Dislocation Density Measurements Research Articles

Chemical mechanical polishing for decoration and measurement of dislocations on freestanding GaN wafers

The dislocation density in freestanding gallium nitride wafers was measured using atomic force microscope (AFM) imaging of chemical mechanically polished (CMP) samples and with transmission electron microscopy (TEM). Etch pits were introduced after chemical mechanical polishing of the gallium side of the GaN wafer and the pits easily imaged with the AFM. TEM was also utilized to measure the dislocation density. Good agreement was found between the dislocation density measured by TEM and the etch pit density measured by AFM, demonstrating that chemical mechanical polish of the GaN(0001) surface decorates threading dislocations and that the AFM technique provides a reasonably accurate and convenient measure of the dislocation density. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Application of a Modified Jogged-Screw Model for Creep of Titanium Aluminides: Evaluation Of The Key Substructural Parameters

AbstractA modification of the jogged-screw model has been adopted recently by the authors to explain observations of 1/2[110]-type jogged-screw dislocations in equiaxed Ti-48Al under creep conditions. The aim of this study has been to verify and validate the parameters and functional dependencies that have been assumed in this previous work. The original solution has been reformulated to take into account the finite length of the moving jog. This is a better approximation of the tall jog. The substructural model parameters have been further investigated in light of the Finite Length Moving Line (FLML) source approximation. The original model assumes that the critical jog height (beyond which the jog is not dragged) is inversely proportional to the applied stress. By accounting for the fact that there are three competing mechanisms (jog dragging, dipole dragging, dipole bypass) possible, we can arrive at a modified critical jog height. The critical jog height was found to be more strongly stress dependent than assumed previously. The original model assumes the jog spacing to be invariant over the stress range. However, dynamic simulation using a line tension model has shown that the jog spacing is inversely proportional to the applied stress. This has also been confirmed by TEM measurements of jog spacings over a range of stresses. Taylor's expression assumed previously to provide the dependence of dislocation density on the applied stress, has now been confirmed by actual dislocation density measurements. Combining all of these parameters and dependencies, derived both from experiment and theory, leads to an excellent prediction of creep rates and stress exponents. The further application of this model to other materials, and the important role of atomistic and dislocation dynamics simulations in its continued development is also discussed.

Effects of pressure on high-temperature dislocation creep in olivine

Effects of pressure on high-temperature, dislocation creep in olivine ((Mg, Fe) 2 SiO 4 ) aggregates have been determined under both water-poor ('dry') and water-saturated ('wet') conditions. New experimental data were obtained at pressures of 1-2 GPa under 'dry' and 'wet' conditions using a newly developed high-resolution dislocation density measurement technique to estimate the creep strength. These data are compared with previous data at lower and higher pressures to determine the pressure dependence of high-temperature dislocation creep in olivine aggregates. We find that the creep strength under 'dry' conditions increases monotonically with increasing pressure, whereas the creep strength under 'wet' conditions changes with pressure in a non-monotonic fashion: it first decreases rapidly with increasing pressure and then becomes less sensitive to pressure at above 1 GPa. Such behaviour can be described by the following formula: where the subscripts d and w refer to parameters for 'dry' and 'wet' conditions respectively. The present study gives A d = 10 6.1 -0.2 s m1 (MPa) mn , , and r = 0 for 'dry' conditions, and A w m10 2.9 -0.1 s m1 (MPa) mn mr , , and r = 1.20 -0.05 for 'wet' conditions ( n = 3.0 -0.1 for both 'dry' and 'wet' conditions). The large activation volume for 'wet' conditions can be interpreted as due to the additional contribution from the activation volume for dissolution of OH in the olivine structure ( ). The value of r ( ,1.2) is consistent with a model in which creep in olivine is rate controlled by the motion of positively charged jogs through the diffusion of silicon via an interstitial mechanism.

Application of a Modified Jogged-Screw Model for Creep of Titanium Aluminides: Evaluation Of The Key Substructural Parameters

AbstractA modification of the jogged-screw model has been adopted recently by the authors to explain observations of 1/2[110]-type jogged-screw dislocations in equiaxed Ti-48Al under creep conditions. The aim of this study has been to verify and validate the parameters and functional dependencies that have been assumed in this previous work. The original solution has been reformulated to take into account the finite length of the moving jog. This is a better approximation of the tall jog. The substructural model parameters have been further investigated in light of the Finite Length Moving Line (FLML) source approximation. The original model assumes that the critical jog height (beyond which the jog is not dragged) is inversely proportional to the applied stress. By accounting for the fact that there are three competing mechanisms (jog dragging, dipole dragging, dipole bypass) possible, we can arrive at a modified critical jog height. The critical jog height was found to be more strongly stress dependent than assumed previously. The original model assumes the jog spacing to be invariant over the stress range. However, dynamic simulation using a line tension model has shown that the jog spacing is inversely proportional to the applied stress. This has also been confirmed by TEM measurements of jog spacings over a range of stresses. Taylor's expression assumed previously to provide the dependence of dislocation density on the applied stress, has now been confirmed by actual dislocation density measurements. Combining all of these parameters and dependencies, derived both from experiment and theory, leads to an excellent prediction of creep rates and stress exponents. The further application of this model to other materials, and the important role of atomistic and dislocation dynamics simulations in its continued development is also discussed.

