A multi-slice simulation algorithm for grazing-incidence small-angle X-ray scattering

S. V. Venkatakrishnan; Jeffrey Donatelli; Dinesh Kumar; Abhinav Sarje; Sunil K. Sinha; Xiaoye S. Li; Alexander Hexemer

doi:10.1107/S1600576716013273

A multi-slice simulation algorithm for grazing-incidence small-angle X-ray scattering

S. V. Venkatakrishnan, Jeffrey Donatelli, Dinesh Kumar, Abhinav Sarje, Sunil K. Sinha, Xiaoye S. Li, Alexander Hexemer

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

Grazing-incidence small-angle X-ray scattering (GISAXS) is an important technique in the characterization of samples at the nanometre scale. A key aspect of GISAXS data analysis is the accurate simulation of samples to match the measurement. The distorted-wave Born approximation (DWBA) is a widely used model for the simulation of GISAXS patterns. For certain classes of sample such as nanostructures embedded in thin films, where the electric field intensity variation is significant relative to the size of the structures, a multi-slice DWBA theory is more accurate than the conventional DWBA method. However, simulating complex structures in the multi-slice setting is challenging and the algorithms typically used are designed on a case-by-case basis depending on the structure to be simulated. In this paper, an accurate algorithm for GISAXS simulations based on the multi-slice DWBA theory is presented. In particular, fundamental properties of the Fourier transform have been utilized to develop an algorithm that accurately computes the average refractive index profile as a function of depth and the Fourier transform of the portion of the sample within a given slice, which are key quantities required for the multi-slice DWBA simulation. The results from this method are compared with the traditionally used approximations, demonstrating that the proposed algorithm can produce more accurate results. Furthermore, this algorithm is general with respect to the sample structure, and does not require any sample-specific approximations to perform the simulations. This paper presents an accurate numerical algorithm for simulating grazing-incidence small-angle X-ray scattering patterns of nanostructures using the multi-slice distorted-wave Born approximation. The method overcomes the typical challenge of requiring the users to manually specify a way to approximate their samples by utilizing properties of Fourier transforms to automate the computation.

Original language	English
Pages (from-to)	1876-1884
Number of pages	9
Journal	Journal of Applied Crystallography
Volume	49
Issue number	6
DOIs	https://doi.org/10.1107/S1600576716013273
State	Published - Dec 1 2016
Externally published	Yes

Funding

SVV and AH were supported by AH's Early Career Award from the US Department of Energy (DoE). The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, US DoE, under contract No. DE-AC02-05CH11231. This work was partially supported by the Center for Advanced Mathematics for Energy Research Applications (CAMERA). SKS's work at UCSD was supported by the Office of Basic Energy Sciences, US DoE, under grant No. DE-SC0003678. We thank Yi Yang and Jingjin Song, Department of Physics, University of California San Diego, for helpful discussions.

Funders	Funder number
Center for Advanced Mathematics for Energy Research Applications	DE-SC0003678
U.S. Department of Energy	DE-AC02-05CH11231
Office of Science
Basic Energy Sciences
University of California, San Diego

Keywords

GISAXS
distorted-wave Born approximation
grazing-incidence small-angle X-ray scattering
multi-slice algorithm

Access to Document

10.1107/S1600576716013273

Cite this

@article{d40ceab76db74dce87bd7af793ece8c4,

title = "A multi-slice simulation algorithm for grazing-incidence small-angle X-ray scattering",

abstract = "Grazing-incidence small-angle X-ray scattering (GISAXS) is an important technique in the characterization of samples at the nanometre scale. A key aspect of GISAXS data analysis is the accurate simulation of samples to match the measurement. The distorted-wave Born approximation (DWBA) is a widely used model for the simulation of GISAXS patterns. For certain classes of sample such as nanostructures embedded in thin films, where the electric field intensity variation is significant relative to the size of the structures, a multi-slice DWBA theory is more accurate than the conventional DWBA method. However, simulating complex structures in the multi-slice setting is challenging and the algorithms typically used are designed on a case-by-case basis depending on the structure to be simulated. In this paper, an accurate algorithm for GISAXS simulations based on the multi-slice DWBA theory is presented. In particular, fundamental properties of the Fourier transform have been utilized to develop an algorithm that accurately computes the average refractive index profile as a function of depth and the Fourier transform of the portion of the sample within a given slice, which are key quantities required for the multi-slice DWBA simulation. The results from this method are compared with the traditionally used approximations, demonstrating that the proposed algorithm can produce more accurate results. Furthermore, this algorithm is general with respect to the sample structure, and does not require any sample-specific approximations to perform the simulations. This paper presents an accurate numerical algorithm for simulating grazing-incidence small-angle X-ray scattering patterns of nanostructures using the multi-slice distorted-wave Born approximation. The method overcomes the typical challenge of requiring the users to manually specify a way to approximate their samples by utilizing properties of Fourier transforms to automate the computation.",

