Title\tnoteref{label1
Name\corref{cor1
A. Andrle
P. H\"{o
G. Gwalt
P.-I. Schneider
Y. Kayser
F. Siewert
F. Scholze
V. Soltwisch
The characterization of nanostructured surfaces with sensitivity in the sub-nm range is of high importance for the development of current and next generation integrated electronic circuits. Modern transistor architectures for e.g. FinFETs are realized by lithographic fabrication of complex, well ordered nanostructures. Recently, a novel characterization technique based on X-ray fluorescence measurements in grazing incidence geometry has been proposed for such applications. This technique uses the X-ray standing wave field, arising from an interference between incident and the reflected radiation, as a nanoscale sensor for the dimensional and compositional parameters of the nanostructure. The element sensitivity of the X-ray fluorescence technique allows for a reconstruction of the spatial element distribution using a finite-element method. Due to a high computational time, intelligent optimization methods employing machine learning algorithms are essential for a timely provision of results. Here, a sampling of the probability distributions by Bayesian optimization is not only fast, it also provides an initial estimate of the parameter uncertainties and sensitivities. The high sensitivity of the method requires a precise knowledge of the material parameters in the modeling of the dimensional shape provided that some physical properties of the material are known or determined beforehand. The unknown optical constants were extracted from an unstructured but otherwise identical layer system by means of soft X-ray reflectometry. The spatial distribution profiles of the different elements contained in the grating structure were compared to scanning electron and atomic force microscopy and the influence of carbon surface contamination on the modeling results were discussed. %were additionally used for an independent validation of the nanostructured surface reconstructed from the GIXRF measurements. %\textcolor{red{Remark: Abstract eventuell noch besser anpassen: Methode bereits eingeführt etc. %\textcolor{red{Der Abstract enthält keinen Hinweis auf den Aspekt mit der Kohlenstoffkontamination.
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\title{Shape- and element-sensitive reconstruction of periodic nanostructures with grazing incidence X-ray fluorescence analysis and machine learning}

%\title{GIXRF and machine learning as metrological tools for shape and element sensitive reconstructions of periodic nano devices}

%\title{GIXRF and machine learning as metrology instruments for shape and element sensitive reconstructions of periodic nanostructures}

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\author{A. Andrle}
\email{anna.andrle@ptb.de}
\affiliation{Physikalisch-Technische Bundesanstalt (PTB), 
Abbestr. 2-12, 10587 Berlin, Germany}

\author{P. H\"{o}nicke}
\affiliation{Physikalisch-Technische Bundesanstalt (PTB), 
Abbestr. 2-12, 10587 Berlin, Germany}

\author{G. Gwalt}
\affiliation{Helmholtz Zentrum Berlin für Materialien und Energie (HZB), Department Optics and Beamlines, Albert-Einstein-Str. 15, 12489 Berlin, Germany}

\author{P.-I. Schneider}
\affiliation{JCMwave GmbH, Bolivarallee 22, 14050 Berlin, Germany}
\affiliation{Zuse Institute Berlin, Takustrasse 7, 14195 Berlin, Germany}

\author{Y. Kayser}
\affiliation{Physikalisch-Technische Bundesanstalt (PTB), 
Abbestr. 2-12, 10587 Berlin, Germany}

\author{F. Siewert}
\affiliation{Helmholtz Zentrum Berlin für Materialien und Energie (HZB), Department Optics and Beamlines, Albert-Einstein-Str. 15, 12489 Berlin, Germany}

%\author{F. Scholze}
%\affiliation{Physikalisch-Technische Bundesanstalt (PTB), 
%Abbestr. 2-12, 10587 Berlin, Germany}

\author{V. Soltwisch}
\affiliation{Physikalisch-Technische Bundesanstalt (PTB), 
Abbestr. 2-12, 10587 Berlin, Germany}

