Dislocation Density Measurements Research Articles

Thermodynamic aspects of (Te,S)-double-doped GaSb crystal growth

A series of GaSb single crystals double doped with tellurium and sulphur were grown using the Czochralski method without encapsulant in an atmosphere of flowing hydrogen. The Hall carrier concentration of these crystals was measured and compared with the calculated values. Very good agreement appeared for the sulphur concentration C s for total amounts of dopants (Te and S) smaller than 12 at.%. If C s exceeds a value of 12 at.%, the theoretical and practical values of the Hall concentration differ from each other. It seems that this effect was caused by the creation of a Te-S solid solution and by the subsequent elimination of dopants from the GaSb lattice. This assumption is supported by measurements of dislocation density. In the case of C s ⪆ 12 at.% the dislocations were uniformly distributed on the surface of GaSb〈111〉 sample because the so-called “glide phenomena” could be suppressed by the formation of some precipitates of the Te-S solid solution which might generate dislocations in the whole volume of the GaSb single crystals.

Selective etching of AlAs for preparation of III-V semiconductor thin foils.

A new method of thin section preparation of III-V semiconductors and multilayers for transmission electron microscopy (TEM) is presented that exhibits considerable advantages over conventional methods such as ion beam milling and jet thinning. GaAs thin films and multilayers of GaAs/In chi Ga1-chi As/GaAs are grown over an etch release layer of AlAs on GaAs substrates by molecular beam epitaxy (MBE). Planar TEM sections prepared by selective etching from these samples show improved ability to image film morphology and dislocation arrangements, and the resulting large thin electron transparent areas facilitate dislocation density measurements and detection of spatial variations. Avoidance of radiation effects and wedge shaping, both common to ion milled samples, allows this method to be used to prepare uniform thickness standards of single layer GaAs films for EDS analysis or lattice imaging.

X-ray measurement of deformation and dislocation density in semiconductor strained layers

Double-crystal X-ray diffraction is commonly used to measure the misfit strain and relaxation of epitaxial semiconductor layers. In this paper, a framework is developed which links the measured parameters Δ d / d and Δø to the deformation tensor of a semicoherent layer. Isotropic elasticity theory and the Frank-Bilby equation are used to derive an analytical expression for this deformation. By combining X-ray measurements of different planes, it is possible to obtain the misfit strain and details of the misfit dislocation array in a strained layer grown on a substrate of arbitrary orientation. In (001) layers, it is shown that the misfit strain and relaxation can be found from just six rocking curves, although the most accurate measurements require twelve rocking curves.

The measurement of local plastic deformation in a metal‐matrix composite by electron back‐scatter patterns

SUMMARYHigh dislocation densities in the matrices of metal‐matrix composites (MMCs) contribute to the strengthening of particulate MMCs, whilst heterogeneous nucleation of precipitates at these defects can cause marked differences in the age hardening of many matrix alloys. Electron back‐scatter patterns (EBSPs) and transmission electron microscopy (TEM) have been used to examine the dislocation distribution in continuous‐fibre SiC/Al alloy MMCs. TEM observations showed dislocation densities as high as 3 times 1014m−2, with a marked increase as thinner matrix regions were observed. From EBSP measurements on bulk specimens, a much lower dislocation density of 2 times 1012 m−2 was estimated. To resolve this discrepancy, EBSP measurements were made from thinned TEM specimens and these showed that the dislocation density had increased during specimen thinning. However, both TEM and EBSP measurements from unreinforced matrix material prepared for TEM using the same procedures showed no such increase in dislocation density. Redistribution of internal stresses during thinning of the composite to a transparent foil must therefore be the cause of the observed rise in dislocation density. The EBSP technique was demonstrated to be an excellent means of examining the distribution of plastic deformation in MMCs. It was concluded that TEM measurements of dislocation densities in continuous‐fibre MMCs can be erroneously high.

