Multi-dimensional analysis of nano-scale periodic structures using EUV and X-RAY characterization: theoretical concepts and applications

Konstantin Nikolaev

Research output: ThesisPhD Thesis - Research UT, graduation UTAcademic

Abstract

The research described in this thesis concerns X-ray and Extreme UV characterization of periodic nanoscale structures. Advances in this analysis range from characterization of 1D systems, like multilayer short-wavelength mirrors, to nanoscale systems with a 2D or 3D, complex architecture. We have drastically improved the accuracy of the multilayer structure characterization by combining the analysis of X-ray reflectivity data and EUV normal-incidence reflectivity data, as compared to the traditional, sole use of X-ray analysis. This was done by using an uncertainty analysis based on the covariation matrix of the combined goodness of fit criterion for data taken at both wavelengths. It shows that the X-ray data primarily contribute to the accuracy of the layer and interface thicknesses, while the EUV data are more sensitive to the layer densities and atomic compositions.

Multilayer mirrors can have imperfections distributed in all three dimensions. In a W/Si multilayer system for instance, a 3D distribution of density fluctuations was observed in the Si layers. These fluctuations have been studied using grazing-incidence small-angle X-ray scattering. Assuming a 3D para-crystal-like fluctuation of the density distribution, the parameters reconstructed by numeric simulations were found to be in excellent agreement with independent observations by scanning transmission electron microscopy. Moreover, the density fluctuations were noted to affect the morphology of the interface roughness.

In subsequent theoretical research using grazing-incidence X-ray diffraction, the surface structure of monocrystals was further assessed. The structures were considered as 2D objects, assessed by probing the distribution of atoms in depth of the sample and in a chosen set of planes parallel to the surface. Using advances in the dynamical diffraction theory, we predicted an interesting effect: a signature of the off-plane diffraction can be observed by measuring the specular reflectivity. Another interesting aspect is that the intensity of the specular reflection is significantly higher than that of the diffracted beam. This may allow the characterization of the crystal surface,
the surface oxidation and the thin (epitaxial) layers, using a relatively moderate power, lab-scale
X-ray metrology tool as opposed to a synchrotron-based facility conventionally used for these purposes.

The dimensionality was also addressed in the X-ray standing wave technique. Although it allows the analysis of the atomic in-depth distribution of different species, information on the lateral direction is normally lost in this approach. We have derived equations based on the dynamical diffraction theory in a many-beam approximation, which allows the detailed analysis of the 3D atomic distribution in the structure. This has been verified on experimental data measured on a Si3N4 lamellar grating structure using an incident photon energy in the EUV range and on a 3D nano-column Cr structure in the hard X-ray range. The result of simulations using our mathematical model showed a good agreement with nominal structure parameters.

In conclusion, this thesis includes several analytical approaches to extend the scope of current X-ray and EUV analysis. This notably concerns the broadening of the dimensionality of the analysis of nano-scale devices and structures, and methods to arrive at an enhanced precision by combining data from different wavelength ranges.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • University of Twente
Supervisors/Advisors
  • Bijkerk, Fred, Supervisor
  • Makhotkin, Igor A., Co-Supervisor
Award date4 Jul 2019
Place of PublicationEnschede
Publisher
Print ISBNs978-90-365-4798-7
DOIs
Publication statusPublished - 4 Jul 2019

Fingerprint

dimensional analysis
x rays
theses
reflectance
grazing incidence
diffraction
wavelengths
mirrors
goodness of fit
specular reflection
crystal surfaces
standing waves
metrology
laminates
density distribution
mathematical models
synchrotrons
roughness
simulation
incidence

