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Studies of oxide-based thin-layered heterostructures by X-ray scattering methods
Abstract
Some X-ray scattering methods (X-ray reflectometry and Diffractometry) dedicated to the study of thin-layered heterostructures are presented with a particular focus, for practical purposes, on the description of fast, accurate and robust techniques. The use of X-ray scattering metrology as a routinely working non-destructive testing method, particularly by using procedures simplifying the data-evaluation, is emphasized. The model-independent Fourier-inversion method applied to a reflectivity curve allows a fast determination of the individual layer thicknesses. We demonstrate the capability of this method by reporting X-ray reflectometry study on multilayered oxide structures, even when the number of the layers constitutive of the stack is not known a-priori. Fast Fourier transform-based procedure has also been employed successfully on high resolution X-ray diffraction profiles. A study of the reliability of the integral-breadth methods in diffraction line-broadening analysis applied to thin layers, in order to determine coherent domain sizes, is also reported.Examples from studies of oxides-based thin-layers heterostructures will illustrate these methods. In particular, X-ray scattering studies performed on high-k HfO2 and SrZrO3 thin-layers, a (GaAs/AlOx) waveguide, and a ZnO thin-layer are reported.
... X-ray reflectometry (XRR) method is a versatile and nondestructive technique for a fast and accurate thickness determination of thin-layered heterostructures [6]. The modelindependent Fourier-inversion method applied to a reflectivity curve was used to determine the individual thin thicknesses and multi-layers of a stack formed in the SrZrO 3 /Si films elaborated by MOCVD under different conditions. ...
... This implies that the direct extraction of information using model-dependent simulation and fitting procedures, when possible, is very timeconsuming, which limits their applicability. On a previous paper, the use of methods based on the Fourier-inversion technique to extract the individual layer thicknesses from complex X-ray reflectivity profiles, has been reported [6,9]. All samples have been studied with these methods but we have focused on the description of the as-deposited SZO-550 and post-annealed SZO-550-R700 ones. ...
... experiments have revealed the presence on similar samples of a 3 nm thick SiO 2 layer at the SrZrO 3 /Si interface[6,10,11]. Moreover, some XPS and FTIR studies have shown the presence of an amorphous phase on top, with some remaining traces of a carbonate phase. ...
... X-ray reflectometry (XRR) method is a versatile and nondestructive technique for a fast and accurate thickness determination of thin-layered heterostructures [6]. The modelindependent Fourier-inversion method applied to a reflectivity curve was used to determine the individual thin thicknesses and multi-layers of a stack formed in the SrZrO 3 /Si films elaborated by MOCVD under different conditions. ...
... This implies that the direct extraction of information using model-dependent simulation and fitting procedures, when possible, is very timeconsuming, which limits their applicability. On a previous paper, the use of methods based on the Fourier-inversion technique to extract the individual layer thicknesses from complex X-ray reflectivity profiles, has been reported [6,9]. All samples have been studied with these methods but we have focused on the description of the as-deposited SZO-550 and post-annealed SZO-550-R700 ones. ...
... experiments have revealed the presence on similar samples of a 3 nm thick SiO 2 layer at the SrZrO 3 /Si interface[6,10,11]. Moreover, some XPS and FTIR studies have shown the presence of an amorphous phase on top, with some remaining traces of a carbonate phase. ...
High-k SrZrO3 perovskite thin films, suitable for microelectronics applications were deposited under various conditions on plane Si (100) substrates by direct liquid injection metal-organic chemical vapor deposition (MOCVD) method. Depending on the deposition temperature, films were mono- or multi-layered and either crystallized either amorphous. Amorphous films were annealed in order to obtain the expected orthorhombic perovskite structure. The thicknesses of individual layer as well as multi-layers of the stacks were determined with reflectometry measurements. SIMS measurements were also conducted on the thin films to estimate the order of the multi-layers. Thicknesses were successfully confirmed by this destructive method and chemical environment of the films was determined as well as the composition of the layers. Compared with infrared transmission measurements on as-deposited and post-annealed films, it gives clues on desorption of volatile species. Thus, crystallographic and chemical structures were precise on studied samples.
