Analysis of strain and stacking faults in single nanowires using Bragg coherent diffraction imaging

Coherent diffraction imaging (CDI) on Bragg reflections is a promising technique for the study of three-dimensional (3D) composition and strain fields in nanostructures, which can be recovered directly from the coherent diffraction data recorded on single objects. In this paper, we report results obtained for single homogeneous and heterogeneous nanowires with a diameter smaller than 100 nm, for which we used CDI to retrieve information about deformation and faults existing in these wires. We also discuss the influence of stacking faults, which can create artefacts during the reconstruction of the nanowire shape and deformation.

[1]  P. Kirkpatrick,et al.  Formation of optical images by X-rays. , 1948, Journal of the Optical Society of America.

[2]  R. Harder,et al.  Coherent X-ray diffraction imaging of strain at the nanoscale. , 2009, Nature materials.

[3]  D. Nelson,et al.  Random, Non-Random and Periodic Faulting in Crystals , 1994 .

[4]  Cristian Mocuta,et al.  Beyond the ensemble average: X-ray microdiffraction analysis of single SiGe islands , 2008 .

[5]  J R Fienup,et al.  Phase retrieval algorithms: a comparison. , 1982, Applied optics.

[6]  K. Dick,et al.  Controlled polytypic and twin-plane superlattices in iii-v nanowires. , 2009, Nature nanotechnology.

[7]  A. Baez,et al.  Fresnel Zone Plate for Optical Image Formation Using Extreme Ultraviolet and Soft X Radiation , 1961 .

[8]  S. Marchesini,et al.  X-ray image reconstruction from a diffraction pattern alone , 2003, physics/0306174.

[9]  Jian-Min Zuo,et al.  Coordination-dependent surface atomic contraction in nanocrystals revealed by coherent diffraction. , 2008, Nature materials.

[10]  Chanh Q Tran,et al.  Extracting coherent modes from partially coherent wavefields. , 2009, Optics letters.

[11]  R. Gerchberg A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[12]  James R. Fienup,et al.  Ambiguity of phase retrieval for functions with disconnected support , 1981 .

[13]  B. Korgel Twins cause kinks , 2006, Nature materials.

[14]  Garth J. Williams,et al.  Three-dimensional mapping of a deformation field inside a nanocrystal , 2006, Nature.

[15]  V. Dubrovskii,et al.  Growth kinetics and crystal structure of semiconductor nanowires , 2008 .

[16]  M. Burghammer,et al.  Coherent x-ray diffraction imaging with nanofocused illumination. , 2008, Physical review letters.

[17]  J. Susini,et al.  High-efficiency multilevel zone plates for keV X-rays , 1999, Nature.

[18]  S. Marchesini,et al.  Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms. , 2007, Physical review letters.

[19]  Gilles Patriarche,et al.  Why does wurtzite form in nanowires of III-V zinc blende semiconductors? , 2007, Physical review letters.

[20]  E. Bakkers,et al.  Growth kinetics of heterostructured GaP-GaAs nanowires. , 2006, Journal of the American Chemical Society.

[21]  Philippe Caroff,et al.  High-quality InAs/InSb nanowire heterostructures grown by metal-organic vapor-phase epitaxy. , 2008, Small.

[22]  Garth J. Williams,et al.  Coherent diffractive imaging and partial coherence , 2007 .

[23]  A. Snigirev,et al.  High energy X-ray micro-optics , 2008 .

[24]  M. Deem,et al.  A biased Monte Carlo scheme for zeolite structure solution , 1998, cond-mat/9809085.

[25]  Garth J. Williams,et al.  Orientation variation of surface strain , 2007 .

[26]  V. Favre-Nicolin,et al.  Coherent-diffraction imaging of single nanowires of diameter 95 nanometers , 2009 .

[27]  L. Wernersson,et al.  InSb heterostructure nanowires: MOVPE growth under extreme lattice mismatch , 2009, Nanotechnology.

[28]  J. Miao,et al.  Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens , 1999, Nature.

[29]  Elias Vlieg,et al.  Twinning superlattices in indium phosphide nanowires , 2008, Nature.

