Crack formation in strained β-(AlxGa1−x)2O3 films grown on (010) β-Ga2O3 substrates

High-quality LiNbO3 (LN) epitaxial films have been grown on (0 0 1)Al2O3 substrates by pulsed laser deposition. The deposition conditions have been optimized using experimental designs to promote the growth of highly (0 0 1)-oriented, phase pure and light-guiding LN films. The structural and nanostructural properties have been investigated by x-ray diffraction reciprocal space mapping and the guiding properties have been investigated by m-line spectroscopy and measurements of the light propagation losses. In particular it is shown that the film composition, the state of strain, the film thickness, the film roughness, the lateral extension of the crystallites building up the film as well as the mosaicity can be determined by a careful examination of the x-ray reciprocal space maps associated with simulation of the diffracted intensity distribution in reciprocal space. The guiding properties have been correlated with the nanostructural properties of the films: whereas light guiding has been clearly observed in single-crystal-like films, the existence of a mosaic structure, made of nanocrystalline domains, is shown to be detrimental to the guiding properties.

The effect of heteroepitaxial β-(AlxGa1−x)2O3 film thickness and Al content on surface morphology was characterized to experimentally determine the critical thickness limitations of the (010) β-(AlxGa1−x)2O3/Ga2O3 heterostructure. High-resolution x-ray diffraction was used to assess the strain state of the films; reciprocal space mapping (RSM) revealed that even cracked films were still fully strained. In cracked films, diffuse scattering was observed in RSMs, indicating lattice tilting. Cracking of the films was investigated using atomic force microscopy (AFM), x-ray topography (XRT), bright-field scanning transmission electron microscopy (BF-STEM), and high-resolution transmission electron microscopy. Using both AFM and XRT, the [001] direction was observed to be the most prevalent crack direction; however, cracks were also observed in the [100] direction. In uncracked regions of the films, XRT revealed the alignment of threading dislocations along the [001] direction. Cross-sectional imaging of the crack geometry and propagation was performed using BF-STEM, and it was observed that the cracks in the [001] direction extended through the thickness of the β-(AlxGa1−x)2O3 film (∼205 nm) and a further ∼100–200 nm into the β-Ga2O3 substrate. Experimental data for critical film thickness showed good agreement with previous theoretical calculations based on the Griffith criterion for crack propagation.

1. Background and purpose Since carbon (C) has a smaller lattice constant than silicon (Si), Si doped with C approximately 1% or less (Si:C: carbon-doped silicon) also has a smaller lattice constant than Si. By using Si:C as the source / drain material of the n-type metal-oxide-semiconductor field-effect transistor, the tensile strain can be applied to the channel region to improve electron mobility [1]. However, the nano-fabrication of Si:C causes strain relaxation, which hinders the improvement of electron mobility. We have reported the in-plane biaxial strain relaxation for Si:C nanowires evaluated with Raman spectroscopy, assuming that there is no out-of-plane strain relaxation [2]. In this study, we evaluated anisotropic strain relaxation, including not only in-plane but also out-of-plane direction, for Si:C nanowire by reciprocal lattice space mapping (RSM) measurement using synchrotron radiation X-rays. 2. Experimental method Si:C thin films were grown on (001) Si substrate by molecular beam epitaxy, and then nano-fabricated into nanowire by electron beam lithography and dry etching. The film thicknesses were 43, 50, and 37 nm, with C concentration of 0.60%, 0.83%, and 1.1%, respectively, confirmed by cross-sectional transmission electron microscope and secondary ion mass spectrometry measurements. In the Si:C nanowire, the length direction was parallel to the [110] direction and the width direction was parallel to the [-110] direction, respectively. The nanowire width (W) was varied as 1000, 500, 200, and 100 nm, while the nanowire length (L) was fixed at 10 μm. In order to obtain sufficient signals for RSM, 30,000 identical nanowires in the case of W = 1,000 and 500 nm, and 50,000 identical nanowires in the case of W = 200 and 100 nm were fabricated in approximately 1.5 mm × 1.5 mm areas, respectively. The X-ray energy was set to 10 keV. The RSMs of Si:C nanowires were obtained around 337 diffractions for C concentrations of 0.60% and 0.83% samples (Si:C0.83%), and around 115 diffraction for C concentration of 1.1% sample, respectively. 3. Results and Discussion Figures 1 (a) and (b) show the RSMs of the unprocessed and the nanowires with W of 500 nm of Si:C0.83% films, respectively. In Fig. 1 (a) and (b), the profiles near qx = 4.91 Å- 1, qz = 8.11 Å- 1 correspond to the hem of the 337 diffraction profiles for the Si substrate, and the peaks around qz = 8.165 Å- 1 are the diffraction profiles for the Si:C0.83% film or the Si:C0.83% nanowires, respectively. Here, qx and qz are components of scattering vector in the in-plane and out-of-plane directions, respectively. Figure 1 (a) shows that the profiles for Si substrate and Si:C0.83% film were obtained on the same qx, which indicates that the in-plane lattice constant of Si:C0.83% film before nano-fabrication was equal to that of Si substrate, and the tensile strain has been applied to Si:C0.83% film. Figure 1 (b) shows that qx increases and qz decreases for the Si:C0.83% nanowires with W of 500 nm as compared with the Si:C0.83% film, which indicates that the in-plane lattice constant of Si:C0.83% decreased and the out-of-plane lattice constant of Si:C0.83% increased due to the nano-fabrication. Thus, we clarified that the tensile strain applied to Si:C thin film was relaxed by nano-fabrication in both the in-plane and the out-of-plane directions. 4. Acknowledgment The RSM measurements for Si:C nanowires were performed at BL19B2 in SPring-8 approved by JASRI with proposal number of 2020A1748 and 2020A1849. References Tsung-Yang Liow, et al., IEEE Trans. Electron Devices 55, 2476 (2008).Yoshioka, et al., ECS Trans. 92 (4), 33-39 (2019). Figure 1