... It is well-known, for instance, that the broadening of the (00.l) reflections in the ω/2θ mode can be used to estimate the correlation length of the diffraction domains (coherent domain size) in the growth direction, after separating both the strain and the correlation length components responsible for the IB widening, through the Halder and Wagner parabolic approach [22], a variant of the Williamson-Hall plots method. In particular, when considering the ZnO epitaxial thin films investigated in the present paper, the growth-direction coherent-domain-size has been found [23] to be comparable with the layer thickness (determined by XRR) bringing to the fore the high-crystalline-quality in the growth direction. Then, any overall measurement of the structural quality will include a contribution from in-plane defects. ...
... A process of deconvolution to allow for the instrumental profile was also carried out, as described elsewhere [23]. In the following, β refers to the instrument-corrected IB. [24]) displays a peak centered at 178.1 nm ± 0.2 nm The thickness fringes could be followed up to an S Z value as large as 0.55 nm -1 , indicating that both the film-air and film-substrate interfaces were relatively flat. ...
X-ray scattering methods were applied to the study of thin mosaic ZnO layers deposited on c-Al2O3 substrates using Pulsed Laser Deposition. High Resolution (HR) studies revealed two components in the ω scans (transverse scans) which were not resolved in conventional “open-detector” ω rocking curves: a narrow, resolution-limited, peak, characteristic of long-range correlation, and a broad peak, attributed to defect-related diffuse-scattering inducing a limited transverse structural correlation length. Thus, for such mosaic films, the conventional ω rocking curve Full Width at Half Maximum linewidth was found to be ill-adapted as an overall figure-of-merit for the structural quality, in that the different contributions were not meaningfully represented. A “Williamson-Hall like” integral breadth (IB) metric for the HR (00.l) transverse-scans was thus developed as a reliable, fast, accurate and robust alternative to the rocking curve linewidth for routine non-destructive testing of such mosaic thin films. For a typical ZnO/c-Al2O3 film, the IB method gave a limited structural correlation length of 110nm±9nm. The results are coherent with a thin film containing misfit dislocations at the film-substrate interface.
... www.advancedsciencenews.com the weaker reflections. The results of the integral breadths (IB) analysis with pseudo-Voigt fits [48,49] are illustrated in Figure 1e (the Methods section is described in Equations S1-S5 and Figure S1 in the Supporting Information). From the peak analysis in Figure 1e, the correlation lengths are found equal to 48.5 nm for MAPbI 3 hot-cast thin film on LiNiO and 33.9 nm on PEDOT:PSS substrate. ...
Hybrid perovskites are on a trajectory toward realizing the most efficient single-junction, solution-processed photovoltaic devices. However, a critical issue is the limited understanding of the correlation between the degree of crystallinity and the emergent perovskite/hole (or electron) transport layer on device performance and photostability. Here, the controlled growth of hybrid perovskites on nickel oxide (NiO) is shown, resulting in the formation of thin films with enhanced crystallinity with characteristic peak width and splitting reminiscent of the tetragonal phase in single crystals. Photophysical and interface sensitive measurements reveal a reduced trap density at the perovskite/NiO interface in comparison with perovskites grown on poly(3,4-ethylene dioxy thiophene) polystyrene sulfonate. Photovoltaic cells exhibit a high open circuit voltage (1.12 V), indicating a near-ideal energy band alignment. Moreover, photostability of photovoltaic devices up to 10-Suns is observed, which is a direct result of the superior crystallinity of perovskite thin films on NiO. These results elucidate the critical role of the quality of the perovskite/hole transport layer interface in rendering high-performance and photostable optoelectronic devices.
... The integral widths deduced from the transverse extraction over the MT reflections from the three other samples (Tg from 350 1C to 450 1C), in the longitudinal and transversal directions, give the correlation lengths of the MT in these two dimensions (according to the Scherrer's formula) [23,24]. The correlation lengths of MT in their two dimensions (transversal and longitudinal) are reported in Table 1. ...
