Two-beam Diffraction Conditions Research Articles

Non-radiative recombination centres in InGaN/GaN nanowires revealed by statistical analysis of cathodoluminescence intensity maps and electron microscopy

The methodology of statistical analysis of cathodoluminescence (CL) intensity mappings on ensembles of several hundreds of InGaN/GaN nanowires (NWs) used to quantify non-radiative recombination centres (NRCs) was validated on InGaN/GaN NWs exhibiting spatially homogeneous cathodoluminescence at the scale of single NWs. Cathodoluminescence intensity variations obeying Poisson's statistics were assigned to the presence of randomly incorporated point defects acting as NRCs. Additionally, another type of NRCs, namely extended defects leading to spatially inhomogeneous cathodoluminescence intensity at the scale of single InGaN/GaN NWs are revealed by high resolution scanning transmission electron microscopy, geometrical phase analysis and two-beam diffraction conditions techniques. Such defects are responsible for deviations from Poisson's statistics, allowing one to achieve a rapid evaluation of the crystallographic and optical properties of several hundreds of NWs in a single cathodoluminescence intensity mapping experiment.

Dislocation structure of tungsten irradiated by light ions

Single crystalline tungsten samples were irradiated by He, D, and H at room temperature, with a calculated damage level in the peak maximum up to 0.04 dpa and with He up to 0.5 dpa. The dislocation structure of the whole damage zone was investigated perpendicular to the irradiated surface by Transmission Electron Microscopy (TEM) under four different two-beam diffraction conditions g =−200, 020, −110, 110 close to the [100] zone axis, taking bright-field kinematical images. The depth of the damage zone observed by TEM is in good agreement with the damage depth calculated by SRIM. The damage zones of the tungsten samples irradiated by He, D, H up to 0.04 dpa can be subdivided into four subzones. Significant differences in the dislocation structures between the different ion species despite comparable calculated damage levels were found at the depth close to the damage peak maximum. In this depth, the damage zone of tungsten irradiated by He consists of small dense dislocation loops (⩽3 nm) with high strain fields. Irradiation by D creates large dislocation loops with an average diameter of 15–22 nm depending on the set diffraction condition. The damage zone of H-irradiated tungsten is dominated by long dislocation lines at the depth of the damage peak maximum. No transition from dislocation loops to lines was found in the sample irradiated with He up to 0.5 dpa. This is probably due to He bubbles, which hinder the loops to aggregate into lines. This work shows that the displacement damage obtained by the irradiation of tungsten at room temperature with light ions is significantly different to tungsten irradiated to the same calculated damage level by medium to high-mass ions (Wielunska et al 2022 Nucl. Fusion 62 096003 [1]).

Dislocation structure of tungsten irradiated by medium to high-mass ions

Single crystalline tungsten was irradiated by the medium-mass ion Si with 7.5 MeV and high mass-ion W with 20.3 MeV up to a calculated peak damage level of 0.04 dpa and 0.5 dpa. The obtained dislocation structure of the damage zone was investigated by transmission electron microscopy and systematically compared with each other. Bright-field kinematical images were taken under four different two-beam diffraction conditions g = −200, 020, −110, 110 close to the [100] zone axis. The observed damage depth and damage peak position is in good agreement with the SRIM calculated damage depth profiles. The dislocation structures were investigated at the region of the damage peak because there the damage levels are comparable. In both irradiations (Si and W), the dislocation structures were similar. At the low damage level of 0.04 dpa dislocation loops and dislocation-loop clusters were found. The size of the dislocation loops in the W-irradiated tungsten sample was up to 20% higher than for the Si-irradiated sample. At the high damage level of 0.5 dpa a dislocation network consisting of dislocation-loop chains and dislocation lines was found for both irradiations. The dislocation line density was about 12% higher for the W-irradiated sample. Through comparison of the damage zone to SRIM damage depth profiles it was found that the transition from dislocation loops and dislocation-loop clusters to an ordered dislocation network takes place at about 0.08–0.1 dpa. Despite the large differences in ion mass and irradiation energy the dislocation structures were very similar.

