Role of the strained substrate in the x-ray diffraction of free-standing epitaxial nanostructures under grazing incidence conditions

S. Lazarev, P. Schroth, D. Grigoriev, M. Riotte, T. Slobodskyy, A. A. Minkevich, D. Z. Hu, D. Schaadt, T. Baumbach

Research output: Contribution to journalArticle

Abstract

Semiconductor heteronanostructures are of interest for a vast field of applications in optoelectronics. Fast and reliable characterization of their structural properties is of high importance for industry and science. By the example of free-standing In0.6Ga0.4As quantum dots (QDs), we discuss the contributions of the strained epitaxial surface nanostructures and the substrate to the scattered x-ray intensity under grazing incidence conditions. In the frame of the distorted wave Born approximation, we take into account multiple scattering and coherent interactions of the x-ray beams involved in the diffraction process. Employing the finite-element method, we give a detailed analysis of the strain distribution inside the nanostructure and the substrate. Further, analyzing the experimental and simulated x-ray diffraction patterns in x-ray grazing incidence diffraction, we demonstrate the importance of accounting for strain in the substrate and interference effects between the surface and the QDs for strain analysis of the nano-objects. The advantages of our approach are demonstrated by comparison with the standard isostrain approach that is commonly used for strain analysis of the nanostructures. We show that neglecting the substrate contribution to the x-ray scattering causes errors in the standard isostrain approach. Finally, the substrate contribution itself may yield information sufficient for a novel and fast approach for the structural characterization of strained semiconductor heteronanostructures.

Original languageEnglish
Article number195432
JournalPhysical Review B
Volume99
Issue number19
DOIs
Publication statusPublished - 17 May 2019

Fingerprint

grazing incidence
Nanostructures
x ray diffraction
Diffraction
X rays
Substrates
Semiconductor quantum dots
quantum dots
Semiconductor materials
Born approximation
x rays
strain distribution
Multiple scattering
x ray scattering
diffraction
Optoelectronic devices
Diffraction patterns
Structural properties
finite element method
diffraction patterns

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Role of the strained substrate in the x-ray diffraction of free-standing epitaxial nanostructures under grazing incidence conditions. / Lazarev, S.; Schroth, P.; Grigoriev, D.; Riotte, M.; Slobodskyy, T.; Minkevich, A. A.; Hu, D. Z.; Schaadt, D.; Baumbach, T.

In: Physical Review B, Vol. 99, No. 19, 195432, 17.05.2019.

Research output: Contribution to journalArticle

Lazarev, S, Schroth, P, Grigoriev, D, Riotte, M, Slobodskyy, T, Minkevich, AA, Hu, DZ, Schaadt, D & Baumbach, T 2019, 'Role of the strained substrate in the x-ray diffraction of free-standing epitaxial nanostructures under grazing incidence conditions', Physical Review B, vol. 99, no. 19, 195432. https://doi.org/10.1103/PhysRevB.99.195432
Lazarev, S. ; Schroth, P. ; Grigoriev, D. ; Riotte, M. ; Slobodskyy, T. ; Minkevich, A. A. ; Hu, D. Z. ; Schaadt, D. ; Baumbach, T. / Role of the strained substrate in the x-ray diffraction of free-standing epitaxial nanostructures under grazing incidence conditions. In: Physical Review B. 2019 ; Vol. 99, No. 19.
@article{2aa7c6cf9e5b4f8d80e82a64b22caa80,
title = "Role of the strained substrate in the x-ray diffraction of free-standing epitaxial nanostructures under grazing incidence conditions",
abstract = "Semiconductor heteronanostructures are of interest for a vast field of applications in optoelectronics. Fast and reliable characterization of their structural properties is of high importance for industry and science. By the example of free-standing In0.6Ga0.4As quantum dots (QDs), we discuss the contributions of the strained epitaxial surface nanostructures and the substrate to the scattered x-ray intensity under grazing incidence conditions. In the frame of the distorted wave Born approximation, we take into account multiple scattering and coherent interactions of the x-ray beams involved in the diffraction process. Employing the finite-element method, we give a detailed analysis of the strain distribution inside the nanostructure and the substrate. Further, analyzing the experimental and simulated x-ray diffraction patterns in x-ray grazing incidence diffraction, we demonstrate the importance of accounting for strain in the substrate and interference effects between the surface and the QDs for strain analysis of the nano-objects. The advantages of our approach are demonstrated by comparison with the standard isostrain approach that is commonly used for strain analysis of the nanostructures. We show that neglecting the substrate contribution to the x-ray scattering causes errors in the standard isostrain approach. Finally, the substrate contribution itself may yield information sufficient for a novel and fast approach for the structural characterization of strained semiconductor heteronanostructures.",
author = "S. Lazarev and P. Schroth and D. Grigoriev and M. Riotte and T. Slobodskyy and Minkevich, {A. A.} and Hu, {D. Z.} and D. Schaadt and T. Baumbach",
year = "2019",
month = "5",
day = "17",
doi = "10.1103/PhysRevB.99.195432",
language = "English",
volume = "99",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "American Institute of Physics",
number = "19",