[30]  Ana Diaz,et al.  Coherent diffraction imaging of a single epitaxial InAs nanowire using a focused x-ray beam , 2009 .

[32]  V. Chamard,et al.  Evidence of stacking-fault distribution along an InAs nanowire using micro-focused coherent X-ray diffraction , 2008 .

[33]  V. Dubrovskii,et al.  Growth thermodynamics of nanowires and its application to polytypism of zinc blende III-V nanowires , 2008 .

[34]  J. Chevrier,et al.  Probing the elastic properties of individual nanostructures by combining in situ atomic force microscopy and micro-x-ray diffraction , 2009 .

[35]  S. Hark,et al.  Size‐Dependent Periodically Twinned ZnSe Nanowires , 2004 .

[36]  Zhong Lin Wang,et al.  Periodically twinned nanowires and polytypic nanobelts of ZnS: The role of mass diffusion in vapor-liquid-solid growth. , 2006, Nano letters.

[37]  U Weierstall,et al.  Coherent X-ray diffractive imaging: applications and limitations. , 2003, Optics express.

[38]  L. Samuelson,et al.  Structural properties of 〈111〉B -oriented III–V nanowires , 2006, Nature materials.

[39]  L. Wernersson,et al.  MOVPE growth and structural charactrization of extremely lattice-mismatched InP-InSb nanowire heterostructures , 2009, 2009 IEEE International Conference on Indium Phosphide & Related Materials.

[40]  L. Wernersson,et al.  GaAs/GaSb nanowire heterostructures grown by MOVPE , 2008 .

[41]  P. Eklund,et al.  Coherent twinning phenomena: towards twinning superlattices in III-V semiconducting nanowires. , 2006, Nano letters.

[42]  Lars Samuelson,et al.  Solid-phase diffusion mechanism for GaAs nanowire growth , 2004, Microscopy and Microanalysis.

[43]  V. Chamard,et al.  Local strain in a 3D nano-crystal revealed by 2D coherent X-ray diffraction imaging , 2007 .

[44]  Zhong Lin Wang,et al.  Structures of planar defects in ZnO nanobelts and nanowires. , 2009, Micron.

[45]  P. N. Keating,et al.  Effect of Invariance Requirements on the Elastic Strain Energy of Crystals with Application to the Diamond Structure , 1966 .

[46]  Defect cores investigated by x-ray scattering close to forbidden reflections in silicon. , 2007, Physical review letters.

[47]  A. G. Cullis,et al.  Hard-x-ray lensless imaging of extended objects. , 2007, Physical review letters.

[48]  B. Lengeler,et al.  Focusing high-energy x rays by compound refractive lenses. , 1998, Applied optics.

[49]  J S Wu,et al.  Reconstruction of complex single-particle images using charge-flipping algorithm. , 2005, Acta crystallographica. Section A, Foundations of crystallography.

[50]  Federico Capasso,et al.  Optical properties of rotationally twinned InP nanowire heterostructures. , 2008, Nano letters.

[51]  R. Harder,et al.  Coherent x-ray diffraction imaging of grown-in antiphase boundaries in Fe65Al35 , 2007 .

[52]  I. Robinson,et al.  Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction. , 2001, Physical review letters.

[53]  Ian K Robinson,et al.  Longitudinal coherence function in X-ray imaging of crystals. , 2009, Optics express.

[54]  V. Favre-Nicolin,et al.  Strain and shape of epitaxial InAs/InP nanowire superlattice measured by grazing incidence X-ray techniques. , 2007, Nano letters.

[55]  I. Robinson,et al.  Three-dimensional imaging of microstructure in Au nanocrystals. , 2003, Physical review letters.

[56]  Takashi Fukui,et al.  Control of InAs nanowire growth directions on Si. , 2008, Nano letters.

[57]  J. Miao,et al.  An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[58]  Frédéric Livet,et al.  Diffraction with a coherent X-ray beam: dynamics and imaging , 2007, Acta Crystallographica Section A: Foundations of Crystallography.