X-ray diffraction analysis of multilayer porous InP(001) structure

Lomov, A. A.; Пунегов, В. И.; Васильев, А. Л.; Nohavica, D.; Gladkov, P.; Kartsev, A. A.; Novikov, D. V.

doi:10.1134/s1063774510020033

Cited by 6 publications

(6 citation statements)

References 11 publications

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“…Substituting expression (5) into formula (3) yields the following expression for the intrinsic correlation function of a prolate spheroid: (7) where ξ(ε, θ) = (1 -ε 2 cos 2 θ) 1/2 , θ is the polar angle between the z axis and vector ρ, and ε = (1 -(R/l z ) 2 ) 1/2 < 1 is the coefficient of ellipticity (eccentric ity) characterizing the shape of spheroids. For R = l z , we have ε = 0 and ξ(0, θ) = 1, so that expression (7) converts into the well known correlation function of a sphere of radius R [11].…”

Section: Diffuse X Ray Scattering From a Crystal With Spheroidal Poresmentioning

confidence: 99%

“…[3][4][5][6][7][8]. An important role in the distribution of diffuse scattering is played by the shape of pores.…”

mentioning

confidence: 99%

“…An important role in the distribution of diffuse scattering is played by the shape of pores. Previously, the theory of diffuse X ray scattering employed two models, according to which pores had the shape of rectangular parallelepipeds [3] or cylinders [5][6][7][8]. Diffuse scatter ing from a crystal with elongated ellipsoidal pores has not been analyzed so far.…”

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Diffuse X-ray scattering from a crystal with spheroidal pores

Пунегов

2012

Tech. Phys. Lett.

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The morphology of porous systems created using electrochemical anodization techniques strongly depends on the structural characteristics and chemical properties of the initial materials, concentration of impurities, current density, process duration, and electrolyte composition [1]. Depending on the tech nological conditions, pores of various shapes and sizes are formed in the crystalline matter. Moreover, the morphology of a porous crystal can change under the action of external factors. For example, heat treatment of porous InP leads to the formation of ellipsolidal (in particular, spherical) pores [2]. This behavior is char acteristic of both current line oriented (vertical) and crystallographic (inclined) pores.Analysis of the diffuse X ray scattering provides information about the pore sizes, their orientation rel ative to the crystal surface, the presence or absence of a spatial order, azimuthal anisotropy, etc. [3][4][5][6][7][8]. An important role in the distribution of diffuse scattering is played by the shape of pores. Previously, the theory of diffuse X ray scattering employed two models, according to which pores had the shape of rectangular parallelepipeds [3] or cylinders [5][6][7][8]. Diffuse scatter ing from a crystal with elongated ellipsoidal pores has not been analyzed so far.This investigation is devoted to diffuse X ray scat tering from a crystal with pores having an elongated spheroidal shape, representing a prolate ellipsoid with equal semiaxes in the lateral plane, which are shorter than the vertical semiaxis.Using the formalism of Kato's statistical theory of diffraction [9], an expression for the intensity of the diffuse X ray scattering as a function of vector q (devi ation from the reciprocal lattice vector h) in the kine matical approximation can be written as follows:(1) Here, V 0 is the x ray irradiated volume of the crystal, f is the static Debye-Waller factor, a h is a parameter that characterizes the scattering ability of the crystal, and τ(q) is the so called correlation volume. It should be noted that relation (1) does not take into account dynamical effects in the diffuse X ray scattering the ory-in particular, the primary extinction of the transmitted X ray intensity and the secondary extinc tion in the scattering of incoherent waves. For addi tional simplification, we will also ignore the spatial correlation of pores [6,10]. Under these conditions, the correlation volume τ(q) is given by the Fourier transform of the Kato intrinsic correlation function g(ρ):(2)The intrinsic correlation function of pores in a crystal can be represented as follows [11,12]:where V p is the pore volume and D(r) is a function that depends on the random deformations field and describes local damage of the crystalline lattice [11,12]. In the case under consideration, these distortions are caused by the presence of voids in the crystalline matrix. Denoting by c p the concentration of pores in the matrix and using the D(r) function, we can express the static Debye-Waller factor as follows [11]:(4)) . e...

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Section: Diffuse X Ray Scattering From a Crystal With Spheroidal Poresmentioning

confidence: 99%

“…[3][4][5][6][7][8]. An important role in the distribution of diffuse scattering is played by the shape of pores.…”

mentioning

confidence: 99%

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Diffuse X-ray scattering from a crystal with spheroidal pores

Пунегов

2012

Tech. Phys. Lett.