A method for avoiding errors in measurements of dislocation density in specimens with a high dislocation density

The measurement of dislocation density from electron microscope images of dislocations is an important tool in the hands of the materials scientist. Weak beam images are often chosen for this purpose. In cases where the dislocation density is high, there is a strong possibility that the imaging electrons propagating through the thin foil would encounter several dislocations before emerging from the bottom surface. A question which arises is what effect this may have on image contrast and whether this affects measurements of dislocation density.The authors of this paper have addressed this question by examining the contrast obtained in the case where two dislocations overlap so that the imaging electrons encounter two dislocations before reaching the bottom surface of the specimen. The details of these calculations are presented elsewhere and will not be repeated here. For purposes of this paper, the results can be summarized by stating that, for certain diffraction conditions and dislocation separations, the contrast exhibited by the overlapping dislocation configuration is very weak with the result that the dislocations would not be observed.

The formation and annealing of dislocation damage from high-dose self-ion implantation of aluminum

Quantitative electron channeling and weak-beam transmission electron microscopy (TEM) measurements of dislocation density have been used to study the formation and annealing of the dislocation network in self-ion-implanted aluminum. The channeling linewidth is found to be proportional to the dislocation density. Several mathematical expressions for the dislocation network growth are examined. One by Igata et al. [in Effects of Radiation on Materials: Proceedings of the 10th International Symposium, edited by D. Kramer, H. R. Brager, and J. S. Perrin, STP 725 (ASTM, Philadelphia, 1980), p. 627] is found to describe the implantation data accurately. This model has a linear growth term and terms for dislocation loss due to surface effects and recovery. The fit is insensitive to the relative importance of the two loss terms. Annealing is found to occur in two stages; roughly one third of the dislocation density is gone by 300 °C, corresponding to typical recovery processes, while the remaining network is stable to about 500 °C.

Formation of dislocations with local mechanical damage to a silicon surface at room temperature

A study is made of the formation of dislocations in silicon with local damage to the surface at room temperature and subsequent annealing within the range 1073–1473 K. The damages to the surface are modeled with the use of micro-hardness indentations. Measurements of mean linear dislocation density in a ray of the indentation rosette show that the number of dislocations in the rosette is independent of both the temperature and duration of isothermal annealing. It was found that annealing at 573–773 K leads to partial relaxation of elastic stresses from the indentation due to the formation of sections of silicon with a hexagonal structure near the indentation. Further annealing at high temperatures leads to the disappearance of these sections and the formation of a normal dislocation rosette, with the number of dislocations in the rays corresponding to the case of one-stage annealing. The results are empirical confirmation of the hypothesis of “incomplete shear.” In accordance with the latter, dislocations are formed during deformation at room temperature, not during subsequent annealing.

Grain-size strengthening in terms of dislocation density measured by resistivity

The effect of grain size on flow stress has been investigated in terms of dislocation density. The measurement of dislocation density was made for nickel having a high stacking fault energy, by means of electrical resistivity with which the dislocation density can be measured up to larger strains compared with transmission electron microscopy. It was found that the dislocation density for a given strain in specimens deformed in tension at 77 and 295 K increases in a linear manner with the reciprocal of grain size. It was also ascertained that the flow stress is proportional to the square root of dislocation density, irrespective of grain size, deformation temperature and the amount of plastic strain (ϵ). From the above two relationships, an equation between flow stress and grain size was obtained in a general form, which gives the Hall-Petch relation as the limited case at yield point or at small strains.

Harper-Dorn and power law creep in uranium dioxide

The creep behavior of uranium dioxide is reviewed based on the results of seven separate investigations. The data fall into two regimes: a power-law region at high stresses where the stress exponent, n, is about five and a Newtonian-viscous region at low stresses where the stress exponent is unity. It is shown that the data in the region where n = 1 cannot be explained by a Coble diffusional creep mechanism. This result negates the recent conclusion of Knorr, Cannon, and Coble who claim that “it is conclusively shown that Coble creep is the dominant mechanism” in the viscous region. It is demonstrated, rather, that Harper-Dorn creep describes the creep behavior of polycrystalline UO 2 above 0.6 T m and in single crystalline material in the region where n =1. Harper-Dorn creep in uranium dioxide is analyzed using an internal stress model developed to describe pure metal behavior. The value of the modulus-compensated internal stress, which is a measure of the random dislocation density, is shown to be higher for both polycrystalline and single crystalline uranium dioxide than it is for pure metals.

