Dislocation Length Research Articles

Temperature behaviour of photoluminescence and electron-beam-induced currentrecombination behaviour of extended defects in solar grade silicon

The temperature dependence of D-band and band-to-band (BB) luminescencewas measured in EFG samples between 80 K and room temperature fordefects/dislocations presenting different amounts of contamination. Thecontamination density was estimated from the temperature behaviour of theelectron-beam-induced current contrast, ranging between about 104 and 106impurities cm-1 dislocation length. The D1 line became already visible at roomtemperature but its intensity was found to exhibit a maximum at about150 K. D2, D3 and D4 start to show up at about 250, 190 and 170 K,respectively, and increase their intensities upon lowering temperature. At roomtemperature the width of the D1 line is broad and becomes narrowerupon lowering the temperature. D2 shows the opposite behaviour. Theintensities of D1 and D2 were observed to show strong variations across thesample, whereas this was not observed for the pair D4/D3. In particular, theorigin of the lines D1 and D2 is still far from being understood. Twomore lines at 1.040 and 0.987 eV were found in regions where the BBrecombination is strong. They appear without any defect contributionand are explained as phonon replicas of the band edge luminescence.

Study of the relaxation process during InGaAs/GaAs (001) growth from in situ real-time stress measurements

Strain evolution during In0.2Ga0.8As/GaAs (001) growth by molecular beam epitaxy has been monitored in real time. We have detected that three main relaxation stages, related to different mechanisms, take place during growth, and we have obtained the thickness range where those mechanisms are active. The in situ measured relaxation behavior in the plastic stages has been described by means of a simple equilibrium model that takes into account dislocations generation and interaction between them. The excellent agreement between the experimental data and the model allows us to determine the value of the formation energy per unit length of a misfit dislocation and the extent of the interaction between dislocations in this material system.

Mechanisms and effect of microstructure on creep of TiAl-based alloys

Transmission Electron microscopy studies on crept samples of an equiaxed Ti–48Al alloy deformed to strains near the minimum strain rate show a microstructure dominated by unit 1/2[110] type dislocations. These dislocations are pinned by jogs of varying heights. The jogged-screw model is adopted, where the rate controlling step is assumed to be the non-conservative dragging of the jogs along the length of the screw dislocations. The presence of tall jogs and the existence of a stress-dependent upper bound to the height of tall jogs which can be dragged have been incorporated into the model. These modifications lead to excellent agreement with experimental data. The evolution of the creep curve is also qualitatively predicted. In contrast, lamellar structures show a highly inhomogeneous deformation behavior with dislocation activity in lamellae above a critical thickness and negligible activity below that limit. This limit is related to the minimum stress required to cause channeling of dislocations. The observation of jogged segments in the thicker lamellae suggests that a modification of the jogged-screw velocity law could be used by incorporating an effective stress approach. Qualitative analysis of a probable method of evaluating the creep rate is discussed. Finally, microstructural changes during the aging process in K5 and K5SC alloys have also been studied. Aging causes the dissolution of metastable α 2. The effect of Si and C on the aging behavior and precipitation of the silicide and carbide particles during aging and following creep is discussed. These results suggest that microstructural stability is critically important in order to achieve the highest possible creep strengths.

Misfit dislocation and threading dislocation distributions in InGaAs and GeSi/Si partially relaxed heterostructures

Single and compositionally graded InGaAs/GaAs and SiGe/Ge partially relaxed heterostructures of equivalent lattice mismatch and thickness have been characterized by high resolution X-ray diffraction and by X-ray double crystal topography. X-ray topography evidences a rapid decrease of the average length of misfit dislocation segments with the increase of the density of misfit dislocations both in InGaAs and GeSi/Si structures. For an equivalent amount of strain release, SiGe/Si heterostructures exhibit shorter misfit dislocation lengths with respect to InGaAs/GaAs heterostructures. Compositionally graded InGaAs/GaAs heterostructures show much longer misfit dislocation segments with respect to equivalent single heterostructures, thus confirming the effectiveness of composition grading to reduce the dislocation interaction. The threading dislocation density evaluated from the lattice mismatch and the average length of the misfit dislocations on the basis of a simple formula increases more rapidly as a function of strain release in GeSi/Si heterostructures with respect to InGaAs/GaAs ones.