A Revised Jogged-Screw Model For Creep Of Equiaxed γ-TiAl: Identification Of The Key Substructural Parameters.

ABSTRACTA modification of the classic jogged-screw model has been previously adopted to explain observations of 1/2[110]-type jogged-screw dislocations in equiaxed Ti-48Al under creep conditions. The aim of this study has been to verify and validate the parameters and functional dependencies that have been assumed in that model. The original solution has been reformulated to take into account the finite length of the moving jog. This is a better approximation of the tall jog. The substructural model parameters have been further investigated in light of the Finite Length Moving Line (FLML) source approximation. The original model assumes that the critical jog height (beyond which the jog is not dragged) is inversely proportional to the applied stress. By accounting for the fact that there are three competing mechanisms (jog dragging, dipole dragging, dipole bypass) possible, we can arrive at a modified critical jog height. The critical jog height was found to be more strongly stress dependent than assumed previously. The original model assumes the jog spacing to be invariant over the stress range. However, dynamic simulation using a line tension model has shown that the jog spacing is inversely proportional to the applied stress. This has also been confirmed by TEM measurements of jog spacings over a range of stresses. Taylor's expression assumed previously to provide the dependence of dislocation density on the applied stress, has now been confirmed by actual dislocation density measurements. Combining all of these parameters and dependencies, derived both from experiment and theory, leads to an excellent prediction of creep rates and stress exponents.

Measurement of screw and edge dislocation density by means of X-ray Bragg profile analysis

The type of dislocations produced during plastic deformation is necessary to know for the fundamental understanding anisotropy of hardening processes. By studying X-ray line broadening in several reflections, the fraction of certain dislocation types can be determined experimentally. The contribution of strain to line broadening is generally anisotropic. On the basis of the dislocation model, the modified Williamson–Hall and Warren–Averbach procedures have been suggested where g and g 2 are replaced by g C ̄ and g 2 C ̄ , with C ̄ as the average dislocation contrast factor. C ̄ can be evaluated theoretically for different crystal systems and different dislocation types, i.e. edges and/or screws, by numerical methods. On the other hand, by analyzing strain anisotropy C ̄ can be determined from experiment. Comparing experimental with theoretical C-values the specific fraction of dislocation types can be determined. In the present paper this procedure has been carried out for fine grained Cu 99.9% for deformation well into stage III. The ratio starts with a high fraction (90%) of screw dislocations. During deformation up to ε=0.3 this picture changes in favor of edge dislocations (75%).

Defects in heteroepitaxial CeO 2/YSZ/Si(0 0 1) films by precise X-ray rocking curve distribution fitness

In this paper, the theory of dislocation density and curvature measurements from X-ray rocking curves is extended to the case of double oxide heteroepitaxial CeO 2(0 0 1)/YSZ(0 0 1)/Si(0 0 1) films mainly by high-resolution X-ray diffraction. According to this theory, we have successfully resolved the rocking curves of CeO 2 and YSZ by two simple components. Thus, the dislocation density and radius of curvature of each layer can be calculated from the distribution of the square of measured FWHM versus 1/sin 2 θ. The results show that the YSZ layer has a higher dislocation density and a lower radius of curvature than CeO 2. The high-resolution transmission electron microscopy (TEM) image of CeO 2/YSZ interface cross-section shows a high dislocation density along the interface with an average interval ∼3.9 nm.

Quantitative Defect Analysis of GaN Thick Films by TEM and AFM

AbstractEver since the discovery of the astonishing properties of GaN, many research groups have been involved in the processing of the perfect GaN crystal. Iodine Vapor Phase Growth (IVPG) technique was employed to grow GaN epilayer on a MOCVD pre-deposited buffer layer. This new epitaxial system was characterized by TEM, AFM and EFM. A complete AFM study involved the polarity measurements and the etch pit density measurements. For the first time a systematic study was performed of the dislocation density changing as a function of distance from the substrate. TEM performed on the cross-section, as well as the plan view, of the samples showed a remarkable decrease in the dislocations in the current system, compared to the samples that were solely deposited by MOCVD. Advanced analytical methods of polarity and dislocation density measurements have been established to understand the relation between microstructure and electrical properties of the thick film GaN. Electrostatic Force Microscopy has been suggested as a potential tool for obtaining polarity information.

