Bending Of Lattice Planes Research Articles

Visualizing local bending of lattice planes by extending two-azimuth synchrotron X-ray diffraction datasets to asymmetric reflection

Synchrotron X-ray rocking curve imaging (RCI) is modified to visualize local bending of lattice planes of a single crystal substrate (XR-V-LBLP). This method uses two-azimuth RCI datasets of asymmetric reflection or symmetric reflection. The analysis algorithm is described and a Python software code is provided in the Supplementary material. The two symmetrically equivalent 112¯4 datasets obtained from a GaN (0001) 4-inch wafer are reanalyzed using this software. The normal vector, reciprocal-lattice vector, of the local lattice planes, which is approximately parallel to the sample surface, is formulated as the product of two rotation matrices. This vector is written in polar coordinates using the length and two declination angles, newly introduced in this article. The spatial and probability distributions of the declination angles are also presented. The proposed method enables visualization of the local shape or orientation of the lattice planes of the entire wafer. The limits of application of the method are examined for the samples studied. The sample is found to satisfy two conditions regarding the relative d-spacing difference and the curvature of the lattice planes at all 50 adjacent μm positions.

In situ bow reduction during sublimation growth of cubic silicon carbide

Abstract Sublimation growth of cubic silicon carbide (3C–SiC) with diameters of 50 and 100 mm was performed on freestanding homoepitaxial grown seeds. For both seeds and sublimation grown crystals, two different relaxation axes with varying curvature could be observed with the higher bent axis aligned perpendicular to the original wafer flat. A general reduction in the wafer bow independent of the starting curvature and size of the seeds could be observed. Using the X-ray imaging, we could observe in situ that the bow reduction is linked to the growth of new material and cannot be initiated by heat up or cool down processes alone. Raman spectroscopy of the grown crystals revealed that the observed flattening goes along with a tensing of the seeding layers while the surface of the crystals remains free of a stress gradient. A slight concave bending of lattice planes along the main relaxation axis could be observed by high-resolution XRD rocking curve measurements while for the lower bent axis, no lattice plane bending occurred. Full width half maximum values of the (002) reflection showed values as low as 67 arcseconds proofing the possibility to grow large-area, high-quality 3C–SiC using sublimation growth.

Nanodomain structure of single crystalline nickel oxide

In this work we present a comprehensive study of the domain structure of a nickel oxide single crystal grown by floating zone melting and suggest a correlation between point defects and the observed domain structure. The properties and structure of domains dictate the dynamics of resistive switching, water splitting and gas sensing, to name but a few. Investigating the correlation between point defects and domain structure can provide a deeper understanding of their formation and structure, which potentially allows one to tailor domain structure and the dynamics of the aforementioned applications. A range of inhomogeneities are observed by diffraction and microscopy techniques. X-ray and low-energy electron diffraction reveal domains on the submicron- and nanometer-scales, respectively. In turn, these domains are visualised by atomic force and scanning tunneling microscopy (STM), respectively. A comprehensive transmission electron microscopy (TEM) study reveals inhomogeneities ranging from domains of varying size, misorientation of domains, variation of the lattice constant and bending of lattice planes. X-ray photoelectron spectroscopy and electron energy-loss spectroscopy indicate the crystal is Ni deficient. Density functional theory calculations—considering the spatial and electronic disturbance induced by the favourable nickel vacancy—reveal a nanoscale distortion comparable to STM and TEM observations. The different inhomogeneities are understood in terms of the structural relaxation induced by ordering of nickel vacancies, which is predicted to be favourable.

Characterization of Dislocations in 4H-SiC Single Crystals at the Initial Growth Stage by Synchrotron X-ray Topography

