Change In Dislocation Density Research Articles

Plasticity, Microstructure and the Thermal Dependence of Flow Stresses in Aluminum Thin Film Interconnects

ABSTRACTA study was conducted towards fundamentally understanding the nature and magnitude of thermal stresses in aluminum thin films on silicon and correlating them with deformation mechanisms that serve to relax the stresses imposed by the thermal strain. A number of experiments and theoretical considerations are described in order to describe the sources of strengthening and stress relaxation in such films. It is shown that the flow stress of an aluminum film corresponds to the critical stress required to drive dislocation glide events. This mechanism entails an inverse flow stress dependence on the film thickness and grain size. A novel set of experiments in which the effects of strengthening due to finite film thickness and the grain size were separated and quantified is described. The variation of these strengthening components with temperature during heating and cooling were noted. Theoretical considerations of diffusional relaxation combined with the results of grazing incidence X-ray scattering (GIXS) experiments suggest that grain boundary diffusion is much less effective in limiting film flow stress than would be expected from the strain rate relation derived for a free-standing film. Line broadening observations in the GIXS experiments suggested large changes in dislocation density in the tested films during thermal cycling. The nature of these variations are qualitatively consistent with those of the film flow stress, suggesting that strain hardening could be an additional strengthening mechanism in Al films during thermal cycling.

Electroplasticity and Electromigration

AbstractIt is known that an electric current can interact with dislocations in metals. Recent studies suggest that these interactions include current-induced dislocation motion and multiplication (electroplasticity) through both glide and climb mechanisms. Such interactions might be expected to effect both the mechanical properties and the electromigration behavior of the thin metal conductor lines used in integrated circuits. The mechanical properties would be directly modified through changes in dislocation density and mobility. Changes in microstructure and strength could affect electromigration lifetime and failure morphology. In order to investigate the effects of current-dislocation interactions, we conducted three sets of experiments in unpassivated aluminum conductor lines: First, a nanoindentation device was used to measure the mechanical properties of the lines during application of current densities up to 6 MA/cm2. Second, the mechanical properties of the lines were measured ex situ as a function of time in accelerated electromigration testing conditions. Third, the nanoindentation device was used to damage the lines at specific sites and damage morphology was examined during subsequent electromigration experiments by means of in situ scanning electron microscopy. To date we observe no direct effect of electric current on the mechanical properties of conductor lines and no clear correlation between mechanical damage and electromigration failure characteristics. Based on theoretical calculations and previous experiments on bulk samples, these results were not expected.

Effect of loading frequency on the physicomechanical properties of aluminum alloys during fatigue

A procedure and specially developed equipment are described for performing fatigue tests at frequencies of 180 Hz, 2.8, 8.8, 17.6, and 44 kHz and with random loading. It is shown that with an increase in loading frequency the cyclic endurance of the test materials increases. The nature of the occurrence of the fatigue process is traced from the change in dislocation density, sizes of blocks, macrostresses, microhardness, and electrical conductivity. It is established that it is not monotonic.

Alloying of iron powder base alloys with chromium and its compounds

The creep deformation of a 2.5%Cr-1%Mo-0.11%C steel was investigated as a function of various thermal treatments. The substructural changes that occurred during deformation were examined using transmission electron microscopy. The high creep resistance observed in both bainite and martensite was analyzed in terms of the high dislocation densities, the fine carbides and the ultrafine matrix lath sizes in these structures. The activation energy and other deformation parameters measured during the the creep process indicate that the deformation mechanism is mainly diffusion controlled. The changes in dislocation density and spacing occurring during the creep process were monitored by following the changes in internal stress and creep rate and by using thin foil transmission electron microscopy.

Process parameters for bonding copper powder to oxygen free high conductivity (OFHC) copper substrate by CIP and sintering

The creep deformation of a 2.5%Cr-1%Mo-0.11%C steel was investigated as a function of various thermal treatments. The substructural changes that occurred during deformation were examined using transmission electron microscopy. The high creep resistance observed in both bainite and martensite was analyzed in terms of the high dislocation densities, the fine carbides and the ultrafine matrix lath sizes in these structures. The activation energy and other deformation parameters measured during the the creep process indicate that the deformation mechanism is mainly diffusion controlled. The changes in dislocation density and spacing occurring during the creep process were monitored by following the changes in internal stress and creep rate and by using thin foil transmission electron microscopy.