MOVPE growth of lattice-mismatched Al 0.88In 0.12As on GaAs (1 0 0) for space solar cell applications

We report, for the first time, the growth and characterization of lattice-mismatched Al 0.88In 0.12As on GaAs (1 0 0) as part of a program to develop a high-efficiency, triple-junction space solar cell. The expected practical efficiency of this cell is 31%. The proposed triple-junction cell consists of a 2.1 -eV Al 0.88In 0.12As top cell, a 1.6 -eV In 0.48Ga 0.52As 0.23P 0.77 middle cell, and a 1.2 -eV In 0.13Ga 0.87As bottom cell. The Al 0.88In 0.12As layers were grown on GaAs (1 0 0) wafers cut 6° off-axis, using metal organic precursors trimethylaluminum, trimethylindium and the hydride arsine in a horizontal, reduced-pressure metal organic vapor-phase epitaxy (MOVPE) reactor. Crystalline quality was evaluated through triple-axis X-ray diffractometry. Reciprocal lattice mapping showed that the Al 0.88In 0.12As layers were relaxed to a large extent, and were of high crystalline quality. Doping was performed using silane (n-type) and diethylzinc (p-type). Secondary ion mass spectrometry (SIMS) and electrochemical C– V profiling showed that it was possible to obtain abrupt doping profiles to the levels required for solar cell fabrication. Details of these results and those of dislocation density measurement using transmission electron microscopy (TEM) are described in this paper.

The Deviation from Matthiessen's Rule and Electrical Dislocation Density Measurement in Dilute Cu-Au Alloys

The method of electrical dislocation density measurement, which was successful in plastically deformed pure noble metals, is applied for the first time to dilute alloys, and the parameters for the electrical dislocation density measurement, i.e. the temperature dependence of the deviation from Matthiessen's rule and of the low-field Hall coefficient were investigated in Cu–Au alloys with 0.075 and 0.3 at% gold. The results for the dislocation density, which rely on the modelling of the true dislocation resistivity by means of the two-group model are especially satisfactory for the 0.075 at% alloy. Additionally the dislocation density was checked by X-ray Bragg profile analysis. The comparison of the latter method with the electrical method shows that small dislocation loops originating from the agglomeration of deformation induced vacancies are part of the total dislocation density.

X-ray diffraction study and quantitative measurements of high dislocation densities in superlattices and single crystal layers of heteroepitaxial systems with pronounced lattice mismatch

Plastic deformation in a single-crystal layer of the In0.12Ga0.88As/(111)InP solid solution is identified by the methods of X-ray diffractometry (XRD) and the double-crystal pseudorocking curves (DCPRC). X-ray topographs showed the generation of three intersecting systems of straight dislocations in the layer. In a one-layer ZnSe/GaAs structure and multilayer ZnSe/ZnSe1 − x Sx/ZnSe/GaAs structures, the elastic and plastic strains were detected by the combined XRD-DCPRC method. The major components of the thermoelastic and plastic-deformation tensors were determined as exx = eyy = 3.5 × 10−3 and ezz = 2.35 × 10−3. Using these data, the dislocation densities were determined as N d ∼ 2.5 × 108 cm−2 and N d ∼ 3 × 1010 cm−2 for the 7 µm-thick ZnSe and 1 µm-thick InAs layers, respectively. In a superlattice of the AlxGa1 − x As/GaAs/⋯/GaAs-type with a large lattice parameter, the plastic deformation was detected. X-ray topography confirmed that the dislocation density in this superlattice equals ∼105 cm−2.

Modelling plastic stress relaxation in shaped sapphire crystal growth

Thermally induced stresses in growing shaped sapphire crystals are modelled using transient finite element simulations. Boundary conditions and mass changes are fixed on an expanding remeshed and updated grid. The actual stresses are obtained taking into account plastic relaxation through dislocation glide along basal, prismatic and pyramidal slip planes. For this purpose, phenomenological creep laws available for this material are implemented in the frame of thermally activated plasticity. The model is calibrated by comparison with directional mechanical tests, and validation is performed by growth simulations and dislocation density measurements on as-grown crystals.

Microstructural evolution during creep of single-phase gamma TiAl

Mechanical experiments and transmission electron microscope (TEM) observations indicate that single-phase γ-TiAl does exhibit primary, secondary, and inverse creep, but not steady-state creep. Constant stress creep tests of γ-Ti-51Al-2Mn conducted at 550 °C, 597 °C, and 703 °C have been interrupted at different stages in the creep process. The TEM observations of these specimens were used to document the microstructural evolution that occurs during creep. Superdislocation motion was activated and subsequently exhausted during primary creep. Ordinary dislocations were observed to be pinned during primary creep, but with time, these dislocations began to bow past their pinning points. The extended region of inverse creep has been related to the bowing and multiplication of these ordinary dislocations. Quantitative measurements of dislocation density were performed, and while the density of superdislocations remained constant, the density of ordinary dislocations increased by an order of magnitude during the life of a creep test. The acceleration in the creep rate has been related to this increase in the density of ordinary dislocations, but the change in dislocation density was not high enough to account for the increase in the creep rate. This suggests that both the mobility and density of ordinary dislocations increase as creep progresses.