TEM observations of [formula omitted] heteroepitaxial layers on (100)Si using a GaAs lift-off technique

Lift off of GaAs epitaxial layers on Al x Ga 1− x As/Si has been accomplished by using a hot HF etch for the underlying AlGaAs. The resultant lifted structures were investigated by TEM in order to determine the thickness dependence of antiphase boundaries and dislocations. It is shown that direct observations of antiphase domains and measurement of dislocation density are possible.

Determination of Dislocation Densities in Hexagonal Close-Packed Metals using X-Ray Diffraction and Transmission Electron Microscopy

AbstractX-ray diffraction (XRD) line-broadening analysis has been used to determine dislocation densities in zirconium alloys with hexagonal closepacked (hep) crystal structures and a complex distribution of dislocations reflecting the plastic, anisotropy of the material. The validity of the technique has been assessed by comparison with direct measurements of dislocation densities in deformed polycrystalline and neutron-irradiated single crystal material using transmission electron microscopy (TEM). The results show that-there is good agreement between the XRD and TEM for measurements on the deformed material whereas there is a large discrepancy for measurements on the irradiated single crystal; the XRD measurements significantly underestimating the TEM observations.

Dislocation Arrays in Epitaxial Interfaces.

ABSTRACTA method for analysing the form of dislocation arrays which accommodate misfit at epitaxial interfaces based on the Frank-Bilby expression of the dislocation content of an interface is presented. Emphasis is placed on the deformation of a crystal in the presence of a dislocation array, and ease of formulation through use of an orthogonal reference frame. Several aspects of epitaxial growth are subsequently addressed, including the uniqueness of a dislocation array accommodating a given misfit. In the case of growth on vicinal cubic surfaces, it is shown that dislocations generated to relieve misfit may also lead to misorientation of the overlayer. From experimental measurements of dislocation densities using transmission electron microscopy, it is possible to calculate the state of strain in a metastable misfitting epitaxial layer. When misfit is not isotropic in the interface (such as for silicon or niobium grown on sapphire) it is shown that dislocation line directions may not lie along low index directions in either crystal, a point which is particularly important with regard to studies of interfacial structure by high resolution electron microscopy.

Strain hardening and recovery of nickel alloy 600 by X-ray measurements of dislocation density

A quantitative link between microdeformation and macrodeformation and kinetic recovery of nickel-base Alloy 600 was established by X-ray rocking curve measurements, supported by transmission electron microscopy. Using a calibration curve relating dislocation density, rocking curve halfwidth and strain, it was possible to use the non-destructive X-ray method to monitor deformation levels. The X-ray rocking curve measurements provided a sensitive indicator of work-hardening characteristics. By correlating the defect structure analysis to kinetic recovery studies of the alloy, including determination of activation energies, it was possible to obtain an insight into the dislocation obstacles responsible for hardening at different strain levels on the basis of their thermal stability. It was shown that Alloy 600, owing to its low stacking fault energy, exhibited the typical deformation characteristics of a Taylor lattice. For a 0.3% plastically strained sample, the dislocations, predominately generated by grain boundary carbides, moved by planar slip without having any major obstacles to overcome. A low activation energy of 25.6 kcal mol −1, attributed to grain boundary self-diffusion, sufficed to result in complete recovery. On analysis of the strain distribution of a large population, it was shown that the alloy underwent inhomogeneous deformation. At a plastic strain of 2%–3%, several intersecting slip systems became operative, resulting in the formation of dislocation obstacles that could only be overcome at elevated temperatures by bulk diffusion and dislocation climb. The activation energies required to obtain 20%, 40% and 50% recovery were 73.0 kcal mol −1, 67.6 kcal mol −1 and 64.1 kcal mol −1 respectively, indicating that more energy was required for strain release at the early stage of the recovery process.