We report on the quantitative study of microtwins (MT) defects in the GaP/Si(0 0 1) thin film grown by Molecular Beam Epitaxy and the optical properties of GaAsP(N)/GaP(N) quantum wells grown on top of the GaP/Si pseudo-substrates. A 780 nm photoluminescence at room temperature from the GaAsPN quantum wells is measured on silicon. Time-resolved photoluminescence has been performed and evidences the influence of non-radiative defects originated from the GaP/Si interface. The structural defects such as MT are quantitatively analyzed by synchrotron X-ray diffraction (XRD) combined with transmission electron microscopy (TEM) analyses. We show that the XRD measurements are in good agreement with TEM observation and reveal a strong contribution of MT in the [1 1 1] direction. The MT density appears to be directly correlated with the growth temperature.
... Fig. 5 shows the evolution of the (00.l) broad-component defect-induced IB for 3 different ZnO samples (labelled samples 1, 2 and 3, respectively) versus the scattering vector. Their respective thicknesses were, from sample 1 to sample 3, 145 nm, 172 nm and 226 nm, as measured by XRR using a Fourier transform-based procedure (AutoCorrelation Function) applied to the corrected XRR profile [22] [35]. Since the aim of the present paper is to develop a reliable, fast, and robust "figure-of-merit" in order to compare samples, it is beyond this scope to develop a comprehensive study of the effect of different growth parameters on the structural parameters. ...
X-ray scattering methods were applied to the study of thin mosaic ZnO layers deposited by Pulsed Laser Deposition on c-Al2O3 substrates and thin mosaic GaP layers deposited by Molecular Beam Epitaxy (MBE) on Si(001) substrates. For both systems, High Resolution (HR) studies revealed two components in the omega scans (transverse scans) which were not resolved in conventional "open-detector" omega rocking curves: a narrow, resolution-limited, peak, characteristic of longrange correlation, and a broad peak, due to defect-related diffuse-scattering giving a limited transverse structural correlation length. Thus, for such mosaic films, the conventional omega rocking curve Full Width at Half Maximum linewidth was found to be inadapted as an overall figure-of-merit for the structural quality, in that, first, the different contributions were not meaningfully represented, and, second, the linewidth depends more strongly on the film thickness than on the dispersion in the crystallographic orientation or the defect density. A "Williamson-Hall like" integral breadth (IB) metric for the HR (00.l) transverse-scans was developed as a reliable, fast, accurate and robust alternative to the rocking curve linewidth for routine non-destructive testing of such mosaic thin films. For ZnO/c-Al2O3 films of various thicknesses, it was deduced from the transverse scans profiles that this finite lateral correlation length may arise from misfit dislocations which accommodate the lattice-mismatch at the film-substrate interface. This WHL method is shown to be a generic approach applicable to the study of other mosaic, epitaxial, thin-film systems as illustrated through the study of mosaic GaP thin films grown by MBE on Si(001) 4°-off substrates. For this heterogeneous system, it was found from the transverse scan profiles around (002) and (006) that anti-phase crystalline domains can be evidenced. A finite correlation length associated with lateral anti-phase domain size was proposed.
... X-ray diffraction measurements revealed epitaxial growth 8,9 with a FWHM of 0.006°for the ͑0002͒ peak high resolution omega scan and an ͑open-detector͒ omega rocking curve value of about 0.05°, characteristic of a highly oriented material with very low crystallographic dispersion. The 2scan of the ͑0002͒ peak gave a c lattice parameter of 5.215 Å. ...
Zinc Oxide thin films were grown on c-sapphire substrates using pulsed laser
deposition. Pump power dependence of surface emission spectra, acquired using a
quadrupled 266 nm laser, revealed room temperature stimulated emission
(threshold of 900 kW/cm2). Time dependent spectral analysis plus gain
measurements of single-shot, side-emission, spectra pumped with a nitrogen
laser revealed random lasing indicative of the presence of self-forming laser
cavities. It is suggested that random lasing in an epitaxial system rather than
a 3-dimensional configuration of disordered scattering elements, was due to
waveguiding in the film. Waveguiding causes light to be amplified within
randomly-formed closed-loops acting as lasing cavities.