Room-temperature luminescence and electron-beam-induced current (EBIC) recombination behaviour of crystal defects in multicrystalline silicon

Crystal defects such as dislocations and grain boundaries may show a detrimental influence on solar cell performance due to their recombination activity. The contamination of the defects by impurities strongly affects their recombination strength. Recently, it was shown that the temperature behaviour of the recombination activity of defects measured with EBIC, c( T), gives a quantitative access to the amount of contamination at dislocations. We have compared the mapping of the band-to-band and the defect (D1) photoluminescence (PL), measured at room temperature in multicrystalline Si, with the electron-beam-induced current temperature behaviour. Intensive D1 luminescence band and a remarkable reduction of the band-to-band PL intensity are observed at the defect sites. We have found that wafer regions with pronounced D1 band corresponds to dislocations with a weak contamination level down to a few tens of impurity atoms per μm of the dislocation length.

Effects of thickness on the characteristic length scale of dislocation plasticity in Ag thin films

The effects that film thickness has on the length scale over which dislocation motion takes place were studied to elucidate the origin of the thickness dependence of the strength of polycrystalline Ag thin films on substrates. At low temperatures (below 200°C), where dislocation-mediated plasticity is the dominant inelastic mechanism, the thickness dependence of two plasticity parameters, the activation volume and the length of mobile dislocation segments, was investigated. The experimental results indicate that the distance between pinning points along the length of mobile dislocations increases with film thickness, and that it is significantly smaller than the film thickness and the average grain size. The thickness-dependence of the length over which individual inelastic events occur, which is the characteristic length scale for dislocation plasticity, clarifies the origin of the dependence of the low-temperature strength of thin films on film thickness.

Misfit Dislocation Nucleation Study in p / p + Silicon

Different edge treatments were used during the processing of 150 mm diameter highly boron-doped silicon substrate wafers to create a variation of crystallographic damage around the wafer edges. We studied the wafer edge as misfit dislocation generation sites in epitaxial silicon wafers. These strain-relaxing defects nucleate heterogeneously at the lattice-mismatched interface. We examined the effect of a variation of wafer edge treatments on misfit dislocation formation in silicon test wafers. We determined that a lower microroughness of the wafer edge results in a decrease in the misfit dislocation density and length. We were able to show that a careful combination of edge treatments including damage removal steps helps significantly reduce misfit dislocations in strained layer epitaxy. © 2001 The Electrochemical Society. All rights reserved.

Three-dimensional analysis of scale dependence of sub-micron polycrystals due to configuration entropy

The authors proposed a plausible explanation for the deviation of experimental data for sub-micron polycrystals from the Hall-Petch relation by introducing the configuration entropy. The present paper extends the previous two-dimensional analysis to the three-dimensional case. The statistical distribution of dislocation lengths within a spherical grain and the bow-out of dislocations are considered. According to Ashby's model, analyses are pursued for the statistically stored dislocations and geometrically necessary dislocations, respectively. It is confirmed that the configuration entropy model can predict the abnormal Hall-Petch dependence for grain sizes in the sub-micron range.

Benefits and shortcomings of the continuous theory of dislocations

Out of the vast field of microstructural mechanical behaviour of solids, we choose the area of elastoplasticity of crystalline solids. It is emphasized that elastoplastic deformation proceeds through defects in the ordered crystalline structure. Most important, at least in our investigation, are the defects dislocations that produce plasticity by motion at all temperatures and, in addition, point defects that become active at a higher temperature. It is shown that for two reasons, the elastoplasticity of crystalline solids does not fit well into the scheme of continuum mechanics: (i) The conventional tensor of dislocation density counts only excess dislocations of one sign, whereas the observed hardening and softening is due to the dislocations of two signs. (ii) The motion of the typical defects in the crystalline structure destroys the particles that constitute the body whose particles, therefore, do not persist during the elastoplastic motion. For this reason, the elastoplastic crystalline solid is not a differentiable material manifold. During the elastoplastic deformation, an irregular, often densifying dislocation network develops that can be seen in the electromicroscope and therefore is characteristic for the internal mechanical state. The network can be described by the infinite set on n-point correlation functions of dislocations. It is proposed that solutions are classified as of first, second, third, etc. order according to the highest order of correlation function which is included. The first-order theory is the so-called mean field theory, a well-known concept within the statistical physics. The two-point autocorrelation function gives the often used total length of dislocations in a unit volume, also a state quantity. The present state of the theory, in particular of the dynamics, is still rather underdeveloped.

Numerical study of the athermal annihilation of edge-dislocation dipoles

Abstract The stability against recombination of narrow edge-dislocation dipoles of the vacancy type is investigated in aluminium and copper by using atomistic-scale numerical simulation and phenomenological n-body potentials adapted to these metals. Stable and metastable equilibrium positions of edge dipole configurations have been considered and the influence of the dissociation width has been examined. The calculations show that, in aluminium, edge dipoles athermally annihilate at distances much larger than the Burgers vector length of perfect dislocations while, in copper, the dislocations forming the dipole recombine only when they are in close contact. These results are discussed in terms of surface energetics and in the framework of existing theoretical and experimental work.