Evolution of dislocation structures and deformation behavior of iron at different temperatures: Part I. strain hardening curves and cellular structure

The deformation behavior of iron has been investigated at different temperatures by means of tension tests. There exist two temperature ranges for deformation. In the low-temperature range(T < 293 K), the flow stress σ, the work-hardening rate θ at e = 0.06, and the yield stress σy decrease with increasing temperature, but in the higher temperature range(T ≥: 293 K), σ and θ at the same strain increase while σy decreases more slowly. The change of dislocation density, with temperature, ate = 0.06 exhibits the same tendency as that of the flow stress. The strainhardening rates decrease almost linearly with increasing stress up to necking in the low-temperature range, except the initial strain range. At the higher temperature range, the hardening rates decrease linearly with stress only at the early stage of deformation, but above certain strains, the decreases become more gradual; that is, the G-cr curves deviate from the linear region. The evolution of dislocation structure has also been observed by transmission electron microscopy (TEM). The results show that a substructural transition takes place in the nonlinear range of G-cr curves. In the linear decreasing region of strain-hardening curves, the deformation is controlled by the uniformly distributed dislocations or cell multiplication prevails. However, in the nonlinear region of G-cr curves, cell multiplication seems to be balanced by cell annihilation.

Investigation of Misfit Dislocation Configurations in Mbe-Grown InGaAs Layers on Misaligned GaAs (001) Substrates

ABSTRACTThe configurations of misfit dislocations in In0.2Ga0.8As/GaAs(001) hetero structures grown on slightly misoriented substrates was investigated by transmission electron microscopy (TEM). Layers 6 nm, 20 nm and 40 nm thick were grown by MBE. The substrate was tilted in [110], [110], [120], [210] and [010] directions at angles between 0° and 10°. Only in the 40 nm thick layers networks of 60° and 90° dislocations were formed. Misfit dislocations were found at the interface in &lt;110&gt; directions. In the substrate tilting range between 0° and 4° the changes in dislocation density can be explained by the differentcharacter of α and β dislocations. For a substrate tilting above 6° the different dislocation sets show an increased anisotropy. The misfit dislocations at the interface were decorated by In atoms. The influence of three-dimensional crystal growth on increasing surface roughness is discussed.

Computer Model for Prediction of Carbonitride Precipitation during Hot Working in Nb-Ti Bearing HSLA Steels.

A computer model which predicts complex precipitation behavior quantitatively in Nb-Ti bearing steel has been developed on a theoretical basis. The solubility and composition of the complex precipitates, and the chemical driving force of the precipitates from supersaturated austenite are estimated by means of thermodynamic analysis of regular solution composed of four-binary compounds. The change in dislocation density which acts as a nucleation site during hot working is calculated by using dislocation theory. And the time dependence of volume fraction and the particle radius of strain induced precipitation are also predicted on the basis of classical nulceation theory. In order to estimate the effect of deformation on nucleation, the change in elastic energy of dislocation with nucleation is calculated.Experimental results showed that combination of Nb and Ti addition, decreased the solubility of carbonitrides and accelerated the precipitation rate from supersaturated austenite because of the formation of complex precipitates. Such experimental results are in good agreement with the prediction by the present model. And both the acceleration of precipitation rate and the refinement of precipitates particles due to hot deformation are also quantitatively explained.

The Thermal Stability of Heavily Carbon-Doped GaAs Grown by Metalorganic Molecular Beam Epitaxy

ABSTRACTHeavily carbon-doped GaAs thin films with a hole concentration of 5.8 × 1020 cm-3, grown by metalorganic molecular beam epitaxy (MOMBE), were annealed at 900°C for 30 minutes. The microstructural changes due to annealing were investigated by transmission electron microscopy. Electron diffraction study showed some evidence of carbon clustering on {111} in as-grown samples. A high density of precipitates was found in the annealed sample, together with a decrease of the lattice contraction and hole concentration. In the as-grown layer, misfit dislocations with only one type of Burgers vector were observed, while misfit dislocations with the several Burgers vectors were observed in [110] direction after annealing. The density of misfit dislocations in both &lt;110&gt; directions increased significantly even though the lattice contraction in carbon-doped GaAs decreased after annealing. A model is proposed to explain the change of misfit dislocation density in heavily carbon-doped GaAs layer.