Identification of type of threading dislocation causing reverse leakage in GaN p\u2013n junctions after continuous forward current stress

Power devices are operated under harsh conditions, such as high currents and voltages, and so degradation of these devices is an important issue. Our group previously found significant increases in reverse leakage current after applying continuous forward current stress to GaN p–n junctions. In the present study, we identified the type of threading dislocations that provide pathways for this reverse leakage current. GaN p–n diodes were grown by metalorganic vapor phase epitaxy on freestanding GaN(0001) substrates with threading dislocation densities of approximately 3 × 105 cm−2. These diodes exhibited a breakdown voltage on the order of 200 V and avalanche capability. The leakage current in some diodes in response to a reverse bias was found to rapidly increase with continuous forward current injection, and leakage sites were identified by optical emission microscopy. Closed-core threading screw dislocations (TSDs) were found at five emission spots based on cross-sectional transmission electron microscopy analyses using two-beam diffraction conditions. The Burgers vectors of these dislocations were identified as [0001] using large-angle convergent-beam electron diffraction. Thus, TSDs for which b = 1c are believed to provide current leakage paths in response to forward current stress.

Analysis of crystal defects by scanning transmission electron microscopy (STEM) in a modern scanning electron microscope

Dislocations and stacking faults are important crystal defects, because they strongly influence material properties. As of now, transmission electron microscopy (TEM) is the most frequently used technique to study the properties of single dislocations and stacking faults. Specifically, the Burgers vector b of dislocations or displacement vector R of stacking faults can be determined on the basis of the g·b = n (g·R = n) criterion by setting up different two-beam diffraction conditions with an imaging vector g. Based on the reciprocity theorem, scanning transmission electron microscopy (STEM) can also be applied for defect characterization, but has been less frequently used up to now. In this work, we demonstrate g·b = n (g·R = n) analyses of dislocations and stacking faults in GaN by STEM imaging in a scanning electron microscope. The instrument is equipped with a STEM detector, double-tilt TEM specimen holder, and a charge-coupled-device camera for the acquisition of on-axis diffraction patterns. The latter two accessories are mandatory to control the specimen orientation, which has not been possible before in a scanning electron microscope.

Simulations of weak-beam diffraction contrast images of dislocation loops by the many-beam Schaeublin–Stadelmann equations

Based on many-beam Schaeublin–Stadelmann diffraction equations and elasticity theories of defects, the transmission electron microscopy (TEM) diffraction contrast of dislocation loops within thin TEM foil is investigated systematically. Firstly, TEM diffraction contrast images of Frank dislocation loops in ion-irradiated copper are simulated with two-beam Howie–Whelan and many-beam Schaeublin–Stadelmann diffraction equations for verification; Then, the classic L–g–b relation of dislocation loop diffraction contrast is revisited, and effects of two-beam and many-beam diffraction conditions on the image contrast features are compared. Afterward, effects of anisotropic ratio on the black–white lobe features of dislocation loops are studied. Additionally, effects of loop depth within thin foil on the black–white lobes feature of dislocation loops are studied, and anisotropy will not change the flipping feature of the diffraction contrast lobes.

Identifying dislocations and stacking faults in GaN films by scanning transmission electron microscopy

The application of annular bright field (ABF) and medium-angle annular dark field (MAADF) scanning transmission electron microscopy (STEM) imaging to crystalline defect analysis has been extended to dislocations and stacking faults (SFs). Dislocations and SFs have been imaged under zone-axis and two-beam diffraction conditions. Comparing to conventional two-beam diffraction contrast images, the ABF and MAADF images of dislocations and SFs not only are complementary and symmetrical with their peaks at dislocation core and SFs plane, but also show similar extinction phenomenon. It is demonstrated that conventional TEM rules for diffraction contrast, i.e. g · b and g · R invisibility criteria remain applicable. The contrast mechanism and extinction of dislocation and SFs in ABF and MAADF STEM are illuminated by zero-order Laue zone Kikuchi diffraction.

Dislocation characterization in fatigued Cu with nanoscale twins

Previous studies have shown that strain-controlled cyclic stability was maintained in bulk Cu samples with highly oriented nanoscale twins. In order to explore the underlying fatigue mechanism, transmission electron microscopy observations under two-beam diffraction condition were utilized to characterize the dislocation configurations in the twin/matrix layers of as-fatigued nanotwinned Cu. It was clarified that the threading dislocations with Burgers vector parallel to twin boundaries are mainly active during fatigue. A three-dimensional stereo projection was re-configured for demonstrating the special structure of dislocations in nanoscale twins.

Dynamical effects in strain measurements by dark-field electron holography.

Here, we study the effect of dynamic scattering on the projected geometric phase and strain maps reconstructed using dark-field electron holography (DFEH) for non-uniformly strained crystals. The investigated structure consists of a {SiGe/Si} superlattice grown on a (001)-Si substrate. The three-dimensional strain field within the thin TEM lamella is modelled by the finite element method. The observed projected strain is simulated in two ways by multiplying the strain at each depth in the crystal by a weighting function determined from a recently developed analytical two-beam dynamical theory, and by simply taking the average value. We demonstrate that the experimental results need to be understood in terms of the dynamical theory and good agreement is found between the experimental and simulated results. Discrepancies do remain for certain cases and are likely to be from an imprecision in the actual two-beam diffraction conditions, notably the deviation parameter, and points to limitations in the 2-beam approximation. Finally, a route towards a 3D reconstruction of strain fields is proposed.