Light relaxes hybrid perovskites
Ion migration in organic-inorganic perovskite solar cells limits device stability and performance. Tsai et al. found that a cesium-doped lead triiodide perovskite with mixed organic cations underwent a uniform lattice expansion after 180 min of exposure at 1 sun of illumination. This structural change reduced the energy barriers for charge carriers at the contacts of solar cells. The resulting increase in power conversion efficiency from 18.5 to 20.5% was maintained for more than 1500 hours of illumination.
Science , this issue p. 67
Wavelet transform is used to analyze the grazing incidence X-ray reflectivity curve of nanometer multilayer structures. For the structures including oxide layers, interlayers or thickness fluctuations, which are difficult to determine, wavelet transform can be used to get structure parameters from the peak positions and peak intensities of auto-correlation functions. Using these results as initial model of further curve fitting, the multilayer structures can be characterized accurately. The oxide layer of vanadium monolayer is determined to be about 3 nm, the interfacial roughness of Mo/Si multilayer structures is about 0.42 nm, and the results show that the thickness fluctuations of layers close to surface and substrate are over 5%.
Fourier transform is used to analyze the grazing incidence X-ray reflectivity curve of nanometer multilayer structures. The influences of preparing and measuring conditions on measuring results of multilayer structure parameters are simulated and the applicability and accuracy of Fourier transform is verified. The results show that the Fourier transform is more intelligible and quicker than traditional curve fitting method. The Fourier transform can exactly determine complex multilayer structure parameters without any subjective layer-structure model, which is a powerful analysis method for characterization of multilayer structures.
The semiconductor ZnO has gained substantial interest in the research community in part because of its large exciton binding energy (60 meV) which could lead to lasing action based on exciton recombination even above room temperature. Even though research focusing on ZnO goes back many decades, the renewed interest is fueled by availability of high-quality substrates and reports of p-type conduction and ferromagnetic behavior when doped with transitions metals, both of which remain controversial. It is this renewed interest in ZnO which forms the basis of this review. As mentioned already, ZnO is not new to the semiconductor field, with studies of its lattice parameter dating back to 1935 by
Bunn [Proc. Phys. Soc. London 47, 836 (1935)
], studies of its vibrational properties with Raman scattering in 1966 by
Damen et al. [Phys. Rev. 142, 570 (1966)
], detailed optical studies in 1954 by
Mollwo [Z. Angew. Phys. 6, 257 (1954)
], and its growth by chemical-vapor transport in 1970 by
Galli and Coker [Appl. Phys. Lett. 16, 439 (1970)
]. In terms of devices, Au Schottky barriers in 1965 by
Mead [Phys. Lett. 18, 218 (1965)
], demonstration of light-emitting diodes (1967) by
Drapak [Semiconductors 2, 624 (1968)
], in which Cu2O was used as the p-type material, metal-insulator-semiconductor structures (1974) by
Minami et al. [Jpn. J. Appl. Phys. 13, 1475 (1974)
], ZnO/ZnSe n-p junctions (1975) by
Tsurkan et al. [Semiconductors 6, 1183 (1975)
], and Al/Au Ohmic contacts by
Brillson [J. Vac. Sci. Technol. 15, 1378 (1978)
] were attained. The main obstacle to the development of ZnO has been the lack of reproducible and low-resistivity p-type ZnO, as recently discussed by
Look and Claflin [Phys. Status Solidi B 241, 624 (2004)
]. While ZnO already has many industrial applications owing to its piezoelectric properties and band gap in the near ultraviolet, its applications to optoelectronic devices has not yet materialized due chiefly to the lack of p-type epitaxial layers. Very high quality what used to be called whiskers and platelets, the nomenclature for which gave way to nanostructures of late, have been prepared early on and used to deduce much of the principal properties of this material, particularly in terms of optical processes. The suggestion of attainment of p-type conductivity in the last few years has rekindled the long-time, albeit dormant, fervor of exploiting this material for optoelectronic applications. The attraction can simply be attributed to the large exciton binding energy of 60 meV of ZnO potentially paving the way for efficient room-temperature exciton-based emitters, and sharp transitions facilitating very low threshold semiconductor lasers. The field is also fueled by theoretical predictions and perhaps experimental confirmation of ferromagnetism at room temperature for potential spintronics applications. This review gives an in-depth discussion of the mechanical, chemical, electrical, and optical properties of ZnO in addition to the technological issues such as growth, defects, p-type doping, band-gap engineering, devices, and nanostructures.