High and Low-Cycle Fatigue Damage Evaluation of Multilayer Thin Film Structure

A five-layered (Cu/Cr/Kapton® /Cr/Cu) metallic thin film structure was subjected to a completely reversed bending fatigue cycling with a wide ranges of applied strain amplitudes from 0.25 percent to about 30 percent. A new model for determination of the number of cycles to fatigue failure NF was proposed for single-crack and multi-crack formations. Within a strain amplitude ranging from 1 to 10 percent, a Manson-Coffin’s relationship was recognized for both the number of cycles to crack initiation NC and NF with exponents of 0.39 and 0.51, respectively. Selected fatigued test samples were further subjected to X-ray diffraction line analysis for dislocation density (ρ) calculation, which was related to the number of fatigue cycles N and strain amplitude (Δ εT) in an empirical formula. It was also found that dislocation densities accumulated up to both Nc and NF were related to applied strain amplitudes. Consequently, if applied strain amplitude is known and progressive change in dislocation density is measured, one can predict the remaining fatigue life as well as fatigue cycles which were already consumed.

Compositional dependence of dislocation loop development and microstructures in austenitic Fe-Ni-Cr alloys under proton irradiation

In order to examine the compositional dependence of dislocation loops and other microstructural changes under irradiation in austenitic Fe-Ni-Cr alloys, eight solution-annealed ternary Fe-Ni-Cr alloys whose Ni content varies from 25 to 45 wt% and Cr content from 5 to 15 wt% were irradiated by 200 keV protons at 873 K to 0.4, 1.6 and 15 dpa after helium pre-injection to 10 appm. Dislocation loop diameter increased but loop number density decreased with increasing Ni content and decreasing Cr content. A discernible compositional change of dislocation density was not detected. With increasing Ni content and decreasing Cr content, swelling decreased because of the drastic decrease of void number density. The attachment of dislocation lines to the voids, tiny voids smaller than 3 nm in diameter, and black contrast, which could be the contrast from void embryos smaller than 10 nm in diameter, were observed in the alloys irradiated to 1.6 dpa.

Localized deformation of SiCAl composites

Tensile tests of SiC-6061 Al composites containing various volume fractions of whiskers or particles (20, 5 and 0 vol.%) showed that for samples containing a high volume fraction (20 vol.%) the fracture process was very localized, i.e. a very narrow neck. As the volume fraction of whiskers or particles decreased, the deformed region spread out. One might expect that the microstructure should correspond to the macroscale changes. In the highly deformed region the dislocation density is expected to be higher, in the less deformed regions the dislocation density should be lower, and if the deformation is very localized, then the high dislocation density should also be limited to a very narrow region. Overall, there is good agreement between the microstructure (dislocation density) change and the macroscale deformation of SiCAl composite tensile samples. The mechanism proposed to account for this change in deformation behavior as a function of volume fraction of SiC in aluminum is related to the expansion of the plastic zone (due to differences in thermal coefficients of expansion between SiC and aluminum) when the external stress is applied. Also, the localized deformation is related to localized clusters of SiC particles. There is a cooperative effect which leads to a region of very localized plastic deformation.

Structure and property evolution during drawing and wall ironing of aluminum alloy 3004

The evolution of mechanical properties and dislocation substructure during the commercial-scale can making (deep drawing, wall ironing, and “baking”) operations of the aluminum alloy 3004 H19 has been investigated. At each stage the samples were obtained from the deep-drawn cup or wall-ironed can wall and subjected to tensile tests and transmission electron microscopy characterization. The strength decreased (and ductility increased) during deep drawing and increased during wall ironing. The “sizing” of can wall during drawing superimposes a strain hardening effect on these strength and ductility variations. The corresponding changes in dislocation density and cell or microband boundary configuration were observed at each stage. The strain localization and microstructural inhomogeneities were particularly prevalent in the upper parts of the cup and can wall. The cell size and bank thickness did not vary significantly during can making.