In this and in the next chapters we show that the scattered intensity can be expressed as a function of the scattering vector $$ Q = K - {K_i},$$ (3.1) if the the direction of the perfectly monochromatic incident plane wave is described by its wave vector K i and that of scattered wave by K. Therefore, the angular distribution of the scattered intensity, representing the properties of the sample, can be described by its distribution in reciprocal space (reciprocal-space map). Strictly speaking, this expression is applicable only if the wave vectors K and K i and the surface normal vector n lie in the same plane (scattering plane). This scattering geometry is called coplanar. As we show later, in the non-coplanar scattering geometry (in particular, in the grazing-incidence diffraction — GID, see Sect. 4.3) the scattered intensity depends on both vectors K i and K independently.

The wide-bandgap semiconductor Ga2O3 is a promising candidate for high-power electronics. Alloying with Al for (AlxGa1-x)2O3 films enables heterostructures that are essential for device applications. However, the limited thickness of (AlxGa1-x)2O3 films grown on Ga2O3 substrates is a serious obstacle. Here we employ first-principles calculations to determine the brittle fracture toughness of such films for three growth orientations of the monoclinic structure: [100], [010] and [001]. Surface energies and elastic constants are computed for the end compounds—monoclinic Ga2O3 and Al2O3—and used to interpolate to (AlxGa1-x)2O3 alloys. The appropriate crack plane for each growth orientation is determined, and the corresponding critical thicknesses of (AlxGa1-x)2O3 films are calculated based on Griffith’s theory. Our in-depth analysis of surface energies for both relaxed and unrelaxed surfaces provides important insights into the factors that determine the relative stability of different surfaces. We conclude that the critical thickness is largest for (AlxGa1-x)2O3 films grown along [100].

High-resolution X-ray diffraction (HRXRD) and triple-axis diffractometry (TAD) are used to investigate Si1−x C x epilayers and Si n /C/Si n superlattices. The samples were annealed in several steps to obtain information about their thermal stability. During annealing defects are formed in the epitaxial layers as well as in the substrates, leading to a contribution of diffusely scattered intensity around the particular reciprocal lattice points. A comparison of the measured intensity distribution in reciprocal space with model calculations based on a theory by Krivoglaz shows that the defects in the layers are different from those in the substrates, and that the assumption of small spherical defects in the epilayers leads to a quite good agreement between measurement and simulation. The comparison of different samples also shows that the formation of the defects depends on the particular sample structure.

