Lattice strain of hydrogen-implanted silicon: Correlation between X-ray scattering analysis and <i>ab-initio</i> simulations

Rieutord, F.; Mazen, F.; Reboh, S.; Penot, Jean-Daniel; Bîlteanu, Liviu; Crocombette, Jean-Paul; Valeš, Václav; Holý, V.; Capello, L.

doi:10.1063/1.4800538

Cited by 16 publications

(18 citation statements)

References 19 publications

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“…The origin of strain/stress in H-implanted Si is related to the introduction of foreign atoms and lattice disorder in the material. 8,10,[14][15][16] These structural modifications cause a localized increase of volume within the damaged layer, or an isotropic intrinsic strain e. 14-16 Along the z-direction perpendicular to the surface, there is no restriction to deformation and the system can assume its new configuration. In the directions parallel to the surface (defined here as x and y), however, the thick substrate imposes a restriction to relaxation.…”

Section: Resultsmentioning

confidence: 99%

“…(13)), we introduced Boussinesq forces on the surface. 18 The Airy's function for our system can be written then as uðy; zÞ ¼ u edge ðy; zÞ þ u image ðy; zÞ þ u Boussinesq ðy; zÞ: (14) For a dipole of edge dislocation running along the y-axis, separated by a length 2a, at a distance -c from the surface and centered in the z-axis (with |c| ¼ 4|a|) it follows that u dipole ðy; zÞ ¼ ÀDyln ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðz þ cÞ 2 þ ðy þ aÞ 2 q þ Dyln ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðz À cÞ 2 þ ðy þ aÞ 2 q þ 2Dazy ðz À cÞ 2 þ y 2 þ Dyln ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðz þ cÞ 2 þ ðy À aÞ 2 q À Dy:ln ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðz À cÞ 2 þ ðy À aÞ 2 q À 2Dazy ðz þ cÞ 2 þ y 2 :…”

Section: Resultsunclassified

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Nanoscale organization by elastic interactions between H and He platelets in Si

Reboh

Barbot

Vallet

et al. 2013

Journal of Applied Physics

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We used ion implantation of H and He in Si and thermal treatments to produce two systems allowing to study the effects of global and local mechanical stress fields on the formation energy of H-precipitates called H-platelets. In the first part of the work, the depth-distribution of different crystallographic orientations of the precipitates formed along the implanted layer was characterized by transmission electron microscopy. The global strain in the region was measured by X-ray diffraction, and the depth distribution of strain was reconstructed using a dynamical-theory-based code. Elasticity theory was used to develop a model based on mechanical interactions, explaining the preferential presence of (001)-oriented precipitates in the more stressed region of the implanted layer. In a second part, local sources of stress of nanometer size and cylindrical symmetry were introduced in a deeper region of the matrix, before the nucleation of H-platelets. The local stresses were embodied by (001) He-plate precipitates. Upon annealing, a specific arrangement of crystallographic variants of {111}-oriented H-platelets in a four-fold configuration was observed. To explain these experimental observations, and to calculate the variations of the formation energy of the precipitates under the presence of local stress tensors components, analytical and numerical (finite element method) approaches were used to develop 2D and 3D models based on elasticity theory. The concepts and modeling strategy developed here paves the way for determining the required conditions to create controlled architecture of precipitates at the nanoscale using local stress engineering.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsunclassified

Nanoscale organization by elastic interactions between H and He platelets in Si

Reboh

Barbot

Vallet

et al. 2013

Journal of Applied Physics

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“…The appearance of modern power X‐ray sources, namely, X‐ray tubes with a rotating anode and synchrotron radiation facilities, provided the possibility for the wide use of triple crystal diffractometers to measure reciprocal space maps and, consequently, in more details analyze the complicated displacement fields caused by various configurations of radiation‐induced defects. Such diffuse scattering measurements, in combination with substantially increased computing power, made it possible to perform the investigations with using the atomistic simulation methods by which the diffuse X‐ray scattering can be calculated for an arbitrary finite‐sized defect in any material where reliable interatomic force models exist .…”

Section: Characterization Of Ion‐implanted Crystals By X‐ray Diffractmentioning

confidence: 99%

Dynamical X‐ray diffraction theory: Characterization of defects and strains in as‐grown and ion‐implanted garnet structures

Olikhovskii

Molodkin

Skakunova

et al. 2017

Physica Status Solidi (b)

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The generalized dynamical theory of X-ray diffraction by imperfect single crystals is extended to characterize structure imperfections of real single crystals with complex basis and similar crystalline films with inhomogeneous strain fields. The influence of various defects (intrinsic and extrinsic point defects, nanoclusters, and microdefects), simultaneously presented in such structures, on changing both average and fluctuating strain fields as well as structure factors are taken into account. The analytical expressions connecting immediately the coherent and diffuse components of the scattering intensity with statistical characteristics of these defects are obtained. Thus, the self-consistent description of the coherent and diffuse dynamical diffraction intensity components is provided. Some examples of the application of the developed theoretical model to treat rocking curves measured from various garnet structures by using high-resolution double-crystal X-ray diffractometer are reviewed. Possibilities for the quantitative characterization of structural defects and strain profiles in the as-grown and ion-implanted garnet single crystals and yttrium iron garnet films are demonstrated.The self-consistent dynamical description of coherent and diffuse scattering intensities from imperfect crystal structures with inhomogeneous strain fields and randomly distributed defects make it possible to determine the parameters of strain profiles and statistical characteristics of defects by analytical treating the coherent and diffuse components of rocking curves measured by the high-resolution double-crystal X-ray diffractometer with widely open detector window.

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“…In material physics, the addition of defects (vacancies, self-interstitials, impurities) modifies the macroscopic volume of the sample. This situation is particularly relevant for the swelling of materials under irradiation [1], for the elastic interaction between impurities and dislocations [2][3][4][5], or for stress induced by implantation in thin films [6]. This is quantified by the relaxation volume of a defect.…”

Section: Introductionmentioning

confidence: 99%

Pressure, relaxation volume, and elastic interactions in charged simulation cells

et al. 2015

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The ab initio calculation of charged supercells within density-functional theory is a necessary step to access several important properties of matter. The relaxation volume of charged point defects or the partial molar volume of ions in solution are two such examples. However, the total energy and therefore the pressure of charged systems is not uniquely defined when periodic boundary conditions are employed. This problem is tightly related to the origin of the electrostatic potential in periodic systems. This effect can be easily observed by modifying the electrostatic convention or modifying the local ionic potential details. We propose an approach to uniquely define the pressures in charged supercells with the use of the absolute deformation potentials. Only with such a definition could the ab initio calculations provide meaningful values for the relaxation volumes and for the elastic interactions for charged defects in semiconductors or ions in solution. The proposed scheme allows one to calculate sensible data even when charge neutrality is not enforced, thus going beyond the classical force-field-based approaches.

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Lattice strain of hydrogen-implanted silicon: Correlation between X-ray scattering analysis and ab-initio simulations

Cited by 16 publications

References 19 publications

Nanoscale organization by elastic interactions between H and He platelets in Si

Nanoscale organization by elastic interactions between H and He platelets in Si

Dynamical X‐ray diffraction theory: Characterization of defects and strains in as‐grown and ion‐implanted garnet structures

Pressure, relaxation volume, and elastic interactions in charged simulation cells

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