Relation between tensile properties and microstructure in type 316 stainless steel SA weld metal

Tensile properties of a thick, multipass, submerged-arc (SA) weld-deposited type 316 are investigated by tests at room temperature and at 400 ° C and by microstructural and compositional analyses. The as-deposited metal, which shows a lower yield strength, a comparable ultimate tensile strength and a lower total elongation compared to the (solution-annealed) parent metal, is characterized by systematic variations in tensile properties across its thickness, with the highest strength and the lowest ductility in the weld centre. These variations are related to material variability (mainly changes in dislocation density) within the weld metal due to local dissimilarities in thermal and mechanical histories during welding.

Investigation of the reversibility of deformation in silicon sheets

We have investigated the degree to which plastic deformation is reversible in silicon by bending and re-flattening initially defect-free single-crystal Czochralski silicon samples using four-point bending to simulate the deformation experienced during ribbon crystal growth. Optical and scanning electron microscopy of etched sample cross-sections after single bending and bending and re-flattening at 1100° C and 1200° C revealed that the dislocation densities in the re-flattened samples were lower than in singly-bent samples by 60–90%, indicating that dislocations are either being annihilated within the silicon bulk or are exiting the silicon at the free surfaces. There was little evidence of dislocation interaction in the singly-bent single-crystal samples investigated with transmission electron microscopy, so the latter mechanism is more likely. Although the re-flattened specimens have a lower dislocation density, there is little improvement in the minority-carrier diffusion length, measured by electron-beam induced current, which in all cases ranged from 10–20 μm. Since the minority-carrier diffusion length changed little, even with a change in dislocation density from 106 dislocations/cm2–108 dislocations/cm2, other defects must be controlling the diffusion length. There is some correlation between dislocation density and minority-carrier diffusion length within a given sample, but this may be due to indirect effects such as generation of point defects by moving dislocations.

The Constitutive Equation for Silicon and Its Use in Crystal Growth Modeling

A stress analysis that describes the crystal growing process requires a material model that is valid over a wide temperature range and includes dislocation motion and multiplication. The stresses developed in the growing process could induce residual stresses, changes in dislocation density and buckling into the growing crystals. The dislocation density is introduced as an internal variable in the constitutive model. The stress-strain and dislocation density-strain characteristics of silicon crystals are discussed as a function of temperature, strain rate, and initial dislocation density.

Change in physicomechanical properties of steel D1604AT15 during fatigue at different loading frequencies

Results are presented in a statistical arrangement for studying the effect of loading frequency on the fatigue life in bending of plates with a stress concentrator. The nature of change in microhardness, electrical conductivity, dislocation density, and block dimensions during fatigue at frequencies of 2.8, 8.8, and 18 kHz has been demonstrated. It has been established that in spite of some qualitative difference the main indicators of fatigue at these frequencies are retained.

Etch pit study of dislocation formation in Hg1−xCdxTe during array hybridization and its effect on device performance

The relationship between hybridization force, dislocation (etch pit) density, and device performance has been investigated for devices fabricated from Hg1−xCdxTe liquid phase epitaxy (LPE) material. Coldwelded indium column interconnects are the predominant method used to mechanically and electrically attach mosaic arrays to silicon multiplexers. The mismatch in thermal expansion between the Hg1−xCdxTe photodiode arrays and silicon multiplexers stresses the interconnects when the arrays are cooled to their operating temperature (typically 40–120 K) which can lead to failures. Increased hybridization force improves the mechanical stability of the interconnects but can introduce dislocations in the Hg1−xCdxTe. Dislocations have been reported to degrade the performance of some device structures. The dislocation density in the LPE film after growth was ≊8×105/cm2. We have found no significant change in dislocation density at hybridization forces up to ≊3.9×107 N/m2. At forces on the order of 5.9×107 N/m2 (≊10% of the Vickers hardness), the dislocation density in the films increased to 90×105/cm2 in the areas where the indium columns were. The diffusion limited performance of the test structures at 120 K was not significantly degraded by the increased dislocation density. At 80 K, however, where the devices were modeled to be generation–recombination limited, there was an increase in dark current with increased dislocation density. The structures used in the study were fabricated from LPE Hg1−xCdxTe grown on a CdTe substrate. Implantation of boron into the p-type material through a ZnS passivation layer was used to form junctions. A zero-bias junction resistance of 1000 to 7000 Ω cm2 was typical for the test structures which had a cutoff wavelength of 4.7 μm at 120 K.