Investigation of threading dislocation blocking in strained-layer InGaAs/GaAs heterostructures using scanning cathodoluminescence microscopy

Threading dislocation glide relieves strain in strained-layer heterostructures by increasing the total length of interface misfit dislocations. The blocking theory proposed by Freund [J. Appl. Phys. 68, 2073 (1990)] predicts the thickness above which gliding threading dislocations are able to overcome the resistance force produced by existing orthogonal misfit dislocations. A set of wedge-shaped samples of InxGa1−xAs/GaAs (x=0.04) strained-layer heterostructures was grown using molecular-beam epitaxy in order to test the theory of dislocation blocking over a range of thicknesses within one sample. Scanning cathodoluminescence microscopy techniques were used to image the misfit dislocations. The cathodoluminescence results confirm the model proposed by Freund.

Misfit dislocation formation in p/p + silicon vapor-phase epitaxy

We investigated the misfit dislocation nucleation in lightly boron-doped silicon epitaxial layers deposited by vapor-phase epitaxy at 1080°C–1150°C on heavily boron-doped substrates. The substrate resistivity was 4 mΩ cm which produced a misfit of 1.5×10 −4 and the layer thickness was 10 μm. An orthogonal array of 〈1 1 0〉-type dislocations was observed at the interface, as determined by g· b contrast criteria using Lang transmission X-ray topography. The misfit dislocations were observed only around the wafer periphery and the misfit dislocation length was shorter in regions where both orthogonal 〈1 1 0〉 segments existed. The density of the misfit segments was determined at the interface by defect-etching. In regions where the misfits were observed, triple-axis X-ray diffraction measurements determined that the layers were measurably relaxed. The distribution of defects indicates that the wafer periphery possesses heterogeneous nucleation sites for misfit dislocation nucleation.

Estimation of Back Stress Produced by Dislocation Interaction in Icosahedral Al-Pd-Mn

AbstractWe attempted to calculate the breakaway stress σb of dislocation from attractive junction made by reaction of dislocations. Assuming that the force f acting on the unit length of dislocation with the Burgers vector B under a shear stress τa is f τ∣b˝∣ where b˝ is the phonon component of B, and that the elastic energy per unit length of dislocation W is approximated by W = G(∣b˝∣2 + c2 ∣b˔∣2) where G is the shear modulus, b˔ the phason component of B and c2 a coefficient of about 3.1 × 10−3. Using the values G = 48.4 GPa at 1070 K, the Taylor factor M = 3 and the measured dislocation density of 1.8 × 1013 m−2, we calculated σb for 21 possible dislocation reactions. Picking up the most possible dislocation reactions, σb distributed between 50 and 80 MPa, and the average of them was 64 MPa. This result strongly suggested the possibility that the main part of the internal stress of the high-temperature deformation of icosahedral Al-Pd-Mn is explained by σb.

A model for the large-strain deformation of polyethylene

A model for the large strain deformation of polyethylene under uni-axial tension is described. Based on observations made by other researchers, the model describes hardening at large strains by considering dislocation nucleation and reorientation of slip planes within the crystalline phase. The temperature and strain-rate sensitivity of this behaviour are predicted with reasonable accuracy in a pipe-grade high-density polyethylene. The model has only three adjustable parameters which are the crystal shear modulus, the Young's modulus and a critical dislocation length.

An analysis of void swelling dose dependence in ion irradiated V–Fe alloys

The microstructure of V– XFe alloys ( X=0, 2, 5 and 7 at.%) irradiated as thin foils at 625°C with 50 KeV V + ions to damage doses ranging from 2.5 to 40 dpa at averaged dose rate of 5 × 10 −3 dpa/s has been investigated. Data on mean void diameter, void number density, void volume fraction (Δ V/ V) and total dislocation length per unit volume have been obtained. From these data the sink strengths for voids and dislocations were found and the void swelling bias factor (SBF) as a function of iron content was determined. Both Δ V/ V and SBF reveal maxima at about 5 at.% Fe. For an interpretation of a decrease in Δ V/ V and SBF at iron contents above 5 at.%, in the present work, the model developed previously is generalized to account for the diffusivity dependence on alloy composition.