In recent years, 4H-SiC has become a widely acknowledged material applied in high power electronics. 4H-SiC-based devices are able to operate at high voltage, high current and high temperature due to its superior physical properties. However, they have yet to reached to the requirements for mass production, due to the fact of SiC’s relatively inferior crystal quality. Over the past few decades, the effect of various dislocations existing in the crystals such as threading screw/mixed dislocations (TSD/TMDs), threading edge dislocations (TEDs) and basal plane dislocations (BPDs) has been studied and revealed to be main source for degrading the reliability of SiC power devices[1-2]. Recently, studies on the early stages of physical vapor transport (PVT) growth of SiC have been reported by several groups regarding to the investigation of the step morphology and lattice plane bending [3-5]. However, dislocation propagation behavior and their formation mechanism at the early growth stages are yet to be studied in detail.This paper describes the investigation of dislocation behavior during the early stages of PVT-grown 6-inch 4H-SiC crystals by synchrotron monochromatic beam x-ray topography (SMBXT) technique. Ray tracing simulation was applied to simulate the dislocation images. Our studies show that most of the TSDs/TMDs are replicated into the newly grown crystal while most TEDs are generated by either nucleation in pairs at the seed/crystal interface or by redirection of BPDs in the seed crystal. Most BPDs in the newly grown layer are of screw type with 1/3[11-20] and this has been verified by comparison with ray tracing simulated images. TEDs with the same and opposite sign of Burgers vector are found to be deflected on to same basal plane by the overgrowth of macro-steps and start to glide in the same and opposite directions respectively. TMDs deflected on to the basal plane by macro-steps get dissociated into c and a components, with the a segment undergoing glide to form V-shaped configurations.[1] St.G. Muller, J.J. Sumakeris, M.F. Brady, R.C. Glass, H.M. Hobgood, J.R. Jenny, R. Leonard, D.P. Malta, M.J. Paisley, A.R. Powell, V.F. Tsvetkov, S.T. Allen, M.K. Das, J.W. Palmour, and C.H. Carter. Jr., Eur. Phys. J. Appl. Phys. 27, 29 (2004).[2] R. Singh and M. Pecht, IEEE Ind Electron M 2, 19 (2008).[3] E.K. Sanchez, J.Q. Lin, M.De. Graef, M. Skowronski, W.M. Vetter, M. Dudley, J. Appl. Phys. 91 (3) (2002) 1143.[4] C. Ohshige, T. Takahashi, N. Ohtani, M. Katsuno, T. Fujimoto, S. Sato, H. Tsuge, T. Yano, H. Matsuhata, M. Kitabatake, J. Cryst. Growth 1-6, 408 (2014).[5] N. Ohtani, C. Ohshige, M. Katsuno, T. Fujimoto, S. Sato, H. Tsuge, W. Ohashi, T. Yano, H. Matsuhata, M. Kitabatake, J. Cryst. Growth 9-15, 386 (2014). Figure 1

Relationship Between Basal Plane Dislocation Distribution and Local Basal Plane Bending in PVT-Grown 4H-SiC Crystals

The inhomogeneous distributions of basal plane dislocations (BPDs) in PVT-grown 4H-SiC crystal boule due to internal stresses cause lattice plane bending, which strongly affect SiC-based device fabrication. The relationship between BPDs and local basal plane bending in 6-inch 4H-SiC substrates has been investigated. Synchrotron monochromatic beam x-ray topography (SMBXT) imaging shows black and white contrast of BPDs with Burgers vectors of opposite signs based on the principle of ray tracing. We have evaluated the net difference of BPDs with black and white contrast along both [11$$ \bar{2}$$0] and [1$$ \bar{1}$$00] radial directions on the Si face across multiple 6-inch diameter 4H-SiC substrates sliced from the same and different boules and predicted the nature (concave/convex) and amount of bending of the basal plane in these wafers. Line scans of 0008 reflection using high resolution x-ray diffractometry (HRXRD) has been carried out along the two directions to verify the nature of bending in these wafers. Results show quite different bending behavior along [11$$ \bar{2} $$0] and [1$$ \bar{1}$$00] directions, indicating that the Si face of 6-inch substrates creates non-isotropic bending on the basal plane. These observations are correlated quite well with net BPD density analysis. The physical shapes of the wafers were also measured to be not flat due to the surface effect. Quantitative analysis of the degree of basal plane bending based on the SMBXT data was carried out and found to be correlating well with the measured tilt angle from HRXRD. Existence of a high stress center was observed in one of the 6-inch wafers resulting in severe bending which is associated with both large bending angles and abrupt changes in lattice constants a and c.

Relationship between Basal Plane Dislocation and Local Basal Plane Bending in PVT-Grown 4H-SiC Crystals