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“…Nevertheless, numerical simulation of diffuse scattering requires statistical averaging over QD vertical and lateral dimensions, as for porous crystals [128,129]. The size of self-organized QDs in a semiconducting matrix is known to be different, even if their volume variance is not very large.…”

Section: May 2015mentioning

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High-resolution X-ray diffraction in crystalline structures with quantum dots

Пунегов¹

2015

Phys.-Usp.

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We review the current status of nondestructive highresolution X-ray diffractometry research on semiconductor structures with quantum dots (QDs). The formalism of the statistical theory of diffraction is used to consider the coherent and diffuse X-ray scattering in crystalline systems with nanoinclusions. Effects of the shape, elastic strain, and lateral and vertical QD correlation on the diffuse scattering angular distribution near the reciprocal lattice nodes are considered. Using short-period and multicomponent superlattices as an example, we demonstrate the efficiency of data-assisted simulations in the quantitative analysis of nanostructured materials. Contents 1. Introduction. Methods of research on structures with quantum dots 419 2. High-resolution X-ray diffraction 420 2.1 Triple-axis X-ray diffractometry; 2.2 Statistical theory of X-ray diffraction. Coherent and diffuse scattering; 2.3 Direct and inverse X-ray diffraction problems 3. X-ray diffraction in structured media 423 3.1 Multilayer quantum dots; 3.2 Semiconductor structures with self-organized quantum dots; 3.3 Diffraction on 3D periodic quantum dot arrays 4. Influence of the quantum dot shape, size, and elastic strain on X-ray diffuse scattering 426 4.1 Diffuse scattering from epitaxial structures with quantum dots of different shapes; 4.2 Spheroidal quantum dots 5. Spatial correlations in the arrangement of quantum dots 432 5.1 Lateral correlation of quantum dots. Short-range order; 5.2 Vertical correlation of quantum dots 6. Quantitative X-ray diffraction analysis of heterostructures with quantum dots 437 6.1 Short-period superlattices with quantum dots; 6.2 Multicomponent heterostructures with quantum dots 7. Conclusion 443 References 443 Physics ± Uspekhi 58 (5) 419 ± 445 (2015) # 2015 Uspekhi Fizicheskikh Nauk, Russian Academy of Sciences V I Punegov Physics ± Uspekhi 58 (5) V I Punegov Physics ± Uspekhi 58 (5) V I Punegov Physics ± Uspekhi 58 (5)

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“…The data evaluation was carried out by reciprocal space map (RSM) data fitting in the frame of the statistical dynamical diffraction model. The first systematic analysis of diffuse scattering from porous layers in InP was presented by Lomov et al (2006Lomov et al ( , 2010 and Punegov et al (2007). It was shown that high-resolution X-ray diffraction allows determination of the pore parameters, averaged over the sample volume.…”

Section: Diffuse X-ray Scattering From Porous Crystalline Layersmentioning

confidence: 99%

High-resolution synchrotron diffraction study of porous buffer InP(001) layers

Lomov

Пунегов²,

Nohavica³

et al. 2014

J Appl Cryst

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Author(s) of this paper may load this reprint on their own web site or institutional repository provided that this cover page is retained. Republication of this article or its storage in electronic databases other than as specified above is not permitted without prior permission in writing from the IUCr.For further information see http://journals.iucr.org/services/authorrights.html Many research topics in condensed matter research, materials science and the life sciences make use of crystallographic methods to study crystalline and non-crystalline matter with neutrons, X-rays and electrons. Articles published in the Journal of Applied Crystallography focus on these methods and their use in identifying structural and diffusioncontrolled phase transformations, structure-property relationships, structural changes of defects, interfaces and surfaces, etc. Developments of instrumentation and crystallographic apparatus, theory and interpretation, numerical analysis and other related subjects are also covered. The journal is the primary place where crystallographic computer program information is published.Crystallography Journals Online is available from journals.iucr.org J. Appl. Cryst. (2014 X-ray reciprocal space mapping was used for quantitative investigation of porous layers in indium phosphide. A new theoretical model in the frame of the statistical dynamical theory for cylindrical pores was developed and applied for numerical data evaluation. The analysis of reciprocal space maps provided comprehensive information on a wide range of the porous layer parameters, for example, layer thickness and porosity, orientation, and correlation length of segmented pore structures. The results are in a good agreement with scanning electron microscopy data.

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X-ray diffraction analysis of multilayer porous InP(001) structure

Cited by 6 publications

References 11 publications

Diffuse X-ray scattering from a crystal with spheroidal pores

Diffuse X-ray scattering from a crystal with spheroidal pores

High-resolution X-ray diffraction in crystalline structures with quantum dots

High-resolution synchrotron diffraction study of porous buffer InP(001) layers

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