An investigation of the effects of hydroxyl concentration and bubble formation on the electrical conductivity of synthetic quartz

The electrical conductivities of samples of synthetic quartz with (OH) concentrations from 10 to 300 H/10 6 Si have been measured, before and after heat treatments, in order to examine the influence of (OH) on the band structure of quartz. AC measurements were made over a wide range of frequency and the bulk conductivities were determined by complex impedance analysis. It is shown that the as-grown (OH) content has no measurable effect on the conductivity. During a series of heat treatments above 500°C the conductivity increases and this is discussed in relation to the changes in dislocation density which accompany bubble formation at these temperatures.

Shock Metamorphism of Deformed Quartz

Deformed, synthetic quartz containing a dislocation density of 2.9 ± 1.9 × 108/cm2 and abundant bubbles and small inclusions was shocked to peak pressures of 12 and 24 GPa. The resultant material was inhomogeneously deformed and extremely fractured. The 12 GPa sample contained large regions lacking apparent shock deformation, suggesting that the original microstructure of a quartz target may be distinguished in low-stress shocks with minimal annealing. No change in dislocation density was caused by shock loading except in regions containing shock lamellae, where the dislocation density was lowered. Generally the same types of microstructures were induced by shock of deformed quartz as by shock of relatively defect-free as-grown crystals. Glass-filled veins were abundant, especially at lower stresses, and contained angular fragments of quartz welded together. Microfaults formed on $${{\{ 10\bar 11\} } \mathord{\left/ {\vphantom {{\{ 10\bar 11\} } {\{ 01\bar 11\} }}} \right. \kern-\nulldelimiterspace} {\{ 01\bar 11\} }}$$ and $${{\{ 11\bar 22\} } \mathord{\left/ {\vphantom {{\{ 11\bar 22\} } {\{ 1\bar 212\} }}} \right. \kern-\nulldelimiterspace} {\{ 1\bar 212\} }}$$ , inclined close to 45° to the shock propagation direction. Curviplanar features occurred in groups, with contrast indicating Moire patterns, twins, and stacking faults or related structures; most were interpreted as fractures, possibly welded together with glass. Regions containing shock lamellae sets were present. Lamellae sets were uncommon at 12 GPa, but distributed every few microns at 24 GPa. Lamellae occurred in a spectrum of habits ranging from 35–1500 A in thickness, from 35 A upward in spacing, and from closely-packed parallel sets to networks of diverse orientations; some lamellae were not parallel-sided, but wedge-shaped with basal and $${{\{ 10\bar 13\} } \mathord{\left/ {\vphantom {{\{ 10\bar 13\} } {\{ 01\bar 13\} }}} \right. \kern-\nulldelimiterspace} {\{ 01\bar 13\} }}$$ edges, Thick lamellae were connected to glassy veins, and the wedge-shaped type generally narrowed away from veins; they also subdivided and merged along their length. Lamellae were dominantly basal at 12 GPa, and at 24 GPa on $${{\{ 10\bar 12\} } \mathord{\left/ {\vphantom {{\{ 10\bar 12\} } {\{ 01\bar 12\} }}} \right. \kern-\nulldelimiterspace} {\{ 01\bar 12\} }}$$ , with poles normal to the shock direction. We propose that they are not shear features, but rather glass-filled tensile fractures. Vitrification was widespread, especially at 24 GPa, apparently more so than in shock of as-grown material. This suggests that index of refraction is not an appropriate shock paleopiezometer, as it depends on the defect structure of the starting material. Neither lamella width nor spacing was correlated with shock stress; however, the criterion of multiple glass lamellae sets as indications of shock deformation and its intensity are consistent with our measurements. Dislocation density was lowered in lamellae-containing and glassy areas, possibly removed by nucleation of and absorption by lamellae. No high-pressure phases were observed. Based on the complete set of observed features, it appears that shock deformation in quartz is primarily brittle-melt deformation, with an important role played by hot, fluid silica.