Efforts to improve the quality and size of 4H-SiC wafers have resulted in size of 6” and dislocation densities of the order of 103 cm-2. The presence of significant quantities of crystallographic defects in bulk 4H-SiC crystals continues to be a major obstacle for achieving high-quality 4H-SiC substrates. Of particular note is the nucleation and distribution of basal plane dislocations (BPDs). BPDs are deformation-induced and are mostly generated during post-crystal growth cooling or high temperature annealing processes. BPDs have been associated with the formation of Shockley stacking fault leading to an increase in forward voltage degradation and are undesirable. Depending on the PVT growth conditions, internal stresses due to non-uniformity of temperature field cause lattice plane bending. During cooldown, this bending is accommodated by the inhomogeneous distribution of BPDs in a PVT grown 4H-SiC boule and persists in wafers sliced from the boule. Crystal bending affects subsequent wafer processing especially polishing and device fabrication. Therefore, analysis of the BPD distribution (sign and density) enables us to better understand basal plane bending, which provides insight into further improvement of the crystal growth process. Synchrotron Monochromatic Beam X-ray Topography (SMBXT) studies in grazing incidence geometry reveal the appearance of black and white contrast of BPDs which are associated with opposite sign of Burgers vectors. Based on the principle of ray tracing, black contrast BPDs are generated by focusing of diffracted X-rays when the extra half plane is extending away from the imaged surface, while defocusing of X-rays contribute to the generation of white contrast BPDs due to the extra half plane extending towards the surface [1]. The inhomogeneous distribution of the two types of BPD contrast will thus result in concave/convex shape of the basal planes. In our study, we have evaluated the ratio of the black/white contrast of BPDs along 11-20 direction across multiple 6-inch diameter 4H-SiC substrates sliced from the same and different boules and predicted how the lattice is tilted in different substrate wafers. High resolution X-ray diffraction measurements are currently underway to investigate the variation of rocking curve peak shift along 11-20 direction and thus to further verify our result.

Influence of extended defects and oval shaped facet on the minority carrier lifetime distribution in as-grown 4H-SiC epilayers

The minority carrier lifetime distributions in 30 μm–190 μm thick 4H-SiC epilayers grown on 4 inch heavily nitrogen doped 4H-SiC substrates were measured by microwave photoconductive decay (μ-PCD) with a resolution of 1 mm lateral step, revealing three types of distribution patterns: a monotonous decrease in lifetime from the center to the edge (type 1), embedded with scattered regions in lower lifetime (type 2) or an oval shaped dark facet region in higher lifetime (type 3). Then, high resolution lifetime mapping measurements were further performed on these microareas with a lateral step size of 62.5 μm, which are compared with defects characterization results by Candela CS920 at the same position. It is found that the lifetime degradation correlates well with the stacking faults (SFs) and triangle defects. In general, the influence of triangle defect on lifetime degradation is more prominent than SF. In addition, surface roughness, lattice plane bending and crystal quality of oval shaped facet have been investigated by atomic force microscope (AFM) and high resolution X-ray diffraction (HRXRD). One possible reason for the higher lifetime over the oval shaped facet was proposed based on crystal quality and diffusion length.

Influence of surface relaxation of strained layers on atomic resolution ADF imaging

Surface relaxation of thin transmission electron microscopy (TEM) specimens of strained layers results in a severe bending of lattice planes. This bending significantly displaces atoms from their ideal channeling positions which has a strong impact on the measured annular dark field (ADF) intensity.With the example of GaAs quantum wells (QW) embedded in a GaP barrier, we model the resulting displacements by elastic theory using the finite element (FE) formalism. Relaxed and unrelaxed super cells served as input for state of the art frozen phonon simulation of atomic resolution ADF images.We systematically investigate the dependencies on the sample´s geometric parameters, i.e. QW width and TEM sample thickness, by evaluating the simulated intensities at the atomic column´s positions as well as at the background positions in between. Depending on the geometry the ADF intensity can be affected in a range several nm from the actual interface.Moreover, we investigate the influence of the surface relaxation on the angular distribution of the scattered intensity. At high scattering angles we observe an intensity reduction at the interface as well as in the GaP barrier due to de-channeling. The amount of intensity reduction at an atomic column is directly proportional to its mean square displacement. On the contrary we find a clearly increased intensity at low angles caused by additional diffuse scattering. We discuss the implications for quantitative evaluations as well as strategies to compensate for the reduced intensities.

Spatial variation of lattice plane bending of 4H-SiC substrates

Basal plane bending of on- and off-axis 4H-SiC substrates was measured by high-resolution X-ray diffractometry (HRXRD).

Characterization of Lattice Plane Bending and Stress Distribution in Physical Vapor Transport-Grown 4H-SiC Crystals

Basal plane bending and stress distribution in physical vapor transport-grown n-type 4H-SiC crystals were investigated. High resolution X-ray diffraction measurements were performed on commercially available 3-inch-diameter 4H-SiC substrates and along the growth front surface of as-grown 1-inch-diameter 4H-SiC boules. The measurements revealed that structural parameters such as the c-lattice constant, basal plane tilting, and FWHM showed characteristic variations across the substrates and as-gown boules, indicating that the crystals had a non-uniform distribution of dislocations comprising domain structures. Residual stress measured by micro Raman spectroscopy showed a similar behavior, which was an oscillatory spatial variation. On the basis of these results, defect structures in the crystals are elucidated.