\begin{abstract}
The characterization of nanostructured surfaces with sensitivity in the sub-nm range is of high importance for the development of current and next generation integrated electronic circuits. Modern transistor architectures for e.g. FinFETs are realized by lithographic fabrication of complex, well ordered nanostructures. Recently, a novel characterization technique based on X-ray fluorescence measurements in grazing incidence geometry has been proposed for such applications. This technique uses the X-ray standing wave field, arising from an interference between incident and the reflected radiation, as a nanoscale sensor for the dimensional and compositional parameters of the nanostructure. The element sensitivity of the X-ray fluorescence technique allows for a reconstruction of the spatial element distribution using a finite-element method. Due to a high computational time, intelligent optimization methods employing machine learning algorithms are essential for a timely provision of results. Here, a sampling of the probability distributions by Bayesian optimization is not only fast, it also provides an initial estimate of the parameter uncertainties and sensitivities. 
The high sensitivity of the method requires a precise knowledge of the material parameters in the modeling of the dimensional shape provided that some physical properties of the material are known or determined beforehand. The unknown optical constants were extracted from an unstructured but otherwise identical layer system by means of soft X-ray reflectometry. The spatial distribution profiles of the different elements contained in the grating structure were compared to scanning electron and atomic force microscopy and the influence of carbon surface contamination on the modeling results were discussed.
%were additionally used for an independent validation of the nanostructured surface reconstructed from the GIXRF measurements. 
%\textcolor{red}{Remark: Abstract eventuell noch besser anpassen: Methode bereits eingeführt etc.}
%\textcolor{red}{Der Abstract enthält keinen Hinweis auf den Aspekt mit der Kohlenstoffkontamination.}
\end{abstract}

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\section{Introduction}
Since nanotechnology and thus nanostructures of different kind are relevant in many areas of science and technology, metrology techniques that can support design, research and fabrication of such nanostructures are of high importance. Especially in the semiconductor industry, which is probably the most popular field of application for nanotechnology as well as a very strong driver for research in this field, complex 2D and 3D nanostructures with feature sizes in the single-digit nanometer regime~\cite{S.Natarajan2014,markov_limits_2014} are employed in order to keep Moore's law~\cite{more_1965} alive. The performance of these nanostructures crucially depends on a well-controlled fabrication, both in terms of targeted dimensional parameters and 3D element compositions (e.g. dopant distributions). Thus, there is a strong need for metrology techniques which allow to characterize these parameters with sufficient sensitivity~\cite{Orji_2018}.

Typical analytical or dimensional techniques used in this context are scanning and transmission electron microscopy (SEM, TEM)~\cite{raymond_sub-nanometer_2011,erni_atomic-resolution_2009}, atomic force microscopy (AFM)~\cite{ukraintsev_role_2005} and techniques that also address elemental distributions such as secondary ion mass spectroscopy (SIMS) ~\cite{Franquet_2016}, atom probe tomography (APT) ~\cite{vandervorst_dopantcarrier_2014} and energy-dispersive X-ray spectroscopy (EDX) combined with scanning electron microscopy (STEM)~\cite{mertens_vertically_2017}. All these techniques have different advantages and disadvantages regarding sample preparation and consumption, achievable spatial resolution, required duration and other experimental parameters (e.g.~tip sizes). Optical metrology based on light-matter interaction has a significant advantage in terms of measurement speed (with respect to slow techniques, e.g.~APT and STEM) and the ability to statistically measure large areas in contrast to scanning techniques. Optical reflectometry also known as optical critical dimension (OCD)~\cite{silver_fundamental_2007} metrology is still used and continuously improved despite the resolution limits that have been reached. In order to keep pace with shrinking structures, intensive research is being carried out to reduce the wavelength of the employed radiation and to increase the sensitivity via the dispersion of the periodic nanostructured surface. This is called deep ultraviolet (DUV) or extreme ultraviolet (EUV) scatterometry and can be extended into the X-ray spectral range. In X-ray scattering techniques, a distinction is made between measurements in transmission, also known as critical dimension small angle X-ray scattering (CDSAXS)~\cite{Sunday_2015}, and reflection mode known as grazing incidence small angle X-ray scattering (GISAXS)~\cite{levine_grazing-incidence_1989, renaud_probing_2009}. Both techniques have already shown that they allow for the dimensional reconstruction of nanostructures with an uncertainty in the sub-nm range~\cite{Soltwisch2017,FernandezHerrero2020}, but both require a special sample thinning or sample design, which limits the application possibilities~\cite{pfluger_extracting_2020}. Usually, these techniques also employ rather high photon energy X-rays, which limits the optical contrast between different materials within the investigated nanostructures.% A reduction of the photon energy into the soft X-ray spectral range is therefore a promising approach to limit the footprint and to increase the material sensitivity.\\