Strain Estimation by Electron Back Scattered Diffraction

The quality of the Kikuchi patterns obtained for example by electron backscattered diffraction decreases when the dislocation density increases in strained materials, and consequently, it can theoretically be correlated to the strain through the average dislocation density measurement particularly for monotonic deformation paths. For that purpose, in a first step it is necessary to define a quality factor defined in the Hough space or with the Burns method currently used when the Kikuchi patterns are automatically analyzed. Then, and it is the most important point, the quality factor must be linked to the strain through a calibration curve independent of crystallographic orientation.The main objective of this study is to test the reliability of this method in the simple case of the hardness test. This test is simulated using the finite element method and the obtained results are compared to those measured by electron backscattered diffraction. Several calibration methods are defined.

Dielectric response of thick low dislocation-density Ge epilayers grown on (001) Si

Spectroscopic ellipsometry was used to measure the dielectric functions of epitaxial and bulk Ge at photon energies from 1.5 to 5.2 eV. The epitaxial Ge was grown at 400 °C by molecular beam epitaxy on (001) Si substrates. The optical response and the interband critical-point parameters of Ge on Si were found to be indistinguishable from that of bulk single crystal Ge, indicating high optical quality. Dislocation density measurements using an iodine etch verified low surface defect densities. We conclude that epitaxial Ge grown on Si at relatively low temperatures is suitable for optical device applications.

Measurement of Dislocation Density by Residual Electrical Resistivity

Measurement of Dislocation Density by Residual Electrical Resistivity

Dislocation resistivity in Cu: dependence of the deviations from Matthiessen's rule on temperature, dislocation density and impurity content

Measurements of dislocation resistivity and the deviations from Matthiessen's rule (DMRs) are reported for polycrystalline Cu samples with various dislocation densities, impurities and phonons. Since this DMR can reach the same order of magnitude as the dislocation resistivity itself, its quantification is essential in using the electrical resistivity for dislocation density measurement. In the framework of the classical two-group model, a formula for the DMR is derived for the three independent scatterers. The fits by this formula are satisfactory provided that isotropic phonon scattering is chosen for samples with high dislocation densities. While samples with a high purity (residual resistivity ratio (RRR)>or=300) show dislocation scattering anisotropies Adis approximately=0.1 irrespective of dislocation density, the more impure material (purity 99.99%) (RRR=130) exhibits a significant decrease in Adis at low dislocation densities, indicating some contribution of enhanced strain fields in the dislocation structure. This leads to an enhanced DMR contribution in this material and makes the determination of the dislocation density N by the electrical resistivity method less reliable. Nevertheless, in the whole purity range considered, the electrical resistivity yields at least the same measuring resolution as TEM of about Delta N approximately=1*109 cm-2, but a better performance for high dislocation densities up to the order of 1014 cm-2.

Surface strains and measurements of misfit dislocation density by diffraction methods in thin films on substrates

In-plane strain variations near the free surface of an epitaxial thin film containing misfit dislocation shave been calculated. It is shown that strain distribution under the surface of the film is not constant and this distribution also depends on film thickness even for constant misfit dislocation density. The strain derived from diffraction measurements must therefore be corrected to obtain the true misfit dislocation density.

The measurement of threading dislocation densities in semiconductor crystals by X-ray diffraction

The measurement of threading dislocation densities in heteroepitaxial semiconductor layers is important for the development of injection lasers, microwave transistors, and also the integration of devices in disimilar semiconductors. Dislocation density measurements have been made by destructive techniques such as etching and by transmission electron microscopy (TEM). However, X-ray rocking curves provide non-destructive measurements of dislocation densities with accuracy equal to crystallographic etches or TEM. The theory of this technique has been described by Gay, Hirsch, and Kelly [P. Gay, P.B. Hirsch, and A. Kelly, Acta Met. 1 (1953) 315] and Hordon and Averbach [M.J. Hordon and B.L. Averbach, Acta Met. 9 (1961) 237], for the case of highly dislocated metal crystals. In this paper, the theory of dislocation density measurement from rocking curves is extended to the case of (001) zinc-blende semiconductors. It is shown that the measurement of several ( hkl) rocking curve widths with a particular X-ray wavelength allows the calculation of the dislocation density by two independent techniques, thus allowing for a check of self-consistency. It is shown that for the case of epitaxial GaAs on Si(001), dislocation densities determined by these two methods are in good agreement.

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.