Curvature Of Lattice Planes Research Articles

Evolution of lattice distortions in 4H-SiC wafers with varying doping

Lattice distortions (LD) in 4H-silicon carbide (SiC) wafers were quantified using synchrotron X-ray rocking curve mapping (RCM), and were resolved into their two components of lattice strain (Δd/d) and lattice plane curvature (LPC) for 150 mm diameter wafers. The evolution of these LDs were investigated for three sequential substrates from the same boule, one of which was the substrate reference, and the other two had a 10 µm thick, 1 × 1017 and 4 × 1014 cm-3 n-type doped epitaxial layer. The lattice strain, Δd/d, was highest for the lowest doped wafer due to higher mismatch with the substrate wafer. After epitaxial layer growth, the LPC variation across the wafer increases by a factor of 2, irrespective of doping. The LPC maps indicate presence of a twist in the lattice planes that increases after epitaxial growth. The LPC component has higher influence on wafer shape change, which can reduce device yields. The lattice strain component predominantly affects the glide of basal plane dislocations (BPDs), thereby reducing device reliability. From analysis of peak widths, it was determined that threading dislocations in the top 6 microns of the wafer increase after epitaxial layer growth.

High-resolution dislocation imaging and micro-structural analysis of HVPE-βGa2O3 films using monochromatic synchrotron topography

Threading and basal dislocations were observed and their Burgers vectors (b→) were analyzed in 20 µm thick halide vapor phase homoepitaxially grown beta-gallium oxide (β−Ga2O3) films using 15 keV monochromatic synchrotron X-ray topography with symmetric reflection (004) and two asymmetric reflections (205) and (115) in back-reflection and grazing incidence angle geometries, respectively. In a 1 × 1.5 cm2 sample, threading screw dislocations with b→=001 were observed with a density of 30 cm−2, whereas a single threading edge dislocation with b→=100 was observed. Basal dislocations with b→=12112 were observed with a density of ∼20 cm−2, and a single basal dislocation with b→=010 was observed. Rocking curve mapping of the three reflections was also performed on the entire sample with the same setup and a high resolution x-ray camera to obtain the full width at half maximum (FWHM), strain, and curvature maps in two almost orthogonal directions. The epilayer demonstrated excellent crystalline quality with a median FWHM of 8.2 arc sec in the (004) reflection and a very low median strain of ∼|8 × 10−5| obtained from both sample directions. The median radius of curvature was ∼−100 m along the [100] direction and ∼280 m along the [010] sample axis, indicating very low lattice plane curvature that enables high manufacturability and reliability of devices.

Thickness and growth condition dependence of crystallinity in semipolar (20–21) GaN films grown on (22–43) patterned sapphire substrates

We have investigated the crystalline morphology such as lattice plane curvature and lattice plane tilting in (20–21) GaN films on (22–43) patterned sapphire substrates (PSS) by using X‐ray rocking curve (XRC) measurements. The results of the symmetric XRC for the GaN (20–21) plane showed anisotropic lattice plane curvature between the [−1014] and [−12–10] directions. This is due to the large difference of the thermal expansion coefficient in the [0001] direction between GaN and sapphire. From the results of asymmetric XRC for the GaN (20–22) and (12–31) diffractions, it is found that lattice plane tilting is highly dependent on the film thickness and the growth condition. The −c‐plane‐suppressed growth process with tuning the V/III ratio for the (20–21) GaN films on the (22–43) PSS is very effective to suppress the generation of basal plane stacking faults as confirmed by TEM analysis.