Strain relaxation in Ge microcrystals studied by high‐resolution X‐ray diffraction

AbstractDeposition on patterned substrates is a promising method for obtaining high quality, strain and defect free heteroepitaxial layers. In this paper we investigate the crystalline structure of quasi‐continuous Ge layers consisting of closely spaced microcrystals on a Si substrate patterned in the form of a regular net of lithographically defined squared based pillars. Lattice parameters, strain and degree of relaxation of the Ge microcrystals are measured by standard high‐resolution X‐ray diffraction using reciprocal space mapping. In particular, we focus on the impact of Si pillar size and spacing on the Ge crystal quality by analyzing how the bending of crystal lattice planes caused by thermal stress relaxation and random crystal tilts affect the width of the diffraction peaks.

Structural and Electrical Characterization of the Initial Stage of Physical Vapor Transport Growth of 4H-SiC Crystals

Defect formation during the initial stage of physical vapor transport (PVT) growth of 4H-SiC crystals in the [000-1] and [11-20] directions was investigated by x-ray diffraction, defect-selective etching, and micro Raman scattering imaging. X-ray diffraction studies showed that the growths in the [000-1] and [11-20] directions exhibited markedly different behaviors with respect to the defect formation during the initial stage of growth. While a characteristic lattice plane bending was observed for the PVT growth along [000-1], a tilted domain structure was revealed near the grown crystal/seed interface for the growth in the [11-20] direction. Micro Raman scattering imaging revealed that nitrogen enrichment occurred near the grown crystal/seed interface and was associated with compressive stress parallel to the interface. Based on the results, the defect formation mechanisms during the initial stage of PVT growth of 4H-SiC are discussed.

Imaging Structure and Composition Homogeneity of 300 mm SiGe Virtual Substrates for Advanced CMOS Applications by Scanning X-ray Diffraction Microscopy.

Advanced semiconductor heterostructures are at the very heart of many modern technologies, including aggressively scaled complementary metal oxide semiconductor transistors for high performance computing and laser diodes for low power solid state lighting applications. The control of structural and compositional homogeneity of these semiconductor heterostructures is the key to success to further develop these state-of-the-art technologies. In this article, we report on the lateral distribution of tilt, composition, and strain across step-graded SiGe strain relaxed buffer layers on 300 mm Si(001) wafers treated with and without chemical-mechanical polishing. By using the advanced synchrotron based scanning X-ray diffraction microscopy technique K-Map together with micro-Raman spectroscopy and Atomic Force Microscopy, we are able to establish a partial correlation between real space morphology and structural properties of the sample resolved at the micrometer scale. In particular, we demonstrate that the lattice plane bending of the commonly observed cross-hatch pattern is caused by dislocations. Our results show a strong local correlation between the strain field and composition distribution, indicating that the adatom surface diffusion during growth is driven by strain field fluctuations induced by the underlying dislocation network. Finally, it is revealed that a superficial chemical-mechanical polishing of cross-hatched surfaces does not lead to any significant change of tilt, composition, and strain variation compared to that of as-grown samples.

Structural investigation of the seeding process for physical vapor transport growth of 4H–SiC single crystals

Structural investigation of the seeding process for the physical vapor transport (PVT) growth of 4H–SiC single crystals was conducted by high-resolution x-ray diffraction (HRXRD) and synchrotron x-ray topography. Characteristic lattice plane bending behavior was observed in the near-seed regions of the grown crystals. The bending of the (112̄0) lattice plane was localized near the seed/grown crystal interface, and the (0001) basal plane bent convexly in the growth direction near the interface, indicative of the insertion of extra-half planes pointing toward the growth direction during the seeding process for PVT growth. This study discusses a possible mechanism for the observed lattice plane bending and sheds light on defect formation processes during the PVT growth of 4H–SiC single crystals.