Structural characterisation of bismuth germanate single crystals

Structural and spectroscopic properties of BGO crystals, grown by a modified Bridgman method, are examined by means of dislocation density measurements, excitation and emission experiments, and energy resolution measurements.

Growth of ZnSe single crystals by iodine transport

Large ZnSe single crystals (14x14x20 mm 3) have successfully been grown from the vapor phase by iodine transport. Substrates with large area (10x10 mm 2) for epitaxial growth were prepared by cutting the crystal. It is important to control the temperature fluctuation and seed direction for rapid growth. As an etchant for the measurement of dislocation density, the NaOH solution on (111) B is better than the Br-CH 3OH solution on (111) A. The etch-pit density is (2–7)x10 4/cm 2. The iodine concentration in the crystal is about 200 ppm. The resistivity of the ZnSe crystal annealed in molten Zn is 0.03 Ω cm.

Strain relaxation in low lattice mismatch epitaxy of CdTe/Cd0.97Zn0.03Te (001) by channeling

A measurement of the misfit dislocation density at the CdTe(001)/Cd0.97Zn0.03Te (001) interface has been obtained by channeling. This method allows an accurate determination of the critical thickness (390 nm) and appears sensitive for misfit dislocation density determination in systems with lattice mismatch as low as Δa/a≂3×10−4. The formation energy of misfit dislocations is estimated to be about 10−8 J/m.

Dislocation-density studies in MOCVD GaAs on Si substrates

The evaluation of dislocation density as well as EPD in GaAs/Si by plan-view TEM and molten KOH etching has been performed. The dislocation density of GaAs/Si was reduced by in-situ thermal cyclic annealing (TCA) and by the combined growth method including both in-situ TCA and strained-layer-superlattice (SLS) structures. In the combined growth method, three different kinds of SLS structures were grown with or without misfit dislocations. The ratio of EPD to dislocation density varied from 3:10 to 5:10. The experimental results indicate that EPD is a good measure of dislocation density between 106 and 108 cm−2. Experiments also revealed that the combined growth method is more effective than using only TCA for the reduction of the dislocation density in GaAs/Si.

Additive strengthening mechanisms in dispersion hardened polycrystals

Tensile data from polycrystalline samples of copper dispersion strengthened by alumina are analysed. The basis of this analysis is to look at the strain range from 0.05 to 0.20 where the stress-strain curves show a parabolic hardening behaviour and are parallel to one another. The means by which the addition of strength components from various elements of the microstructure and substructure might explain this behaviour are investigated. It is shown that a linear combination of a matrix friction stress, an Orowan bowing stress, a matrix mean stress from the particles and a combined dislocation interaction term can explain this data and also the data from some aluminium-alumina materials. The dislocation interaction term, which dominates, is comprised of terms which cover the pure matrix work hardening, the hardening due to particles and due to the grain boundaries. This term is derived by summing the dislocation density contributions from each of these three sources. The type of additivity suggested here not only gives very good agreement with the stress-strain data but it also uses and is in accord with the experimental measurements of dislocation densities made using transmission electron microscopy.

Optical mapping of residual stress in Czochralski grown GaAs

Despite several detailed theoretical analyses of the stress distribution expected for Czochralski grown GaAs crystals, experimental verification of these calculations has hitherto relied on dislocation density measurements. The present work shows that weak photoelastic patterns are resolvable in the near-infrared transmittance (typically near 1.4 μm) of semi-insulating GaAs wafers. Mapping of these patterns reveals the contours of constant shear stress, with results generally supporting the calculated models for the stress distribution.

Etch patterns on borax crystals

AbstractEtch patterns obtained on habit as well as cleaved matched faces of borax crystals are described. Morphology of all the etch pits is discussed. It is found that all the pits are formed at the sites of dislocations. A report about various dislocation configurations is given. From the dislocation density measurements, it is established that the borax crystals grown are of very good quality.