We precisely determine the contraction of AlAs in multilayer optical waveguides, associated with selective oxidation of AlAs/GaAs epitaxial heterostructures. The average thickness of each layer was determined via x-ray reflectometry before and after oxidation, yielding an induced shrinkage of 11.4%±0.7% normal to the stack. The waveguide refractive indices were evaluated via modal-index measurements in the near-infrared. The achieved accuracy is compatible with form-birefringent phase matching in AlGaAs guided-wave frequency converters
The electrical activity of nitrogen as an acceptor in ZnO has been investigated in two ways. First, nitrogen was introduced by means of diallylamine during metalorganic vapor phase epitaxy (MOVPE) yielding incorporation of nitrogen in the range 1016–1021 cm -3. This led to significant compensation of the natural donors with a minimum electron concentration of 5×1014 cm -3. Second, diffusion of nitrogen was carried out on undoped MOVPE layers under high pressure conditions stemming from the decomposition of NH 4 NO 3. Conversion to p -type conductivity was observed in a systematic way with measured hole concentrations up to 6.5×1017 cm -3. © 2003 American Institute of Physics.
Epitaxial thin films of Y-doped SrZrO3 have been grown on MgO(001) by pulsed laser deposition. The deposition process has been performed at temperatures of 1000–1200 °C and at an oxygen pressure of 1.5×10−1 mbar. The samples are characterized by Rutherford backscattering spectrometry/channeling (RBS/C) and x-ray diffraction (XRD). We found an epitaxial relationship of SrZrO3 (0k0) [101]∥MgO (001) [100]. Good crystalline quality is confirmed by RBS/C minimum yield values of 9% and a FWHM of 0.35° of the XRD rocking curve.
In the present paper, we investigate the effect of thermal annealing on optical and microstructural properties of HfO2 thin films (from 20 to 190nm) obtained by plasma ion assisted deposition (PIAD). After deposition, the HfO2 films were annealed in N2 ambient for 3h at 300, 350, 450, 500 and 750°C. Several characterisation techniques including X-ray reflectometry (XRR), X-ray diffraction (XRD), spectroscopic ellipsometry (SE), UV Raman and FTIR were used for the physical characterisation of the as-deposited and annealed HfO2 thin films. The results indicate that as-deposited PIAD HfO2 films are mainly amorphous and a transition to a crystalline phase occurs at a temperature higher than 450°C depending on the layer thickness. The crystalline grains consist of cubic and monoclinic phases already classified in literature but this work provides the first evidence of amorphous-cubic phase transition at a temperature as low as 500°C. According to SE, XRR and FTIR results, an increase in the interfacial layer thickness can be observed only for high temperature annealing. The SE results show that the amorphous phase of HfO2 (in 20nm thick samples) has an optical bandgap of 5.51eV. Following its transition to a crystalline phase upon annealing at 750°C, the optical bandgap increases to 5.85eV.
We have carried out a transmission electron microscopy based study of AlGaAs–Al(oxide) heterolayers created by lateral sidewall wet oxidation and identify the oxide phase formed as a consequence of the oxidation of AlAs to be Γ-Al2O3, with the cubic Fd 3m structure. The oxide-semiconductor interface is weak and porous, possibly due to the high stress loads developed during oxidation, and we propose that the fast oxidation rates are a consequence of reactants transported to the oxidation front along the porous interface.
SrZrO3 thin films were prepared by sol–gel to explore the possibility of SrZrO3 to be used as a gate material for MOSFET application. Films were spin-coated layer by layer on Pt/TiO2/SiO2/Si and silicon substrates and then annealed by rapid thermal annealing at different temperatures ranging form 500 to 900°C. The energy gap calculated form optical transmittance spectrum of SrZrO3 thin films on quartz is about 4.63eV. Dielectric constant of SrZrO3 film is bout 25 determined by c–f measurement and the film thickness. Microstructure and surface morphology of the films were investigated by X-ray diffraction and scanning electron microscopy (SEM), respectively. The film maintained amorphous until being annealed at a temperature above 800°C.