In two preceding papers by Jagodzinski (Phys. Stat. Sol.(a)146(1994) 477; Acta Crystallogr. A52(1996) 675), a new method of phase determination has been described. Using latent lattices of point scatterers for a single kind of atoms, the structure is generated by shift vectors, displacing the atoms from the origins of the latent lattice into their correct positions. The mathematical treatment of this procedure resulted in very complex formulae for structure factorsE′(h), normalised such thatE′(0) = 1. The three components of the displacement vectors define a new real and reciprocal shift space. The method is briefly described in the first three sections of this paper. There is an important difference between one and higher dimensions: the number of latent lattices with different shift functions is infinite, but only very few of them are optimal. Phases and amplitudes of the Fourier coefficients of the shift function are strongly correlated. This property results from the transformation of diffraction data and the prohibition of trespassing of points, caused by large Fourier coefficients of the shift function. In addition to the well known influence of strong reflections, the approximate [unk]-symmetries of the diffraction data and the areas of minimum intensity play an outstanding role for the selection of the optimal latent lattice. Its corresponding shift function has small displacements and small amplitudes of the Fourier coefficients. In the case of complicated structures, these properties demand a careful computer evaluation of the intensity distribution in reciprocal space, in order to determine the optimal latent lattice of a given structure. – The unit cell of the structure containsM(= number of atoms) cells of the latent lattice. As long asMis a product of three integersMxMyMz, there is no difficulty in finding the optimal latent lattice in diffraction. Each set of directions has to be tested in reciprocal space. In all other cases difficulties arise which may only be overcome with the aid of latent sublattices (smaller cell, more atoms in the structure), or latent superlattices (larger cell, less atoms in the structure). Both cases are discussed, and it is shown that the existence of the various types of latent lattices may be found in the normal diffraction pattern, applying the criteria derived in this paper. The meaning of latent sub- and superlattices is discussed from the structural point of view, and phase relations, caused by the prohibition of trespassing of points, are derived. The great power of the new method will be discussed in a later paper, where differences of shift functions are introduced. Their important consequences for phase determination will be demonstrated with the aid of certain systems of linear equations.

UnwarpCalculator is a command-line utility developed to calculate intensity distribution in reciprocal space. The program uses CIF syntax input files and can work either with periodic crystals or with arbitrary atomic distribution, including incommensurately modulated and defect structures. With this program the intensity can be calculated for any reciprocal space point using the three main options available, including intensity calculation at a point with (h, k, l) coordinates, intensity distribution calculation along a line in reciprocal space and building an unwarped layer pixel by pixel. The program has an interactive interface and uses a fairly simple diffraction calculation model. The tool can be used for teaching crystallography since it offers much easier options and input file creation compared with existing software for defect and diffraction pattern simulations. These features along with input files with CIF syntax allow easy use of the program even for beginners. The utility can also be applied for the interpretation of experimental diffraction patterns and comparison of calculated versus experimental diffraction images to validate crystal structure models.

This review gives first a short introduction to the theoretical relations between experimentally observed diffuse scattering results and the desired information about defects. The situation is discussed under which diffuse scattered X-ray intensity from defects can be distinguished from other diffuse intensities (thermal diffuse scattering, Compton scattering). A typical experimental set-up is described to show what the requirements are in experimental resolution and how intensity distribution in reciprocal space can be measured most conveniently. A few typical experiments are discussed to demonstrate the physical potential of this method for studying impurities in metals and radiation-induced defects and defect clusters in ionic crystals. Special emphasis is given to the comparison of the experimental results with theoretical predictions; the intensity close to the Bragg peaks (Huang scattering) falls off as 1/g2, g being the distance from a reciprocal-lattice point G. The scattering intensity goes as G2. The intensity distribution in reciprocal space gives typical isointensity curves from which the symmetry of the double force tensor and its components can be deduced. Together with the measured shift of a Bragg peak, measurement of absolute scattering intensity gives a unique way of determining the defect concentration. Further away from the Bragg peaks (asymptotic scattering) the intensity is proportional to 1/g4 and shows characteristic oscillations.

Thickness dependence of structural and ferroelectric properties of sol-gel Pb(Zr0.56Ti0.44)0.90(Mg1/3Nb2/3)0.10O3 films

Measurement of optical properties such as the refractive index and thickness of nanocrystalline or smooth diamond films is carried out by the prism coupling technique. The films observed to be absorbing for a standard operating wavelength of 633 nm and higher wavelengths, i.e., 830 and 1300 nm, were used to obtain sharp guided modes and the refractive index and thickness of the films could be measured independently with high accuracy. The index of the nanocrystalline diamond films was found to be homogeneous within the films with negligible changes observed at the film–substrate interface. Information on absorption was also obtained from the half width of the guided modes and was correlated to the graphitic concentration of the films measured by Raman spectroscopy. The thickness measured by the prism coupling technique was found to be in agreement with the thickness measured by cross-sectional transmission electron microscopy. The overall results indicate that the prism coupling technique can be very useful for rapid, easy accurate measurement of the refractive index and thickness of smooth diamond films.

