burgers equation.

Measuring stacking fault densities in shock-compressed FCC crystals using in situ x-raydiffraction

A method is presented of in situ measurements of stacking fault densities in shockedface-centred-cubic (FCC) crystals using x-ray diffraction. Using results from both thesecond and fourth diffraction orders, wherein shifts in the Bragg peaks due to faulting areaccounted for, we calculated fault densities present in a molecular dynamics (MD)simulation of shocked single crystal of copper. The results are in good quantitativeagreement with dislocation density measurements inferred directly from the MDsimulation. The x-ray diffraction method thus presents a real possibility for experimentaldetermination in real time of dislocation densities in crystals during shock wave passage.

Frequency analysis of GaN MESFETs using full‐band cellular Monte Carlo

A full-band electron transport calculation in wurtzite phase GaN based on a detailed model of the electron-phonon interactions using a Cellular Monte Carlo (CMC) approach is applied to the frequency analysis of MESFETs. Realistic polar-optical phonon, impurity, piezoelectric and dislocation scattering is included in the full-band CMC simulator, which shows good agreement with measured velocity-field data. The effect of the dislocation scattering on the MESFET RF characteristics is examined as well, indicating that the computed cut-off frequency is affected by the crystal dislocation density and bias conditions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Response to “Comment on ‘AlN/GaN double-barrier resonant tunneling diodes grown by rf-plasma-assisted molecular-beam epitaxy’ ” [Appl. Phys. Lett. 83, 3626 (2003)

the bottom electrode’’ by recent additional tests with some other samples fabricated in those days, we hereby correct it. We reported in the paper 2 prior to the APL article of concern that the negative differential resistance of nitride resonance tunneling diodes ~RTDs! shows the asymmetric I ‐V curve and there the relationship with piezoelectric effect was suggested. After that, the other group has confirmed theoretically the asymmetry by the self-consistent simulation based on the ‘‘real-time tight-binding Green’s function.’’ 3 This is really an effect resulted mainly from a large piezoelectric field. These results definitely show that the RTD behavior in the GaN/AlN system could not be explained by a simple RTD scheme. In the comment, Belyaev et al. 4 has been insisting that we tried to explain the behavior of nitride RTD with a normal simple resonance concept in the APL letter, but this is misunderstood. In the letter reporting an early demonstration of GaN based RTD, we only gave the trial calculation of resonant levels as an approximation. We also predicted that the GaN/AlN RTD could not be explained completely with a simple model in the system with a large piezoelectric field. Also, Belyaev et al. infer that current‐voltage characteristics are sensitive to the way of voltage sweep, and this would be a phenomenon caused by a large piezoelectric field and electron trapping. We agree that this phenomenon deeply relates to the dislocation density in crystals and insufficient heteroboundaries. In this sense, regretfully, it is unclear that Belyae et al. and us have observed the completely same phenomenon, because between both samples, the RTD device structure is different and moreover the dislocation density included could be different. In the Belyaes sample, an asymmetric thickness combination was utilized for the bottom and top AlN barriers without undoped GaN spacers, which were placed on both sides of the double resonant region in our structure. The great difference is the absence of AlN multiple intermediate layers ~MILs! in their structure. We placed the AlN‐MILs underneath the RTD structure, i.e., just on metalorganic chemical vapor deposition-grown GaN templates to suppress propagation of screw-character threading dislocations to the upper RTD region. According to the previous papers of ours, 5,6 the insertion of AlN MILs functions to suppress the screw-character dislocations by three orders of magnitude. The suppressed screw character dislocation contributes to produce uniform heteroboundaries for molecularbeam epitaxy ~MBE!-grown AlN/GaN heterostructures. Belyaev wrote that we might also observe the current‐ voltage instability or the hysteresis characteristics, but it is not real. As described in the letter, we made the experiment with a single voltage scan mode based on the equipment character we used. During a long period after that, we did not have a chance to fabricate GaN-based RTD devices again,

Dislocation generation in GaAs crystals grown by the vertical gradient freeze method

The objective of this study is to develop a numerical model for predicting the dislocation density in GaAs crystals grown by the vertical gradient freeze (VGF) method at different growth parameters, such as the crystal growth rate, crystal diameter, and imposed temperature gradients on the crucible. Dislocation is an important defect in semiconductors. The production of near-dislocation-free crystal demands the crystal growth parameters to be perfectly adjusted to the properties of the growing material. The relationship between the crystal growth parameters and final dislocation density needs to be understood for the production of low dislocation-density crystals. In this study, dislocation densities in crystals grown by different parameters and growth directions has been calculated and compared with experimental findings. This investigation will provide valuable information for understanding the influence of growth parameters on final GaAs crystal quality.

Defects in semiconductors and their effects on devices

The classification of defects in semiconductors and their electronic properties are discussed. The sources of dislocations in bulk crystals and defects in epitaxial layers have been identified. Some of the approaches used to lower the density of dislocations in crystals and layers are presented. Effects of defects on devices are also considered.

Dislocation reduction in GaAs crystal grown from the Czochralski process

The dislocation density in the gallium arsenide (GaAs) crystal is generated by excessive thermal stresses during the Czochralski (CZ) growth process. A constitutive equation which couples the dislocation density with the plastic deformation is employed to simulate the dislocation density in the crystal. The temperature distribution in the crystal during the growth process is obtained by solving the quasi-steady-state (QSS) heat-transfer equation. The thermal stresses induced by the temperature distribution are calculated using the finite-element method. The crystal is assumed to be an axisymmetrical ingot. The resolved shear stress (RSS) in each slip system is obtained by stress transformation. The RSS in each slip system is no longer axisymmetric. The dislocation motion and multiplication in each slip system are simulated using the constitutive equation. The total dislocation density in the crystal is obtained by summing the dislocation densities in all of the slip systems. Since the thermal stresses are sensitive to the temperature gradients and the dislocations move faster at a higher temperature, the dislocation densities are generated most near to the solid-melt interface. The dislocation density is also found to be affected by the growth orientation, growth speed, ambient temperature and the radius of the crystal. The dislocation density in GaAs crystals grown with the different growth orientation, growth speed, and crystal radius at various ambient temperatures has been calculated so that the influence of these growth parameters on the dislocation density can be understood. Consequently, the growth parameters can be controlled to reduce the dislocation density generated in the crystal during the CZ growth process.

The numerical modelling of dislocation generation in semiconductor crystals during Czochralski growth

The dislocation densities in semiconductor compound crystals have been found to be affected by the growth orientation, crystal radius and the ambient temperature employed during the Czochralski (CZ) growth process. The objective of this paper is to investigate the influence of these growth parameters on the dislocation density and spell out ways to control the growth parameters in order to reduce the dislocation density. The finite-element technique is utilized to solve the governing equations of the quasi-steady-state (QSS) heat transfer and the thermoelasticity to obtain the temperature distribution and the thermal stresses in a growing crystal. The resolved shear stresses (RSSs) in each slip system are obtained through the transformation of thermal stresses. The RSSs are then employed to calculate the plastic deformation and dislocation density in each slip system of the crystal using the constitutive equation. The total dislocation densities in the crystal are obtained by summing the dislocation densities in all the slip systems. The results indicate that ambient temperature and growth direction can be effectively used to reduce the dislocation density in the CZ process.