Strained SiGe Materials for High Quantum Efficiency Photodiodes at µ = 1.3 to 1.5µm

AbstractSilicon-gemanium is a promising materials system for delivering near-IR photodetection on the ubiquitous silicon substrate. The 4% lattice mismatch leads to biaxial strain for SiGe films grown coherently on (100) Si substrates, which both extends the long wavelength detection limit by reducing the band gap and defines the critical thickness for the SiGe film. We have studied the use of strained-layer superlattices grown on high quality relaxed SiGe buffers. Graded buffers are ideal virtual substrates for achieving a complete range of compositions and strains for GeSi alloys. A physical model has been created to map out the absorption coefficient as a function of Ge fraction and (100) biaxial strain. Based on calculated absorption spectra as a function of composition and strain, we have designed and grown a Ge/Ge0.5Si0.5 strain-balanced superlattice on a high quality Ge0.75Si0.25 relaxed buffer using UHV-CVD. The strain-balanced superlattice has an effective absorption coefficient of 5000 cm−1. The relaxed buffer serves as a virtual substrate with relatively low threading dislocation density (106 cm-−2). The effect of the threading dislocations on the leakage current of P-I-N junctions is also investigated. Electron beam induced current (EBIC) is used to determine the dislocation density of SiGe relaxed buffer junctions grown with different grading rates. Mesa isolated devices are used to determine bulk leakage current densities for the SiGe junctions. The bulk leakage current density scales directly with the dislocation density. Bulk leakage currents density per dislocation length (2×10−5 A cml) agrees with deep level transient spectroscopy (DLTS) determined literature values for SiGe capture cross-section and defect density per dislocation in Si.

Elemental Dislocation Mechanisms Involved in the Relaxation of Heteroepitaxial Semiconducting Systems

Laboratoire MATOP associe´ au CNRS,Faculte´ des Sciences et Techniques de St. Je´roˆme, F-13397 Marseille Cedex 20, France(Received September 22, 1998)Different elemental dislocation mechanisms are considered and we try to highlight their specialbehaviour in relation to the layer geometry. The nucleation of misfit dislocations is the first step,we show here that the mechanism proposed by Matthews et al. can actually be observed in lowmisfit systems. The development of dislocations is then studied and we underline some particularproblems which could influence the dislocation length: the role of the cooling step and of the un-certainty on G

Slip Length in Silicon Wafers Caused by Indentation during Heat Treatment

The relationship between the length of slip dislocation and applied stress in silicon wafers was investigated. Czochralski (CZ) silicon wafers [boron-doped, interstitial oxygen concentration [Oi]=(13.8–14.0)×1017/cm3], indented by a Vickers hardness tester, were thermally stressed by insertion into and withdrawal from a horizontal furnace. The length of slip dislocations generated during the heat treatment was measured by X-ray topography (XRT). To estimate the applied thermal stress during the heat treatment, temperature distribution in the wafer was measured with a thermocouple. From the results of XRT observations, slip dislocations were found to be generated at peripheral and central regions during the insertion and the withdrawal, respectively. The length of slip dislocations was calculated using the experimentally estimated thermal stress. It was found that the length of slip dislocation could be explained well by the model, with consideration of the applied stress and the dislocation velocity.

Electronic redistribution in the neighborhood of the nucleus of a linear dislocation

This paper is devoted to a self-consistent solution of the electron-strain interaction in a crystal with linear dislocations. It shows that such self-consistency causes charge to be redistributed in the neighborhood of the dislocation nucleus and hence renormalizes the strain caused by the dislocation. The resulting charge redistribution forms a dipole whose moment is proportional to the length of the dislocation. The dislocation kinetics in the crystal can be affected when an external dynamic or static electric field acts on such a dipole.

Superposition of grain boundary and solid solution strengthening in copper-germanium alloys

The Hall-Petch equation relates the yield strength {sigma}{sub y} of polycrystals to their grain size d: {sigma}{sub y} = {sigma}{sub o} + k d{sup {minus}1/2}, k is often referred to as the Hall-Petch slope. In a plot {sigma}{sub y} versus d{sup {minus}1/2}, the ordinate intercept equals {sigma}{sub y}. Apparently two contributions to {sigma}{sub y} are distinguished: (i) {sigma}{sub o} represents those mechanisms which govern the critical resolved shear stress (CRSS) {tau}{sub c} of single crystals of the same material; (ii) kd{sup {minus}1/2} stands for the hardening effects of the grain boundaries: they limit the slip lengths of dislocations. There are many instances where it is possible to break down {sigma}{sub y} into the two terms {sigma}{sub o} and kd{sup {minus}1/2}, but there are also many systems in which k varies with the intrinsic properties of the material, e.g., with its solute content or with its dispersion of second phase particles. Copper-germanium alloys have been evaluated as to strengthening by grain boundaries and solid solution.