Spatially Resolved X-ray Diffraction Technique for Crystallographic Quality Inspection of Semiconductor Microstructures

There is an increasing demand for techniques that allow detection and visualization of crystalline lattice microdefects. From the many techniques available the X-ray Rocking Curve Imaging (RCI), based on synchrotron X-ray diffraction, has gained much attention recently as a method of wafer defect analysis [1]. However, for most crystal growers laboratory techniques are preferred. Therefore, instead of applying RCI we have developed a microimaging technique based on spatially resolved X-ray diffraction (SRXRD) that makes use of conventional high resolution X-ray diffractometer. Briefly, the size of incident X-ray beam is reduced by a set of slits. Then the sample is moved in small steps while the rest of the system stays fixed. At each sample position X-ray diffraction curve is measured from precisely defined area. Finally, all diffraction curves are collected to construct the X-ray diffraction image of the sample. Both the ω and 2θ/ω scans are performed allowing independent mapping of crystallographic misorientation and lattice parameter distributions across the sample. Spatial resolution offered by the SRXRD technique is smaller than that obtainable with the use of synchrotron radiation based methods. This is due to a limited radiation intensity of conventional X-ray sources. We have checked that in our experimental setup measurable signals can be obtained with the X-ray beam as small as 10/sinθ × 100 μm 2 , where θ is the Bragg angle for the reflection studied. This corresponds to the beam spot size of ~18 × 100 μm 2 for 004 reflections of GaAs and Si. The aim of this report is to present advantages of SRXRD over a standard X-ray diffraction when applied for analysis of crystalline microstructures. First, we focus on SRXRD studies of epitaxial laterally overgrown (ELO) GaAs layers grown by liquid phase epitaxy on SiO2-masked GaAs substrates. ELO layer consists of a few hundreds micrometers wide monocrystalline stripes regularly arranged on a substrate. Since each stripe is strained such samples contain a periodic distribution of strain and/or defects. Thus, they are very suitable to demonstrate potential of the technique. We show that high spatial and angular resolutions of SRXRD allow studying a strong effect of ELO wings tilt towards the mask as well as very fine residual strain caused by dopant concentration inhomogeneity. Direction of the tilt and the distribution of tilt magnitude across width of each wing can be easily determined. In fully overgrown GaAs ELO layers additional strain was observed at a coalescence front where ELO wings grown from adjacent seeds merged. With the use of SRXRD a local structure of the crystal lattice around this coalescence front was studied. In heteroepitaxial GaSb/GaAs ELO layers local mosaicity in the wing area was found. By SRXRD the size of microblocks and their relative misorientation were analyzed. As the final example, we report on strain distribution in thermally oxidized Si wafers. Microscopic curvature of lattice planes confined between two neighboring slip bands was measured allowing its correlation with the dislocation structure. It is noting worthy that all the phenomena presented are difficult to study by standard X-ray diffraction. On the contrary, due to its high spatial resolution the SRXRD technique allows deeper insight into a localized strain fields present in semiconductor microstructures.

X-ray diffractometry and topography of lattice plane curvature in thermally deformed Si wafer

The correlation between the microscopic lattice plane curvature and the dislocation structure in thermal warpage of 200 mm-diameter Czochralski Si (001) wafers has been investigated using high-resolution X-ray diffractometry and topography. It is found that the (004) lattice plane curvature is locally confined between two neighboring slip bands, with the rotation axis parallel to the slip bands. High-resolution topography reveals that the curvature resulted from a fragmented dislocation structure. The local confinement is attributed to the multiplication of the dislocations that are generated between the two slip bands.

6H-SiC Crystals Grown in [015] and [001] Directions Characterized by High Energy Triple-Axis X-Ray Diffraction

A structural characterisation by high energy x-ray diffraction of [015] and [001] grown 6H-SiC crystals is presented. The [015]-grown crystal shows an improved crystal quality, concerning the curvature of lattice planes and the micro domain structure. We relate this to the lowered level of rotational symmetry for the [015]-growth which reduces the number of active slip systems during the growth process.

X‐ray diffraction spot mapping – a tool to study structural properties of semiconductor disk laser devices

AbstractLocal lattice plane curvature of semiconductor disk laser devices is determined by an X‐ray spot mapping technique using white beam synchrotron radiation. This method allows for in‐situ studies of the dependence of the lattice plane profile on device temperature and local heating by optical pumping. The influence of different device mounting procedures on the structural and optical device parameters was investigated. This knowledge was used for device technology optimisation. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

X-ray bright-field imaging analyzes crystalline quality and defects of SiC wafers

A new variety of the recently developed technique `X-ray bright-field imaging' is presented. In its basic version, this approach simultaneously yields diffraction-based information on lattice distortions and radiographic information on structural inhomogeneities, and is based on the detection of reversed diffraction contrast in transmission images. The new version extends the scope of the technique to the quantitative analysis of crystalline quality parameters such as the lattice plane curvature and mosaic distribution in SiC wafers, and makes it possible to correlate such parameters directly with defect (distortions/inhomogeneities) structures.

