A Dynamical Theory of Diffraction for a Distorted Crystal

Takagi, Shun

doi:10.1143/jpsj.26.1239

Cited by 810 publications

(512 citation statements)

References 24 publications

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“…To obtain information about the magnitude of the strain and its depth distribution, simulations of the rocking curves were carried out using Philips PC-HRS Simulation and other simulation programs based on the Takagi-Taupin equations of the dynamical theory of diffraction. 11,12 Bragg reflection curves were simulated using various model strain-depth profiles based on known ion and damage profiles, with lattice strain proportional to displaced atom density. By comparing the measured rocking curves with the simulated ones, the corresponding strain (⌬d/d) Ќ was determined.…”

Section: Methodsmentioning

confidence: 99%

Strain development and damage accumulation during neon ion implantation into silicon at elevated temperatures

Cima

Boudinov

Souza

et al. 2000

Journal of Applied Physics

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The development of mechanical strain and accumulation of damage in silicon single crystals implanted with Ne ions to doses in the range of 0.1-1.0 ϫ10 17 cm Ϫ2 at temperatures from 200 to 600°C were investigated employing Rutherford backscattering spectrometry, high resolution x-ray diffraction ͑HRXRD͒ analysis and cross section transmission electron microscopy ͑XTEM͒. Two distinct layers have been found in the implanted material: A near-surface layer (Ͻ 0.2 m thick͒ where no extended defects are observed and a buried layer (Ϸ0.5 m thick͒ containing a dense array of dislocation loops and defect clusters. XTEM analysis revealed a distribution of small spherical cavities presumably filled with Ne, with a diameter Ͻ4 nm, extending along the entire depth of the implanted layer. HRXRD studies showed the presence of a positive strain ͑of expansion͒, irrespective of the implanted dose and temperature. The findings are discussed in terms of the proposed model which assumes that vacancy-type defects are consumed during the formation of Ne bubbles.

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Section: Methodsmentioning

confidence: 99%

Strain development and damage accumulation during neon ion implantation into silicon at elevated temperatures

Cima

Boudinov

Souza

et al. 2000

Journal of Applied Physics

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“…The TTE linking the plane-wave amplitudes Eo and Eh of the transmitted and diffracted wave fields can be written as (Takagi, 1969)…”

Section: General Foundation Of the Primary-extinction And Absorption mentioning

confidence: 99%

“…Laue, 1960) was very clear to authors of the pioneering papers (Zachariasen, 1967;Becker & Coppens, 1974, B&C hereinafter;Wemer, 1974). Later, there were several papers (Kato, 1976;Becker, 1977;Olekhnovich & Olekhnovich, 1978;Becker & Dunstetter, 1984;Werner et al, 1986;A1 Haddad & Becker, 1990, H&B hereinafter), in which the general approach to evaluate the primary-extinction factor by use of the dynamical Takagi-Taupin equations (Takagi, 1962(Takagi, , 1969Taupin, 1964Taupin, , 1967 was discussed. A meaningful primary-extinction solution (except for X-ray absorption) was first found by Kato (1976) and Becker (1977) and corresponds to the Laue approximation of the pointsource diffractive function that describes X-ray diffraction by finite convex-shaped crystals.…”

Section: Introductionmentioning

confidence: 99%

Primary Extinction and Absorption: a Theoretical Approach Based on the Takagi-Taupin Equations. Application to Spherical Crystals

Chukhovskii

Hupe²,

Rossmanith³

et al. 1998

Acta Cryst Sect A

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The primary-extinction problem for X-ray diffraction by perfect crystals is treated using the Becker-Coppens iterative procedure within the Takagi-Taupin equations. An analytical approximation for the primary-extinction factor yp describing both the effects of the X-ray multiple scattering and the absorption processes within the perfect crystal of an arbitrary shape is derived. The solution differs from the known expressions given by Zachariasen and Becker & Coppens on the basis of the HamiltonDarwin intensity transfer equations and in the limiting case of a non-absorbing crystal it concurs with the KatoBecker formula found in the Laue approximation of the dynamical theory. The theoretical results are consistent with experimental data of a number of reflections of Ge and Si single-crystal spheres measured at X-ray wavelengths A = 0.56, 0.71 and 1.54 A with a laboratory CAD-4 and a Huber four-circle diffractometer at HASYLAB, DESY, Hamburg, Germany. Two novel features are discussed. First, it is shown that by neglecting the X-ray absorption effect the calculated extinction factor yp is close to the value given by the Becker--Coppens formula. Second, it was found that for absorbing spherical crystals with /zR > 1 absorption effects cannot be treated separately from the primaryextinction phenomenon because of imaginary dispersion corrections to the atomic form factors. The experimental data are fitted to the Becker-Coppens and present theoretical models. The best fits are found to relate to the present model and produce relatively low R factors of 3 to 6% for the Bragg intensities measured in the cases of Si and Ge spherical crystals.

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“…TT equations are a set of partial derivative hyperbolic equations (Takagi, 1962(Takagi, , 1969Taupin, 1964) giving the amplitudes of the refracted and reflected waves D O and Dh at any point inside the Borrmann fan ( Fig. 1):…”

Section: Principles Of the Numerical Integrationmentioning

confidence: 99%

The use of an array processor for the simulation of X-ray topographs

Soyer¹,

Epelboin²,

Morris³

1985

J Appl Cryst

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The use of a varying-step algorithm now allows the simulation of traverse topographs and of section topographs taking into account the real width of the incident beam. However, computation time remains a critical factor in practical use. With an array processor it is possible to decrease the computation time significantly• It is shown that pictures of good quality may be obtained in a reasonable time using local facilities• The influence of various parameters on the accuracy of the simulations is discussed• It is demonstrated that local machines can be more useful, in crystallography, than giant computers often difficult to reach through the network of communications.

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A Dynamical Theory of Diffraction for a Distorted Crystal

Cited by 810 publications

References 24 publications

Strain development and damage accumulation during neon ion implantation into silicon at elevated temperatures

Strain development and damage accumulation during neon ion implantation into silicon at elevated temperatures

Primary Extinction and Absorption: a Theoretical Approach Based on the Takagi-Taupin Equations. Application to Spherical Crystals

The use of an array processor for the simulation of X-ray topographs

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