The continuous scaling down of devices dimensions, in silicon technology, imposes to replace silicon dioxide. Among the potential candidates for new capacitors, some perovskite structure materials (such as titanate or zirconate) show interesting characteristics. The first way to develop perovskite films is to use a mixture of two β-diketonates by varying the solution's cationic ratio. However, our previous results on SrZrO3 showed that a wide parametric study had to be carried on. Another way is to design novel heterometallic precursors that contain both cations on the same molecule. The ligands could be chosen so that peculiar evaporation and decomposition temperatures could be obtained.Thus, perovskite films (SrZrO3) were deposited on plane Si(100) substrates by direct liquid injection MOCVD from two original heterometallic precursors Sr2Zr2(OnPr)8(thd)4(nPrOH)2 and Sr2Zr2(thd)4(OiPr)8. The oxide films were deposited at substrate temperature ranging from 550 to 900°C. At the lowest temperatures (550 and 600°C) the as-deposited films were amorphous. After a postannealing at 700°C for 1h under N2/O2, the films deposited at 550°C were crystallized in the SrZrO3 orthorhombic phase. Crystallographic and chemical structures were controlled applying grazing X-ray diffraction and infrared spectroscopy measurements. Results are discussed with respect to experimental synthesis conditions.
The use of the Voigt function for the analysis of the integral breadths of broadened X-ray diffraction line profiles forms the basis of a rapid and powerful single-line method of crystallite-size and strain determination which is easy to apply. To avoid graphical methods or interpolation from tables, empirical formulae of high accuracy are used and an estimation of errors is presented, including the influence of line-profile asymmetry. The method is applied to four practical cases of size-strain broadening: (i) cold-worked nickel, (ii) a nitrided steel, (iii) an electrodeposited nickel layer and (iv) a liquid-quenched AlSi alloy.
Both x-ray reflectometry and high-resolution x-ray diffractometry techniques are used for the assessment of individual layer thicknesses and interfacial profiles inside complicated heterostructures, such as semi-conductor multilayers. In particular, the use of Fourier transform-based numerical treatments applied to both the reflectivity curves and the high-resolution diffraction profiles allows a fast and precise determination of the individual layer thicknesses. Moreover, we show the potentiality of this method by reporting x-ray reflectometry and diffractometry studies on waveguides structures and superlattices. Typical layer thicknesses from 0.5 nm to more than 1 mum are accessible with these methods. We show the complementarity of both x-ray reflectometry and high-resolution diffraction techniques. Finally, the reliability of using a simulation software for the assessment of complicated interfacial roughness, such as segregation profiles, is reported. Key wordx-ray reflectometry, high-resolution x-ray diffractometry, semi-conductor heterostructures, thickness determination, Fourier Transform, interfacial segregation profiles.
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We present studies of the interface abruptness of selectively oxidized AlAs/GaAs multilayer structures using transmission electron microscopy (TEM). High‐resolution cross‐sectional TEM images reveal that the interfaces between oxidized AlAs and unoxidized regions (GaAs and AlAs) are extremely abrupt on atomic scale. The widths of the transitional region are found to be within 4 monolayers for the interface between oxidized AlAs and unoxidized GaAs and 6.5 nm for the one between oxidized and unoxidized AlAs. The oxide layer thickness is found to decrease gradually from the oxidation front over a length of 200 nm. © 1996 American Institute of Physics.