}

TY - JOUR

T1 - Role of the strained substrate in the x-ray diffraction of free-standing epitaxial nanostructures under grazing incidence conditions

AU - Lazarev, S.

AU - Schroth, P.

AU - Grigoriev, D.

AU - Riotte, M.

AU - Slobodskyy, T.

AU - Minkevich, A. A.

AU - Hu, D. Z.

AU - Schaadt, D.

AU - Baumbach, T.

PY - 2019/5/17

Y1 - 2019/5/17

N2 - Semiconductor heteronanostructures are of interest for a vast field of applications in optoelectronics. Fast and reliable characterization of their structural properties is of high importance for industry and science. By the example of free-standing In0.6Ga0.4As quantum dots (QDs), we discuss the contributions of the strained epitaxial surface nanostructures and the substrate to the scattered x-ray intensity under grazing incidence conditions. In the frame of the distorted wave Born approximation, we take into account multiple scattering and coherent interactions of the x-ray beams involved in the diffraction process. Employing the finite-element method, we give a detailed analysis of the strain distribution inside the nanostructure and the substrate. Further, analyzing the experimental and simulated x-ray diffraction patterns in x-ray grazing incidence diffraction, we demonstrate the importance of accounting for strain in the substrate and interference effects between the surface and the QDs for strain analysis of the nano-objects. The advantages of our approach are demonstrated by comparison with the standard isostrain approach that is commonly used for strain analysis of the nanostructures. We show that neglecting the substrate contribution to the x-ray scattering causes errors in the standard isostrain approach. Finally, the substrate contribution itself may yield information sufficient for a novel and fast approach for the structural characterization of strained semiconductor heteronanostructures.

AB - Semiconductor heteronanostructures are of interest for a vast field of applications in optoelectronics. Fast and reliable characterization of their structural properties is of high importance for industry and science. By the example of free-standing In0.6Ga0.4As quantum dots (QDs), we discuss the contributions of the strained epitaxial surface nanostructures and the substrate to the scattered x-ray intensity under grazing incidence conditions. In the frame of the distorted wave Born approximation, we take into account multiple scattering and coherent interactions of the x-ray beams involved in the diffraction process. Employing the finite-element method, we give a detailed analysis of the strain distribution inside the nanostructure and the substrate. Further, analyzing the experimental and simulated x-ray diffraction patterns in x-ray grazing incidence diffraction, we demonstrate the importance of accounting for strain in the substrate and interference effects between the surface and the QDs for strain analysis of the nano-objects. The advantages of our approach are demonstrated by comparison with the standard isostrain approach that is commonly used for strain analysis of the nanostructures. We show that neglecting the substrate contribution to the x-ray scattering causes errors in the standard isostrain approach. Finally, the substrate contribution itself may yield information sufficient for a novel and fast approach for the structural characterization of strained semiconductor heteronanostructures.

UR - http://www.scopus.com/inward/record.url?scp=85066403027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066403027&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.99.195432

DO - 10.1103/PhysRevB.99.195432

M3 - Article

VL - 99

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 19

M1 - 195432

ER -