Theory and application of electron channelling contrast imaging under controlled diffraction conditions

Electron channelling contrast imaging (ECCI) is a powerful technique for observing crystal defects, such as dislocations, stacking faults, twins and grain boundaries in the scanning electron microscope. Electron channelling contrast (ECC) is strongest when the primary electron beam excites so called two-beam diffraction conditions in the crystal. In the present approach this is achieved, by a combination of crystal orientation measurement using electron backscatter diffraction (EBSD) and simulation of electron channelling patterns. From the latter, the crystal is rotated such that two-beam diffraction conditions are achieved. This technique is called “ECCI under controlled diffraction conditions” or cECCI. Following an extensive literature review, this paper presents a simple, yet instructive and demonstrative treatment of the theory of ECC of lattice defects based on Bloch wave theory using a two-beam approach. This is followed by a discussion of technical issues associated with an ideal ECC set-up such as optimum detector position and microscope conditions. Subsequently, the appearance of different types of lattice defects under ECCI conditions; namely of dislocations, stacking faults, slip lines, and nanotwins, is discussed in detail. It is shown how different types of defects are distinguished and which type of crystallographic information can be extracted from such observations. Finally, the limits of the technique, particularly in terms of spatial resolution and depth of visibility are discussed and a comparison with the EBSD and transmission electron microscopy techniques with respect to imaging lattice defects is provided. In contrast to many investigations recently published in the literature, the current paper focuses on ‘true’ backscattering, i.e. on a signal that is recorded with a conventional backscatter detector positioned below the pole piece, and not on forward scattering, where the signal is recorded on a detector usually positioned below the EBSD detector. This has significant advantages in terms of spatial resolution and contrast, which are discussed in the text.

TEM studies of stress relaxation in catalytic Au-Pd core-shell nanoparticles

Transmission electron microscopy and diffraction are used to measure the lattice strain in catalytic Au-Pd core-shell nanoparticles. In order to simplify analysis, single nanoparticles were oriented to achieve strong two-beam diffracting conditions from the nanoparticle centre, such that diffraction was sensitive to the strain parallel to the Au-Pd interface. Corresponding selected area diffraction patterns were used to measure the in-plane strain as a function of the Pd thickness, which is shown to follow the equilibrium (Matthews) theory. These results suggest that, contrary to expectation, strain is not an important factor accounting for the difference in catalytic activity between nanoparticles and thin films. The significance of these results is discussed.

Investigation of grain boundaries in BaSi2 epitaxial films on Si(1 1 1) substrates using transmission electron microscopy and electron-beam-induced current technique

a-Axis-oriented undoped n-BaSi2 epitaxial films were grown on Si(111) substrates by molecular beam epitaxy, and the crystalline quality and grain boundaries were investigated by means of reflection high-energy electron diffraction, X-ray diffraction, and transmission electron microscopy (TEM). The grain size of the BaSi2 films was estimated to be approximately 0.1–0.3μm, and straight grain boundaries (GBs) were observed in the plan-view TEM images. Dark-field TEM images under a two-beam diffraction condition showed that these GBs consist mostly of BaSi2 {011} planes. The diffusion length of minority carriers in n-BaSi2 was found to be approximately 10μm by an electron-beam-induced current technique.

Quantitative characterization of self-assembled coherent islands

We report on plan-view transmission electron microscopy techniques, by which the size, the actual shape and the strain of a coherent island in semiconductor heterostructures can be measured accurately. The bright-field suppressed-diffraction imaging condition where no strong diffracted beam is excited in the sample provides reliable size measurement as well as the detailed shape and aspect ratio. An exact two-beam diffraction condition is employed to produce the strain contrast of a coherent island and the corresponding fringes can be easily utilized to measure the average strain relaxation occurring during island evolution. We also propose an off-axis z contrast technique for the unambiguous determination of composition profile in an island. Finally examples of application of these techniques on the characterization of Ge coherent islands on Si(1 0 0) substrates are demonstrated.

