Nondestructive three-dimensional imaging of crystal strain and rotations in an extended bonded semiconductor heterostructure

Pateras, Anastasios; Allain, Marc; Godard, Pierre; Largeau, L.; Patriarche, G.; Talneau, A.; Pantzas, Konstantinos; Burghammer, Manfred; Minkevich, A. A.; Chamard, Virginie

doi:10.1103/physrevb.92.205305

Cited by 22 publications

(31 citation statements)

References 27 publications

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“…It is used herein to provide the detailed 3D description of the biomineral crystal. Previous works have shown that spatial resolution of a few tens of nanometres, strain sensitivity of a few 10 -4 and lattice rotation sensitivity of 0.005° are reachable 5 . This section covers many aspects of the Bragg ptychography procedure: experiments, preliminary data analysis, inversion procedure, and spatial resolution.…”

Section: -3d Bragg Ptychography: From Data Acquisition To Image Analysismentioning

confidence: 99%

“…Furthermore, as the preliminary analysis of the Bragg diffraction data set evidenced the presence of mis-oriented crystalline domains (presence of several Bragg maxima along the rocking curve, Supplementary Figure 5B), a crystalline displacement field was introduced, mimicking local strain and/or orientations 5 . To this aim, a complex-valued function was introduced to describe the sample, with amplitude and phase related respectively to the sample density and projection of the crystalline displacement 5 . The sample was divided into several domains, with lateral dimensions of 220 × 290 nm 2 and elongated along the thickness direction (according to CARS results and preliminary test inversions).…”

Section: Fig 4 (Suppl): Imaging the Illumination Complex-valued Funmentioning

confidence: 99%

“…Indeed, a finite crystalline strain can be written as a linear phase ramp along the spatial direction parallel to the Bragg vector (resulting in the motion of the Bragg peak along the reference Bragg vector) while a small crystalline rotation can be approximated by a linear phase ramp along the direction perpendicular to the Bragg vector and the rotation axis (and resulting thereby in the motion of the Bragg peak along the plane perpendicular to the Bragg vector). 5,8 Each domain was assigned a constant strain and/or rotations (with randomly chosen values), which could be recovered from the spatial derivatives of the phase map ( Supplementary Figure 6E, F). Finally, the full complex-valued object was transformed from the laboratory frame to a non-orthogonal frame, derived from Fourier conjugation relations applied to the detection frame 6 .…”

Section: Fig 4 (Suppl): Imaging the Illumination Complex-valued Funmentioning

confidence: 99%

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Revealing crystalline domains in a mollusc shell single-crystalline prism

et al. 2017

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Biomineralization integrates complex processes leading to an extraordinary diversity of calcareous biomineral crystalline architectures, in intriguing contrast with the consistent presence of a sub-micrometric granular structure. Hence, gaining access to the crystalline architecture at the mesoscale, that is, over a few granules, is key to building realistic biomineralization scenarios. Here we provide the nanoscale spatial arrangement of the crystalline structure within the 'single-crystalline' prisms of the prismatic layer of a Pinctada margaritifera shell, exploiting three-dimensional X-ray Bragg ptychography microscopy. We reveal the details of the mesocrystalline organization, evidencing a crystalline coherence extending over a few granules. We additionally prove the existence of larger iso-oriented crystalline domains, slightly misoriented with respect to each other, around one unique rotation axis, and whose shapes are correlated with iso-strain domains. The highlighted mesocrystalline properties support recent biomineralization models involving partial fusion of oriented nanoparticle assembly and/or liquid droplet precursors.

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Section: -3d Bragg Ptychography: From Data Acquisition To Image Analysismentioning

confidence: 99%

Section: Fig 4 (Suppl): Imaging the Illumination Complex-valued Funmentioning

confidence: 99%

Section: Fig 4 (Suppl): Imaging the Illumination Complex-valued Funmentioning

confidence: 99%

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Revealing crystalline domains in a mollusc shell single-crystalline prism

et al. 2017

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“…The retrieved 3D effective electron density map contains information on both electron density distribution and crystalline displacements within the sample [9]. From the crystalline displacement information, one can derive 3D strain and rotation maps of the probed crystalline plane family [10]. Spatial resolutions in the 10 nm range can be obtained with strain sensitivity in the order of a few times 10 −4 [11].…”

Section: Introductionmentioning

confidence: 99%

Numerical study of Bragg CDI on thick polycrystalline specimens

Pedersen¹,

Chamard²,

Poulsen³

2018

Opt. Express

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Bragg coherent diffraction imaging (BCDI) is a powerful X-ray imaging technique for crystalline materials, providing high resolution maps of structure and strain. The technique is typically used to study a small isolated object, and is in general not compatible with a bulk polycrystalline sample, due to overlap of diffraction signals from various crystalline elements. In this paper, we present an imaging method for bulk samples, based on the use of a coherent source. The diffracted X-ray beam from a grain or domain of choice is magnified by an objective before being monitored by a 2D detector in the far field. The reconstruction principle is similar to the case of BCDI, while taking the magnification and pupil function into account. The concept is demonstrated using numerical simulations and reconstructions. We find that by using an object-lens distance shorter than the focal length, the numerical aperture is larger than in a traditional imaging geometry, and at the same time the setup is insensitive to small phase errors by lens imperfections. According to our simulations, we expect to be able to achieve a spatial resolution smaller than 20 nm when using the objective lens in this configuration.

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“…19,20 Similar lattice rotation and distortion effects are observed in ptychography studies of III-V heterostructures. 21 Nanobeam diffraction studies of Si/SiGe structures show that the lattice of the Si QW is distorted by the relaxation of the SiGe substrate 22 and by stresses imparted on the semiconductor through interfaces with metal electrodes. 23 Other nanobeam diffraction studies have probed the strain distribution over lateral lengths scales of microns in Ge microstripes, 24 heteroepitaxial Ge, 25 and SiGe via rapid mapping techniques.…”

Section: Introductionmentioning

confidence: 99%

Combining experiment and optical simulation in coherent X-ray nanobeam characterization of Si/SiGe semiconductor heterostructures

Tilka

Park

Ahn

et al. 2016

Journal of Applied Physics

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The highly coherent and tightly focused x-ray beams produced by hard x-ray light sources enable the nanoscale characterization of the structure of electronic materials but are accompanied by significant challenges in the interpretation of diffraction and scattering patterns. X-ray nanobeams exhibit optical coherence combined with a large angular divergence introduced by the x-ray focusing optics. The scattering of nanofocused x-ray beams from intricate semiconductor heterostructures produces a complex distribution of scattered intensity. We report here an extension of coherent x-ray optical simulations of convergent x-ray beam diffraction patterns to arbitrary x-ray incident angles to allow the nanobeam diffraction patterns of complex heterostructures to be simulated faithfully. These methods are used to extract the misorientation of lattice planes and the strain of individual layers from synchrotron x-ray nanobeam diffraction patterns of Si/SiGe heterostructures relevant to applications in quantum electronic devices. The systematic interpretation of nanobeam diffraction patterns from semiconductor heterostructures presents a new opportunity in characterizing and ultimately designing electronic materials.

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Nondestructive three-dimensional imaging of crystal strain and rotations in an extended bonded semiconductor heterostructure

Cited by 22 publications

References 27 publications

Revealing crystalline domains in a mollusc shell single-crystalline prism

Revealing crystalline domains in a mollusc shell single-crystalline prism

Numerical study of Bragg CDI on thick polycrystalline specimens

Combining experiment and optical simulation in coherent X-ray nanobeam characterization of Si/SiGe semiconductor heterostructures

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