This study investigates the compositional analysis and growth of β-(In x Ga1-x )2O3 thin films on (010) β-Ga2O3 substrates using mist chemical vapor deposition (CVD), including the effects of the growth temperature. We investigated the correlation between In composition and b-axis length in coherently grown films, vital for developing high-electron-mobility transistors and other devices based on β-(In x Ga1-x )2O3. Analytical techniques, including X-ray diffraction (XRD), reciprocal space mapping, and atomic force microscopy, were employed to evaluate crystal structure, strain relaxation, and surface morphology. The study identified a linear relationship between In composition and b-axis length in coherently grown films, facilitating accurate composition determination from XRD peak positions. The films demonstrated high surface flatness with root-mean-square roughness below 0.6 nm, though minor relaxation and granular features emerged at higher In compositions (x = 0.083) at the growth temperature of 750°C. XRD results revealed that lattice relaxation were observed at a growth temperature of 700°C despite low In composition. In contrast, at 800°C, the In composition was higher than at 750°C, and coherent growth was achieved. The surface morphology was the flattest at 750°C. These findings indicate that the growth temperature plays a crucial role in the mist CVD growth of β-(In x Ga1-x )2O3 thin films. This study offers insights into the relationship between In composition and lattice parameters in coherently grown β-(In x Ga1-x )2O3 films, as well as the effect of growth conditions, contributing to the advancement of ultra-wide bandgap semiconductor device development.

Phase pure β-(AlxGa1−x)2O3 thin films are grown on (001) oriented β-Ga2O3 substrates via metalorganic chemical vapor deposition. By systematically tuning the precursor molar flow rates, the epitaxial growth of coherently strained β-(AlxGa1−x)2O3 films is demonstrated with up to 25% Al compositions as evaluated by high resolution x-ray diffraction. The asymmetrical reciprocal space mapping confirms the growth of coherent β-(AlxGa1−x)2O3 films (x < 25%) on (001) β-Ga2O3 substrates. However, the alloy inhomogeneity with local segregation of Al along the (2̄01) plane is observed from atomic resolution STEM imaging, resulting in wavy and inhomogeneous interfaces in the β-(AlxGa1−x)2O3/β-Ga2O3 superlattice structure. Room temperature Raman spectra of β-(AlxGa1−x)2O3 films show similar characteristics peaks as the (001) β-Ga2O3 substrate without obvious Raman shifts for films with different Al compositions. Atom probe tomography was used to investigate the atomic level structural chemistry with increasing Al content in the β-(AlxGa1−x)2O3 films. A monotonous increase in chemical heterogeneity is observed from the in-plane Al/Ga distributions, which was further confirmed via statistical frequency distribution analysis. Although the films exhibit alloy fluctuations, n-type doping demonstrates good electrical properties for films with various Al compositions. The determined valence and conduction band offsets at β-(AlxGa1−x)2O3/β-Ga2O3 heterojunctions using x-ray photoelectron spectroscopy reveal the formation of type-II (staggered) band alignment.

This review covers the recent advances in reciprocal space mapping. The experimental techniques as well as the theoretical and conceptual developments are discussed. The advantages of reciprocal space mapping over the conventional single scan X-ray scattering methods become clear from the examples presented. Extracting the additional information from mapping in reciprocal space maps has led to a deeper understanding of materials. Imperfect materials benefit enormously from these methods. Near perfect materials also indicate weak diffuse scattering that can now be interpreted in terms of defects, etc., whereas with single scans the influence is difficult to observe and separate from other features. Reciprocal space maps can be collected with both high and low angular resolution diffractometers, depending on the application, although a combination of resolutions may be necessary. It is also growing in importance in the analysis of materials using specular reflectometry. High-resolution reciprocal space mapping is not restricted to good crystalline quality. Examples of reciprocal space mapping are given for semiconductors, metals, ceramics and biological samples. For semiconductor materials, reciprocal space mapping has now become almost routine in the study of lattice relaxation in thin layers and in the assessment of the “quality” of materials. Combinations of mapping with topography and precision lattice parameter determination are also discussed. The latter part of this review discusses the advantages of three-dimensional reciprocal space mapping, which takes the analysis further. With this method the full three-dimensional shapes in reciprocal space can be studied.

ABSTRACTWe investigated the effect of substrate inclination and direction on the structural properties of an InGaAs linearly compositionally graded buffer layer with a AlGaAs/InGaAs superlattice grown by molecular beam epitaxy on 2° offcut GaAs substrates. Reciprocal space maps were used to determine the relaxation and tilt of the buffer layer and superlattice with respect to each other and to the substrate. From (004) reciprocal space maps, a linear relationship between tilt and In mole fraction was observed for the buffer layer. This tilt was greatly reduced near the top of the buffer which was found to be completely strained. Interestingly, the tilt along a <110> direction was greater than that observed along the miscut axis. This may be due to the miscut axis not being parallel to a low index plane. Reciprocal space maps of asymmetric diffraction planes were used to determine the relaxation of the buffer layer as a function of In mole fraction. Along a <110> direction in which no tilt was seen in the (004), the majority of the buffer layer was found to be completely relaxed. However, the top of the buffer layer was found to be completely strained, corresponding to a denuded zone observed in cross section transmission electron microscopy.