Cite this

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title = "Multi-dimensional analysis of nano-scale periodic structures using EUV and X-RAY characterization: theoretical concepts and applications",
abstract = "The research described in this thesis concerns X-ray and Extreme UV characterization of periodic nanoscale structures. Advances in this analysis range from characterization of 1D systems, like multilayer short-wavelength mirrors, to nanoscale systems with a 2D or 3D, complex architecture. We have drastically improved the accuracy of the multilayer structure characterization by combining the analysis of X-ray reflectivity data and EUV normal-incidence reflectivity data, as compared to the traditional, sole use of X-ray analysis. This was done by using an uncertainty analysis based on the covariation matrix of the combined goodness of fit criterion for data taken at both wavelengths. It shows that the X-ray data primarily contribute to the accuracy of the layer and interface thicknesses, while the EUV data are more sensitive to the layer densities and atomic compositions.Multilayer mirrors can have imperfections distributed in all three dimensions. In a W/Si multilayer system for instance, a 3D distribution of density fluctuations was observed in the Si layers. These fluctuations have been studied using grazing-incidence small-angle X-ray scattering. Assuming a 3D para-crystal-like fluctuation of the density distribution, the parameters reconstructed by numeric simulations were found to be in excellent agreement with independent observations by scanning transmission electron microscopy. Moreover, the density fluctuations were noted to affect the morphology of the interface roughness.In subsequent theoretical research using grazing-incidence X-ray diffraction, the surface structure of monocrystals was further assessed. The structures were considered as 2D objects, assessed by probing the distribution of atoms in depth of the sample and in a chosen set of planes parallel to the surface. Using advances in the dynamical diffraction theory, we predicted an interesting effect: a signature of the off-plane diffraction can be observed by measuring the specular reflectivity. Another interesting aspect is that the intensity of the specular reflection is significantly higher than that of the diffracted beam. This may allow the characterization of the crystal surface,the surface oxidation and the thin (epitaxial) layers, using a relatively moderate power, lab-scale X-ray metrology tool as opposed to a synchrotron-based facility conventionally used for these purposes.The dimensionality was also addressed in the X-ray standing wave technique. Although it allows the analysis of the atomic in-depth distribution of different species, information on the lateral direction is normally lost in this approach. We have derived equations based on the dynamical diffraction theory in a many-beam approximation, which allows the detailed analysis of the 3D atomic distribution in the structure. This has been verified on experimental data measured on a Si3N4 lamellar grating structure using an incident photon energy in the EUV range and on a 3D nano-column Cr structure in the hard X-ray range. The result of simulations using our mathematical model showed a good agreement with nominal structure parameters.In conclusion, this thesis includes several analytical approaches to extend the scope of current X-ray and EUV analysis. This notably concerns the broadening of the dimensionality of the analysis of nano-scale devices and structures, and methods to arrive at an enhanced precision by combining data from different wavelength ranges.",
author = "Konstantin Nikolaev",
year = "2019",
month = "7",
day = "4",
doi = "10.3990/1.9789036547987",
language = "English",
isbn = "978-90-365-4798-7",
publisher = "University of Twente",
address = "Netherlands",
school = "University of Twente",

}

Multi-dimensional analysis of nano-scale periodic structures using EUV and X-RAY characterization : theoretical concepts and applications. / Nikolaev, Konstantin .

Enschede : University of Twente, 2019. 130 p.

Research output: ThesisPhD Thesis - Research UT, graduation UTAcademic

TY - THES

T1 - Multi-dimensional analysis of nano-scale periodic structures using EUV and X-RAY characterization

T2 - theoretical concepts and applications

AU - Nikolaev, Konstantin

PY - 2019/7/4

Y1 - 2019/7/4

N2 - The research described in this thesis concerns X-ray and Extreme UV characterization of periodic nanoscale structures. Advances in this analysis range from characterization of 1D systems, like multilayer short-wavelength mirrors, to nanoscale systems with a 2D or 3D, complex architecture. We have drastically improved the accuracy of the multilayer structure characterization by combining the analysis of X-ray reflectivity data and EUV normal-incidence reflectivity data, as compared to the traditional, sole use of X-ray analysis. This was done by using an uncertainty analysis based on the covariation matrix of the combined goodness of fit criterion for data taken at both wavelengths. It shows that the X-ray data primarily contribute to the accuracy of the layer and interface thicknesses, while the EUV data are more sensitive to the layer densities and atomic compositions.Multilayer mirrors can have imperfections distributed in all three dimensions. In a W/Si multilayer system for instance, a 3D distribution of density fluctuations was observed in the Si layers. These fluctuations have been studied using grazing-incidence small-angle X-ray scattering. Assuming a 3D para-crystal-like fluctuation of the density distribution, the parameters reconstructed by numeric simulations were found to be in excellent agreement with independent observations by scanning transmission electron microscopy. Moreover, the density fluctuations were noted to affect the morphology of the interface roughness.In subsequent theoretical research using grazing-incidence X-ray diffraction, the surface structure of monocrystals was further assessed. The structures were considered as 2D objects, assessed by probing the distribution of atoms in depth of the sample and in a chosen set of planes parallel to the surface. Using advances in the dynamical diffraction theory, we predicted an interesting effect: a signature of the off-plane diffraction can be observed by measuring the specular reflectivity. Another interesting aspect is that the intensity of the specular reflection is significantly higher than that of the diffracted beam. This may allow the characterization of the crystal surface,the surface oxidation and the thin (epitaxial) layers, using a relatively moderate power, lab-scale X-ray metrology tool as opposed to a synchrotron-based facility conventionally used for these purposes.The dimensionality was also addressed in the X-ray standing wave technique. Although it allows the analysis of the atomic in-depth distribution of different species, information on the lateral direction is normally lost in this approach. We have derived equations based on the dynamical diffraction theory in a many-beam approximation, which allows the detailed analysis of the 3D atomic distribution in the structure. This has been verified on experimental data measured on a Si3N4 lamellar grating structure using an incident photon energy in the EUV range and on a 3D nano-column Cr structure in the hard X-ray range. The result of simulations using our mathematical model showed a good agreement with nominal structure parameters.In conclusion, this thesis includes several analytical approaches to extend the scope of current X-ray and EUV analysis. This notably concerns the broadening of the dimensionality of the analysis of nano-scale devices and structures, and methods to arrive at an enhanced precision by combining data from different wavelength ranges.