Many materials systems are currently under consideration as potential replacements for SiO2 as the gate dielectric material for sub-0.1 μm complementary metal–oxide–semiconductor (CMOS) technology. A systematic consideration of the required properties of gate dielectrics indicates that the key guidelines for selecting an alternative gate dielectric are (a) permittivity, band gap, and band alignment to silicon, (b) thermodynamic stability, (c) film morphology, (d) interface quality, (e) compatibility with the current or expected materials to be used in processing for CMOS devices, (f) process compatibility, and (g) reliability. Many dielectrics appear favorable in some of these areas, but very few materials are promising with respect to all of these guidelines. A review of current work and literature in the area of alternate gate dielectrics is given. Based on reported results and fundamental considerations, the pseudobinary materials systems offer large flexibility and show the most promise toward successful integration into the expected processing conditions for future CMOS technologies, especially due to their tendency to form at interfaces with Si (e.g. silicates). These pseudobinary systems also thereby enable the use of other high-κ materials by serving as an interfacial high-κ layer. While work is ongoing, much research is still required, as it is clear that any material which is to replace SiO2 as the gate dielectric faces a formidable challenge. The requirements for process integration compatibility are remarkably demanding, and any serious candidates will emerge only through continued, intensive investigation. © 2001 American Institute of Physics.
Parametric fluorescence in low-loss oxidized aluminum gallium arsenide heterostructure waveguides is quantitatively analyzed. A parametric fluorescence efficiency as high as 6×10−7 W/W has been measured in a 3.2-mm-long waveguide. This corresponds to a normalized conversion efficiency, scaled with the waveguide length, of about 1000% cm−2 W−1, eight times higher than with LiNbO3 waveguides. This opens the perspective of a microoptical parametric oscillation threshold below 100 mW. © 2001 American Institute of Physics.
THE measures of line-breadth most widely used in X-ray and electron diffraction are perhaps the half width and the integral breadth. The measure of dispersion most widely used in mathematical treatments of distributions is, however, the variance or mean-square breadth. Its comparative neglect in crystallographic problems has been due to the large variance of the wave-length spread and of the diffraction profile, the ‘tails’ of the lines approaching zero approximately as the square of the distance from the line centroids. In spite of this, however, the variance has been used in discussions of spectrometer1 and diffractometer2–4 aberrations. When the line profile is ‘truncated’, as it has to be in practical centroid determination5–8, the large contribution to the variance from the tails is eliminated, and it becomes a measure of line-broadening worth serious consideration. It has the great advantage over all other measures of breadth that it can be corrected for geometrical aberrations1 and wave-length spread by simple subtraction, instead of by ‘unfolding’9. Tournarie10 has criticized the use of half width and integral breadth on the ground that they give undue weight to a few isolated points of the diffraction profile, instead of treating all observed points on the same basis, and derived a relation between the crystallite size and the variance of the line profile over a deliberately restricted angular range. Tournarie's result is immediately obtained by considering the asymptotic expressions for the line profile given by Wilson11; in the present communication a unified treatment is outlined which not only recovers Tournarie's particle-size result but also gives analogous expressions applicable to certain types of ‘mistake’ and strain broadening.
Frequency conversion in nonlinear optical crystals is an effective means of generating coherent light at frequencies where lasers perform poorly or are unavailable. For efficient conversion, it is necessary to compensate for optical dispersion, which results in different phase velocities for light of different frequencies. In anisotropic birefringent crystals such as LiNbO3 or KH2PO4 ('KDP'), phase matching can be achieved between electromagnetic waves having different polarizations. But this is not possible for optically isotropic materials, and as a result, cubic materials such as GaAs (which otherwise have attractive nonlinear optical properties) have been little exploited for frequency conversion applications. Quasi-phase-matching schemes, which have achieved considerable success in LiNO3 (ref. 4), provide a route to circumventing this problem, but the difficulty of producing the required pattern of nonlinear properties in isotropic materials, particularly semiconductors, has limited the practical utility of such approaches. Here we demonstrate a different route to phase matching - based on a concept proposed by Van der Ziel 22 years ago - which exploits the artificial birefringence of multilayer composites of GaAs and oxidised AlAs. As GaAs is the material of choice for semiconductor lasers, such optical sources could be integrated in the core of frequency converters based on these composite structures.