In this paper, we employ the grazing incidence X-ray fluorescence analysis (GIXRF)~\cite{D.K.G.DeBoer1995} method and soft X-rays ($<1$keV) instead to analyze the nanostructured surface. This non-destructive technique allows reconstructing the composition of the sample in terms of both their dimensional properties as well as the distribution of different elements, since the emitted X-ray fluorescence (XRF) is characteristic for each element. GIXRF uses the X-ray standing wave (XSW) field ~\cite{Bedzyk_1989,Golovchenko1982}, which results from the interference between the incident and the reflected X-ray beam as a nanoscale sensor. The intensity modulation inside the XSW field significantly influences the X-ray fluorescence intensity of an element depending on its spatial position within the electromagnetic field distribution. Recent studies have shown the potential of the GIXRF technique for the dimensional and compositional nanometrology of periodic 2D~\cite{V.Soltwisch2018} and 3D~\cite{Nikulaev2019,honicke_grazing_2020} nanostructures. 

In this work, we further develop this approach towards being a reliable metrology technique by employing a combined element sensitive reconstruction for the fluorescence signals of oxygen, nitrogen and in parts also carbon from within a silicon nitride grating structure. The integration of machine learning (ML) techniques, such as the Bayesian optimization~\cite{shahriari2016taking} algorithm based on Gaussian processes in combination with a finite-element Maxwell solver~\cite{schneider2019benchmarking} allows to control the computational modeling effort and to derive first estimates of the uncertainties of the parameterized nanostructure. For an even increased reliability, we are experimentally determining the optical constants of the employed materials instead of using tabulated data as these are often not realistic for nanolayers and nanostructures~\cite{zhang_thickness-dependence_2012}. Finally, we compare and validate the results against AFM and SEM cross sections. 

\section{Experimental}
As an example of two-dimensional nanostructures, a lithographically patterned silicon nitride grating on a silicon substrate was investigated. It was manufactured by means of electron beam lithography (EBL) at the Helmholtz-Zentrum Berlin. The nominal pitch of the grating is $p = 100$ $\si{\nm}$, the nominal height is $h = 90$ $\si{\nm}$ and the nominal line width of the sample is $w = 50$ $\si{\nm}$. 
%Further details about the fabrication of a similar grating can be found in ref.~\cite{V.Soltwisch2018}. 
For the manufacturing of the gratings, a silicon substrate with a 90 nm-thick Si$_3$N$_4$ layer was used. ZEP520A, a positive resist (organic
polymer), was spin coated on the substrate and developed with a Vistec EBPG5000+ e-beam writer, operated with an electron acceleration voltage of 100 kV. The grating was etched via reactive ion etching using CHF$_3$ and to remove the remaining resist an oxygen plasma treatment was applied.
A sketch of the cross-section is shown in Fig.~\ref{fig:fem_mesh} a). The total structured area of the grating was 1 mm x 15 mm and the sample area outside the patterned region consists of the originally deposited Si$_3$N$_4$ layer. Directly after fabrication, cross-section SEM images have been recorded on a sister sample.

We performed GIXRF and X-ray reflectometry (XRR) measurements in PTB's laboratory~\cite{B.Beckhoff2009c} at the BESSY II electron storage ring using the plane-grating monochromator (PGM) beamline~\cite{F.Senf1998} for undulator radiation. The sample was mounted in an ultrahigh-vacuum (UHV) measurement chamber~\cite{J.Lubeck2013}, where a 9-axis manipulator allows for an accurate sample alignment with respect to the direction of incident X-ray beam. The incidence angle $\theta$ is defined as the angle between the X-ray beam and the sample surface. The azimuthal angle $\varphi$ is defined as the angle between the incident beam and a plane, which is normal to the sample surface and parallel to the direction of the grating lines such that $\varphi = 0^{\circ}$ is defined as the orientation parallel to the plane of incidence. Both sample rotation axes can be aligned with an uncertainty below 0.01$^{\circ}$.

As we have employed radiometrically calibrated X-ray fluorescence (XRF) instrumentation, we can perform reference-free GIXRF~\cite{Hoenicke2019} and gain a quantitative access to the elemental mass depositions present on the sample~\cite{Beckhoff2008}. At each angular position for $\theta$ and $\varphi$, a fluorescence spectrum is recorded with a calibrated silicon drift detector (SDD)~\cite{F.Scholze2009} and the incident photon flux is monitored by means of a calibrated photodiode. The GIXRF-measurements were performed at an incident photon energy of $E_i = 680$ $\si{\eV}$, allowing for the excitation of N-K${\alpha}$ as well O-K${\alpha}$ fluorescence radiation, which mainly originates from the surface oxide layer on the grating structure. In Fig.~\ref{fig:GIXRF} the obtained and normalized N-K${\alpha}$ a) and O-K${\alpha}$ b) fluorescence intensities for different angles $\theta$ and $\varphi$ are shown.