7-Parameter Automated Measurement of the Shapes of Nanoscale Inclusion by TEM

Abstract The equilibrium shape of liquid inclusions in a crystalline matrix is a direct measure of the orientation dependence, or anisotropy, of the liquid/solid interfacial energy. In this work we have used diffraction contrast imaging in TEM to observe the shape of nanoscale liquid Pb inclusions in a solid Al matrix as a function of temperature. While a previous investigation reported a highly anisotropy equilibrium shape [1], more recent work showed that the inclusion shape depends on size, temperature and thermal history [2-4]. Here we report on a new method to make accurate automated measurements of these particle shapes during in-situ heating above the melting point of the inclusions. Fig.l shows a typical bright field image of an array of liquid Pb inclusions in a solid Al matrix recorded at temperature during in-situ heating to 423°C. Under these two-beam diffraction conditions, particles are visible by absorption contrast and appear dark on a light background.

Transmission electron microscopy of semiconductor quantum dots

We report on plan-view transmission electron microscopy techniques, by which the size, the actual shape and the strain of a coherent quantum dot in semiconductor heterostuctures can be measured very accurately. The bright-field suppressed-diffraction imaging condition where no strong diffracted beam is excited in the sample provides reliable size measurement. Using suppressed-diffraction imaging condition, the intensity contour in a coherent island is related to the height, and thus the detailed shape and the aspect ratio can be extracted. The strain contrast of a coherent island imaged using an exact two-beam dynamical diffraction condition is useful for strain measurement and the corresponding features is related to the shape of an island. The physical origins and accuracy of interpretation of the image contrast are discussed, using the simulations and experimental examples.

Interference effects in inelastic thickness fringes

We discuss the double differential scattering cross section for atomic inner-shell excitations in crystals. We emphasize interference effects and demonstrate them by means of energy-filtered images of silicon monocrystals under two-beam diffraction conditions. In particular, we measure thickness fringes.

SIMCON: a versatile software package for the simulation of electron diffraction contrast images of arbitrary displacement fields

A versatile modular program (SIMCON) for the simulation of electron diffraction contrast images of localized displacement fields resulting from elastic stress concentrations on a submicron scale has been developed. A first module computes the displacement field. Analytical as well as finite-element calculations with existing software are possible. The second module calculates the contrast image based on full two-beam dynamical diffraction theory using the displacement field as computed by the first. The third module can be used to perform image-analysis operations on the calculated intensity distribution and subsequently viewing the result on a computer screen or making hard copies on a PostScript printer. We present some examples of simulations under two-beam diffraction conditions illustrating the power of SIMCON.

TEM characterization of dislocation reduction processes in GaAs/Si

A high density of interfacial dislocations are needed at the GaAs/Si interface to alleviate the 4% lattice mismatch between GaAs and Si. Some remnant dislocations thread through the epilayer and follow the growth interface. Current growth methods are not able to obtain acceptable threading dislocation densities (104 – 105) for devices. Many methods can be used to reduce the number of threading dislocations which include misorienting the substrate to enhance the slip of dislocations on specific [110]{111} planes, annealing during and after growth, and adding strained layer superlattices (SLS's) to block dislocations. Conventional TEM (CTEM), performed using a JEM 100c, has been used to characterize threading dislocations in the epilayer of a GaAs/Si material where in situ thermal annealing and SLS's force dislocation reactions and thereby reduce the threading dislocation density. Using TEM we have viewed dislocations under many two-beam diffraction conditions and with the help of a stereogram have determined their Burgers vectors (b), line directions (u) and habit planes (R).

The direct indexing of two-beam electron diffraction patterns

A technique is described for the direct indexing of two-beam electron diffraction conditions in the electron microscope. The technique involves the calculation of angles between the g-vector to be indexed and a set of three known reference vectors. The experimentally obtained angles may be compared with calculated interplanar angles, leading to an unambiguous indexing of the two-beam situation. In-situ indexing is possible when the microscope is equipped with a device for the direct measurement of diffraction spot positions.

Black-white contrast on transmission electron microscope images of small dislocation loops in elastically anisotropic crystals

Abstract The black-white contrast of small dislocation loops in elastically anisotropic crystals is calculated using the first-order perturbation solution for the dynamical two-beam diffraction condition. It is shown that under realistic conditions the contrast is given essentially by the projection of the displacement field of the dislocation loop onto the image plane. From the Fourier representation [gtilde](k) of the Green's function of the displacement field of point forces the projected displacement field of the loop is obtained by two-dimensional inversion of the Fourier transformation. The final result is applicable for arbitrary directions of the incident electron beam and implies as the critical step the determination of the six roots of the denominator of [gtilde](k) in the image plane. Examples referring to crystals of cubic symmetry demonstrate that the orientation and shape of the black-white contrast figure becomes more and more insensitive to the actual directions of the loop normal n and the loop Burgers vector b as the elastic anisotropy increases.