Composition mapping in InGaN by scanning transmission electron microscopy

We suggest a method for chemical mapping that is based on scanning transmission electron microscopy (STEM) imaging with a high-angle annular dark field (HAADF) detector. The analysis method uses a comparison of intensity normalized with respect to the incident electron beam with intensity calculated employing the frozen lattice approximation. This procedure is validated with an In(0.07)Ga(0.93)N layer with homogeneous In concentration, where the STEM results were compared with energy filtered imaging, strain state analysis and energy dispersive X-ray analysis. Good agreement was obtained, if the frozen lattice simulations took into account static atomic displacements, caused by the different covalent radii of In and Ga atoms. Using a sample with higher In concentration and series of 32 images taken within 42 min scan time, we did not find any indication for formation of In rich regions due to electron beam irradiation, which is reported in literature to occur for the parallel illumination mode. Image simulation of an In(0.15)Ga(0.85)N layer that was elastically relaxed with empirical Stillinger-Weber potentials did not reveal significant impact of lattice plane bending on STEM images as well as on the evaluated In concentration profiles for specimen thicknesses of 5, 15 and 50 nm. Image simulation of an abrupt interface between GaN and In(0.15)Ga(0.85)N for specimen thicknesses up to 200 nm showed that artificial blurring of interfaces is significantly smaller than expected from a simple geometrical model that is based on the beam convergence only. As an application of the method, we give evidence for the existence of In rich regions in an InGaN layer which shows signatures of quantum dot emission in microphotoluminescence spectroscopy experiments.

Observation of Lattice Plane Bending during SiC PVT Bulk Growth Using <i>In Situ</i> High Energy X-Ray Diffraction

We have investigated thermally induced strain in the SiC crystal lattice during physical vapor transport bulk growth. Using high energy x-ray diffraction lattice plane bending was observed in-situ during growth. With increasing growth rate increasing lattice plane bending and, hence, strain was observed. A comparison with numerical modeling of the growth process shows that the latter is related to the heat of crystallization which needs to be dissipated from the crystal growth front. The related temperature gradient as driving force for the dissipation of the heat of crystallization causes lattice plane bending. Optimization of the growth process needs to consider such effects.

The effects of film surface roughness on x-ray diffraction of nonpolar gallium nitride films

Differences in film surface morphology are found to relate to differences in x-ray diffraction data from nonpolar GaN films. Local strain relaxation at an irregular surface can produce lattice plane bending, leading to surface-specific ω-scan broadening and hence abnormally broad peak widths from reflections associated with shallow x-ray penetration depths. Effects related to surface roughness also contribute to the observed rotational ω-scan width anisotropy. Williamson–Hall plots can be used to estimate to what degree surface roughness effects contribute to the overall ω-scan broadening.

Geometric Phase Analysis of Nano-Scale Strain Fields Around 90° Domains in PbTiO3/SrTiO3 Epitaxial Thin Film

AbstractThe nano-scale strain fields analysis around 90° domains and misfit dislocations in PbTiO3/SrTiO3 001 epitaxial thin film has been conducted using the geometric phase analysis (GPA) combined with high angle annular dark field - scanning transmission electron microscopy (HAADF-STEM). The films typically possess a-c mixed domain configuration with misfit dislocations. The PbTiO3 layer was formed from the two layer: the upper 200 nm layer shows the typical a- and c- mixed domain configuration where the a-domains are several tens nm in width; the bottom 100 nm layer shows the different domain configuration that the width is several nm. In the latter case, a-domains are terminated within the film and are short in length. On the other hand, the bottom of a-domains does not contact the film/substrate interface. It keeps away from the interface, and there is completely c-domain layer under a-domains. The HAADF-STEM-GPA shows that the strain fields around an a-domain and a misfit dislocation interact each other: the tensile strain field and lattice plane bending fit together. This result indicates that the a-domain originates from the misfit dislocation.

Strain state analysis of InGaN/GaN – sources of error and optimized imaging conditions

AbstractTransmission electron microscopy investigation of the chemical composition of Inx Ga1–x N/GaN layers by strain state analysis can lead to substantial artefacts. We evaluated simulated images in dependence of specimen thickness, specimen orientation and objective lens defocus. We observed that the measurement is in agreement with the true strain profile for certain conditions only. An analysis of error sources revealed that artefacts are mainly caused by a combination of delocalization and the composition dependence of the phases of the beams contributing to the image formation. The delocalization effect is minimized for interference of the undiffracted beam with one of the 000 ± 2 beams. The least chemical shift of the phases is obtained using the 000 + 2 beam and a strong excitation of 000 + 4. Images simulated for these conditions taking into account lattice plane bending and strain using finite‐element calculations revealed a good agreement of evaluated and true strain profiles. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Observation of local lattice tilts in strain-relaxed Si1-xGex using high resolution channeling contrast microscopy

A ‘cross-hatch’ morphology is often seen in strain-relaxed Si1-xGex virtual substrates grown using the compositional grading technique. High resolution channeling contrast microscopy measurements, which probe both laterally and vertically into the structure, have revealed the association of such cross-hatch patterns with local lattice-plane bending. In this work, we report the influence of the growth temperature on the extent of the local lattice tilts determined from the channeling contrast measurements. Lines of pileup threading dislocations observed on the surface have also been imaged for the first time, providing us with information on their influence on the lattice-tilt arrangements and orientations.