In addition, we have performed XRR experiments on the non-structured Si$_3$N$_4$ layer next to the grating at the same photon energy ($E_i = 680$  $\si{\eV}$). From this we can determine the optical constants of the SiO$_2$ layers and the Si$_3$N$_4$ layer, which are expected to be more reliable in the soft X-ray spectral range than using only tabulated data as in~\cite{andrle_anisotropy_2020}.

For an independent validation of the dimensional GIXRF reconstruction results, additional AFM measurements were performed with an Nanosurf Nanite 25x25. The sample was measured under tapping mode condition and a standard pyramidal shaped silicon probe with a tip radius $<10$ $\si{\nm}$ was used, as it is commonly applied for the inspection of diffraction gratings~\cite{siewert_gratings_2018}. The AFM-probe is characterized by a resonance frequency of $190$ $\si{\Hz}$ and force constant of $48$~$\si{\N}/\si{\m}$. The inspected sample area was $500$x$500$~$\si{nm}^2$ in size covering about 5 grating lines. The height profile, obtained by averaging two in juxtaposition located AFM line profiles, is shown in Fig.~\ref{fig:AFM}.
\begin{figure*}[ht]
\centering
\includegraphics[width=0.85\textwidth]{pic/fancy_plot.png}
	\caption{a) Cross-section with the finite-element mesh-grid showing the layout used for the simulation. The height $h$, the width $w$, the sidewall angle $swa$, the oxide layer thicknesses in the groove $t_g$ and the on the grating line $t_t$ were optimized as independent parameters. The oxide layer on the substrate $t_s$ was kept constant during the optimization.  b) The calculated electric field strength inside and outside the structure is shown for $\theta = 1.2^{\circ}$ and $\varphi = 1.6^{\circ}$. For the nitrogen and oxygen fluorescence the electric field strength is integrated and the reabsorption is calculated with the distance y$_{dis}$ the photon has to travel to leave the structure.}
\label{fig:fem_mesh}
\end{figure*}

\section{Simulation and optimization of fluorescence intensities}
The GIXRF signals are directly related to the XSW field intensity distribution which, besides the incident photon energy and the incidence and azimuthal angles, depends on the shape and material composition of the illuminated nanostructured surface. To reconstruct these sample features from the experimental data, we applied a finite-element method (FEM) based forward calculation of the XSW and optimized the structural parameters to reproduce the experimental data. 

 In Fig.~\ref{fig:fem_mesh}, the basic principle of the FEM procedure is shown. The mesh grid and the model parameters are displayed in Fig.~\ref{fig:fem_mesh} a). The FEM solver calculates the electric near-field for a given structure (Fig.~\ref{fig:fem_mesh} b)). The amount of fluorescence photons generated at a given coordinate depends on the local electric near-field intensity ($E(x,y)$) and the compositional and fundamental parameters of the respective material (mass fraction of the fluorescent element in the material $W_k$, photo-ionization cross section for the incident photon energy $\tau(E_i)$ and the fluorescence yield $\omega_k$, taken from databases~\cite{T.Schoonjans2011} or dedicated experiments~\cite{P.Hoenicke2016a}). These photons can be reabsorbed on the path through the sample towards the detector (Fig.~\ref{fig:fem_mesh} b)) with a probability depending on the materials mass attenuation coefficient $\mu(E_f)$ for the fluorescence photon energy $E_f$, the density $\rho$ of the material and the distance to the surface of the nanostructure $y_{dis}(x,y)$. Eventually, the fluorescence photon will be detected with a given detection efficiency $\epsilon(E_f)$ if it is arriving within the effective solid angle of detection $\Omega$. The overall emitted fluorescence intensity of course also depends on the incident photon flux $N_0$. 
  