keywords = "GISAXS, distorted-wave Born approximation, grazing-incidence small-angle X-ray scattering, multi-slice algorithm",

author = "Venkatakrishnan, {S. V.} and Jeffrey Donatelli and Dinesh Kumar and Abhinav Sarje and Sinha, {Sunil K.} and Li, {Xiaoye S.} and Alexander Hexemer",

note = "Publisher Copyright: {\textcopyright} International Union of Crystallography, 2016.",

year = "2016",

month = dec,

day = "1",

doi = "10.1107/S1600576716013273",

language = "English",

volume = "49",

pages = "1876--1884",

journal = "Journal of Applied Crystallography",

issn = "0021-8898",

publisher = "International Union of Crystallography",

number = "6",

}

TY - JOUR

T1 - A multi-slice simulation algorithm for grazing-incidence small-angle X-ray scattering

AU - Venkatakrishnan, S. V.

AU - Donatelli, Jeffrey

AU - Kumar, Dinesh

AU - Sarje, Abhinav

AU - Sinha, Sunil K.

AU - Li, Xiaoye S.

AU - Hexemer, Alexander

N1 - Publisher Copyright: © International Union of Crystallography, 2016.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Grazing-incidence small-angle X-ray scattering (GISAXS) is an important technique in the characterization of samples at the nanometre scale. A key aspect of GISAXS data analysis is the accurate simulation of samples to match the measurement. The distorted-wave Born approximation (DWBA) is a widely used model for the simulation of GISAXS patterns. For certain classes of sample such as nanostructures embedded in thin films, where the electric field intensity variation is significant relative to the size of the structures, a multi-slice DWBA theory is more accurate than the conventional DWBA method. However, simulating complex structures in the multi-slice setting is challenging and the algorithms typically used are designed on a case-by-case basis depending on the structure to be simulated. In this paper, an accurate algorithm for GISAXS simulations based on the multi-slice DWBA theory is presented. In particular, fundamental properties of the Fourier transform have been utilized to develop an algorithm that accurately computes the average refractive index profile as a function of depth and the Fourier transform of the portion of the sample within a given slice, which are key quantities required for the multi-slice DWBA simulation. The results from this method are compared with the traditionally used approximations, demonstrating that the proposed algorithm can produce more accurate results. Furthermore, this algorithm is general with respect to the sample structure, and does not require any sample-specific approximations to perform the simulations. This paper presents an accurate numerical algorithm for simulating grazing-incidence small-angle X-ray scattering patterns of nanostructures using the multi-slice distorted-wave Born approximation. The method overcomes the typical challenge of requiring the users to manually specify a way to approximate their samples by utilizing properties of Fourier transforms to automate the computation.

AB - Grazing-incidence small-angle X-ray scattering (GISAXS) is an important technique in the characterization of samples at the nanometre scale. A key aspect of GISAXS data analysis is the accurate simulation of samples to match the measurement. The distorted-wave Born approximation (DWBA) is a widely used model for the simulation of GISAXS patterns. For certain classes of sample such as nanostructures embedded in thin films, where the electric field intensity variation is significant relative to the size of the structures, a multi-slice DWBA theory is more accurate than the conventional DWBA method. However, simulating complex structures in the multi-slice setting is challenging and the algorithms typically used are designed on a case-by-case basis depending on the structure to be simulated. In this paper, an accurate algorithm for GISAXS simulations based on the multi-slice DWBA theory is presented. In particular, fundamental properties of the Fourier transform have been utilized to develop an algorithm that accurately computes the average refractive index profile as a function of depth and the Fourier transform of the portion of the sample within a given slice, which are key quantities required for the multi-slice DWBA simulation. The results from this method are compared with the traditionally used approximations, demonstrating that the proposed algorithm can produce more accurate results. Furthermore, this algorithm is general with respect to the sample structure, and does not require any sample-specific approximations to perform the simulations. This paper presents an accurate numerical algorithm for simulating grazing-incidence small-angle X-ray scattering patterns of nanostructures using the multi-slice distorted-wave Born approximation. The method overcomes the typical challenge of requiring the users to manually specify a way to approximate their samples by utilizing properties of Fourier transforms to automate the computation.

KW - GISAXS

KW - distorted-wave Born approximation

KW - grazing-incidence small-angle X-ray scattering

KW - multi-slice algorithm

UR - http://www.scopus.com/inward/record.url?scp=84995511741&partnerID=8YFLogxK

U2 - 10.1107/S1600576716013273

DO - 10.1107/S1600576716013273

M3 - Article

AN - SCOPUS:84995511741

SN - 0021-8898

VL - 49

SP - 1876

EP - 1884

JO - Journal of Applied Crystallography

JF - Journal of Applied Crystallography

IS - 6

ER -

A multi-slice simulation algorithm for grazing-incidence small-angle X-ray scattering

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this