AB - The research described in this thesis concerns X-ray and Extreme UV characterization of periodic nanoscale structures. Advances in this analysis range from characterization of 1D systems, like multilayer short-wavelength mirrors, to nanoscale systems with a 2D or 3D, complex architecture. We have drastically improved the accuracy of the multilayer structure characterization by combining the analysis of X-ray reflectivity data and EUV normal-incidence reflectivity data, as compared to the traditional, sole use of X-ray analysis. This was done by using an uncertainty analysis based on the covariation matrix of the combined goodness of fit criterion for data taken at both wavelengths. It shows that the X-ray data primarily contribute to the accuracy of the layer and interface thicknesses, while the EUV data are more sensitive to the layer densities and atomic compositions.Multilayer mirrors can have imperfections distributed in all three dimensions. In a W/Si multilayer system for instance, a 3D distribution of density fluctuations was observed in the Si layers. These fluctuations have been studied using grazing-incidence small-angle X-ray scattering. Assuming a 3D para-crystal-like fluctuation of the density distribution, the parameters reconstructed by numeric simulations were found to be in excellent agreement with independent observations by scanning transmission electron microscopy. Moreover, the density fluctuations were noted to affect the morphology of the interface roughness.In subsequent theoretical research using grazing-incidence X-ray diffraction, the surface structure of monocrystals was further assessed. The structures were considered as 2D objects, assessed by probing the distribution of atoms in depth of the sample and in a chosen set of planes parallel to the surface. Using advances in the dynamical diffraction theory, we predicted an interesting effect: a signature of the off-plane diffraction can be observed by measuring the specular reflectivity. Another interesting aspect is that the intensity of the specular reflection is significantly higher than that of the diffracted beam. This may allow the characterization of the crystal surface,the surface oxidation and the thin (epitaxial) layers, using a relatively moderate power, lab-scale X-ray metrology tool as opposed to a synchrotron-based facility conventionally used for these purposes.The dimensionality was also addressed in the X-ray standing wave technique. Although it allows the analysis of the atomic in-depth distribution of different species, information on the lateral direction is normally lost in this approach. We have derived equations based on the dynamical diffraction theory in a many-beam approximation, which allows the detailed analysis of the 3D atomic distribution in the structure. This has been verified on experimental data measured on a Si3N4 lamellar grating structure using an incident photon energy in the EUV range and on a 3D nano-column Cr structure in the hard X-ray range. The result of simulations using our mathematical model showed a good agreement with nominal structure parameters.In conclusion, this thesis includes several analytical approaches to extend the scope of current X-ray and EUV analysis. This notably concerns the broadening of the dimensionality of the analysis of nano-scale devices and structures, and methods to arrive at an enhanced precision by combining data from different wavelength ranges.

U2 - 10.3990/1.9789036547987

DO - 10.3990/1.9789036547987

M3 - PhD Thesis - Research UT, graduation UT

SN - 978-90-365-4798-7

PB - University of Twente

CY - Enschede

ER -