Lattice-plane curvature and small-angle grain boundaries in SiC bulk crystals

SiC crystals grown by the physical vapour transport process along the [001] direction show a curvature of the crystal growth front in correspondence with the shape of the isotherms. A large radius for the curvature of the isotherms enhances the formation of an extended facet. Under the facet, the lattice planes are flat with a high crystal quality as expressed by rocking-curve half widths of 0.022°. In the non-faceted region, the lattice planes become bent, following the shape of the isotherms with a radius of typically 0.5 to 0.8 m and an increased rocking-curve half width of 0.3°. A reduction of the growth rate from 300 µm h−1to 70 µm h−1does not affect this behaviour significantly. The lattice-plane curvature and the development of the facet are predominantly affected by the shape of the isotherms. For crystals grown in the [015] direction, the lattice planes adjust only in a one-dimensional manner to the isotherms. In all cases, the lattice-plane curvature results from the formation of a high density of small-angle grain boundaries. They are generated by the condensation of dislocations with Burgers vectors in theabplane.

Domain misorientation in sublimation grown 4H SiC epitaxial layers

High resolution X-ray diffractometry has been applied to study domain misorientation in 4H SiC epitaxial-layers grown by the sublimation epitaxy method. The development of mosaicity of the epitaxial layer has been studied under different growth conditions, i.e. substrate polarity and layer thickness. In the growth experiments on Si-face with a lattice having a concave curvature the mosaicity was increased in the layer. With increasing thickness the structural quality of the layer was improved. Growth of an epilayer on concave C-face resulted in a domain structure comparable to the substrate but the lattice curvature increased considerably. The concave lattice plane curvature is a probable reason for degraded structural quality.

Selective ion-channeling study of misfit dislocation grids in semiconductor heterostructures: Theory and experiments

Planar dechanneling by networks of misfit dislocations was measured in a series of ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ samples (001) grown by molecular-beam epitaxy. At the beginning of the strain-relaxation process the dechanneling probability exhibits different values for nominally equivalent (110) planes. At larger strain relaxation, the dechanneling probability saturates at a value around $$$\frac{1}{2}$ as the beam-energy increases. In order to explain these results a new model for planar dechanneling by dislocations is proposed. This model is based on the harmonic approximation of the continuum potential but anharmonicity effects are taken into account. The perturbation to the harmonic oscillations caused by the lattice plane curvature around a dislocation is written in terms of a distortion function that depends only on the geometrical configuration of the channeling direction and of the dislocation line. This function is explicitly calculated for geometrical configurations relevant to the present samples allowing us then to solve the equation of motion. The results show that the dechanneling probability saturates at a level sensibly lower than 100% due to the quasiplanar distribution of dislocations. Without any adjustable parameter, the comparison between computed and measured dechanneling probabilities supplies dislocation density values in excellent agreement with those measured by transmission electron microscopy and in good agreement with results deduced from previous strain-relaxation data.

In situstudy of the self-accommodating process during the martensitic transformation of A Cu-Zn-Al single crystal by synchrotron X-Ray topography—II. dynamics of the process and role of crystalline defects

The martensitic transformation of Cu-Zn-Al single crystals has been followed in situ and in real time by synchrotron X-ray topography. We have shown that at the M stemperature, the transformation proceeds by nucleation and growth of transformation variants associated by self-accommodating pairs. The nucleation of these variants is triggered by the crystal substructure. When the martensitic transformation is multivariant the behaviour of the crystal substructure and the development of elastic stresses inducing a reversible curvature of lattice planes has been displayed.