Broadening of the Debye-Scherrer lines in x-ray photographs of cold-worked metals has been attributed (i) to breaking up of the crystals into " crystallites " whose linear dimensions are less, similar10⁻⁵ cm., (ii) to the presence of crystal grains of different lattice parameters, and (iii) to distortion of comparatively large crystal grains. The broadening to be expected on the last hypothesis is worked out approximately. It is found that the " apparent strain " is given by ηidentical withβ cot Θ=2/Φhkl(0), where β is the (corrected) integral breadth of the hkl reflection, Θ is the Bragg angle, and Φhhl(e)de is the fraction of the crystal for which the tensile strain in the hkl direction is between e and e+de.
To relate η with the internal stresses requires some approximations. In cubic crystals fairly plausible assumptions lead to the equation η²=A+BH, where A and B are constants involving the elastic moduli and the mean square values of the direct and shear stresses, and Hidentical with(k²l² + l²h² + h²k²)/(h² + k² + l²)². This equation is verified within the rather large experimental error for metal filings and wire. Details of the experimental work will be published elsewhere.
A method is derived, using Fourier analysis, for finding the corrected distribution of intensity across an x-ray diffraction line, and the procedure is illustrated by a numerical example. The method may also be of use in spectrum analysis and statistical problems.
Strontium zirconate perovskite thin films were deposited on Si(1 0 0) substrates by metal organic chemical vapour deposition (MOCVD) in a cold wall reactor using direct injection process of two β-diketonates precursors. Oxide growth was observed over a temperature ranging from 700 to 1000 °C and various metal Sr/Zr ratios in the solution.Using peculiar experimental conditions, an orthorhombic strontium zirconate (SrZrO3(o)) phase is obtained. The results on the films are discussed in relation with the bulk ZrO2–SrO pseudo binary equilibrium phase diagram existing on this compound.
A computer program called IMD is described. IMD is used for modeling the optical properties (reflectance, transmittance, electric-field intensities, etc.) of multilayer films, i.e., films consisting of any number of layers of any thickness. IMD includes a full graphical user interface and affords modeling with up to eight simultaneous independent variables, as well as parameter estimation (including confidence interval generation) using nonlinear, least-squares curve fitting to user-supplied experimental optical data. The computation methods and user interface are described, and numerous examples are presented that illustrate some of IMD’s unique modeling, fitting, and visualization capabilities. © 1998 American Institute of Physics.
With modern experimental technique, it is possible to measure a peak shape with sufficient accuracy to justify an interpretation based on the precise shape of the reflection. The corrected shape is represented by a cosine Fourier series and a set of A n coefficients determined. A plot of the A n coefficients vs. n will distinguish between distortion and particle size broadening. From the A n coefficients, root mean square values of strain averaged over lengths na 3 are obtained. The decrease in these values for increasing length na 3 is a direct indication of the non‐uniform nature of the strains in cold‐worked metal. By measuring several orders of a given plane, it is theoretically possible to obtain a distribution function of the strains directly from a Fourier transform of the A n coefficients.
Both X-ray reflectometry and X-ray diffractometry techniques are used for the assessment of individual layer thicknesses inside complicated semi-conductor heterostructures, in particular for opto-electronic applications. The use of Fast Fourier transform-based numerical treatments applied to the reflectivity curve allows a fast determination of the individual layer thicknesses. We demonstrate the capability of this method by reporting X-ray reflectometry study on superlattices, multiple quantum wells, and other complicated structures. Typical layer thicknesses from 0.5 nm to 500 nm were successfully investigated. Fast Fourier transform-based procedure has also been employed successfully on high resolution X-ray diffraction spectra. We finally show the complementary of both techniques.
Grazing x-ray reflectometry allows analysis of thin-layer stacks. The fitting of the reflectivity curve by a trial and error method can determine the parameters of the films. The Fourier analysis of the experimental reflectivity curve can directly give a rough determination of the profile index. Such results can be useful in choosing a starting model. With the choice of an appropriate model a fit to the reflectivity curve can be undertaken to determine the parameters of the stack. The Fourier analysis method can only be used if the reflectivity data undergo a transformation to produce a periodic curve. Associated artifacts are studied and discussed. Each Fourier peak is associated with two interfaces. The interface roughness spreads the Fourier peaks, adding the squared roughness values. The sample's absorption of the x-rays does not limit the Fourier analysis.
- R A Young
- D B Wiles
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