Thus, the measured emitted fluorescence intensity $\Phi(\theta,\varphi,E_i)$ (derived from the detected count rate $F(\theta,\varphi,E_i)$) can be modeled using the integration over the full area of the fluorescent material of the nanostructure as described by the modified Sherman equation~\cite{V.Soltwisch2018, honicke_grazing_2020}:

\begin{widetext}
\begin{equation}
\Phi(\theta,\varphi,E_i) = \underbrace{ \frac{4\pi\sin\theta}{\Omega}\frac{F(\theta,\varphi,E_i)}{N_0\epsilon(E_f)} }_{\substack{I_{exp}}}= \underbrace{\frac{W_k \rho \tau(E_i) \omega_k }{\sum dx} \cdot \sum_{x}\sum_{y}  |E(x,y)|^2 \cdot \exp\left[-\rho\mu(E_f)y_{dis}(x,y)\right] dx dy}_{\substack{I_{model}}}\textrm{.} 
\label{eq:2Dsherman}
\end{equation}
\end{widetext}

The equation~\ref{eq:2Dsherman} is applied for nitrogen and oxygen fluorescence and has been implemented directly in the Maxwell solver to eliminate errors due to conversion to a regular cartesian grid. The calculated emitted fluorescence intensities $I_{model}$ are then compared against the experimental value $I_{exp}$. By using a global optimization algorithm such as Bayesian optimization (BO)~\cite{shahriari2016taking,schneider2019benchmarking}, an optimal set of the model parameters can then be determined. BO uses a stochastic model, a Gaussian process, of an unknown objective function to be minimized in order to determine promising parameter values~\cite{shahriari2016taking,Garcia-Santiago2018}. In a previous work~\cite{schneider2019benchmarking, Andrle_2019}, it was shown that the BO performs much better than other meta-heuristic optimization approaches with respect to the computing time needed to find the global minimum. Since BO considers all previous function evaluations, it can be more efficient than other meta-heuristic global optimization strategies~\cite{schneider2019benchmarking} and local optimization strategies~\cite{schneider2019using}. This is a crucial benefit here, as one model calculation takes several minutes on a standard desktop computer. Here, we use an implementation of BO which is part of the JCMsuite software package~\cite{jcm_web:accuracy_2020}.

The error function $\chi^2$ 
\begin{equation}
\chi^2(\vec{gp}) = \sum_{\theta,\varphi}{\frac{(I_{exp}(\theta,\varphi) - I_{model}(\vec{gp},\theta,\varphi))^2 }{\sigma_N^2(\theta,\varphi)}}
\label{eq:chi}
\end{equation}
was minimized with respect to the different model parameters of $\vec{gp}$ described earlier (see Fig.~\ref{fig:fem_mesh}~a)) and model errors for the nitrogen $\epsilon_N$ and the oxygen fluorescence signals $\epsilon_O$). These model error parameters are introduced to consider potential errors e.g.~the uncertainty of the employed atomic fundamental parameters or the influence of a thin surface contamination layer into account. Even though material dependent parameters like optical constants or material densities deviate most likely from the tabulated bulk data for the grating materials (SiO$_2$ and Si$_3$N$_4$), we do not include these as free parameters in the model. Indeed, as this would drastically increase the number of model parameters and thus prolong the necessary calculation times, we rather determine these parameters separately by XRR (described in the next section). 
$\sigma_N$ is the calculated experimental error consisting of an error estimation for the effective solid angle of detection $\sigma_{\Omega}(\theta)$, the error contributions originating from counting statistics $\frac{\sqrt{F}}{F}$ for the respective fluorescence line as well as for the spectra deconvolution $\sigma_{num}$.
\begin{equation}
\sigma_N(\theta)^2 = \left( \frac{\sqrt{F(\theta)}}{F(\theta)} \right)^2 + \sigma_{\Omega}(\theta)^2  + \sigma_{num}(\theta)^2 %+ ...
\end{equation}
%The calculated relative error is $\max(\sigma_N(\theta)) = 2.2\%$.

By inverting the Hessian matrix ${\bf H}_{k j}$~\cite{henn_maximum_2012} of the error function,
\begin{equation}
{\bf H}_{k j} = \frac{\partial^2 \chi^2(\vec{gp})}{\partial gp_j \partial gp_k} 
\end{equation}
at the minimum of $\chi^2$ it is possible to determine the confidence intervals $\left(\bf H\right)^{-1}$ of the model parameters, if they are gaussian distributed as assumed.
%\begin{equation}
% {\bf C} = \left(\bf H\right)^{-1}
%\label{eq:Cov}
%\end{equation}

The standard deviation or noise level at the global minimum parameter set is defined as ${\rm STD} = \sqrt{\frac{\chi^2}{\rm DOF}}$, where ${\rm DOF} = N-M$ is the difference between the number of measurement points $N$ and the number of free model parameters $M$ and thus the degrees of freedom. 

The model parameter confidence interval can then be calculated by
\begin{equation}
 \sigma_{\vec{gp}} = {\rm STD}\sqrt{{\rm diag}(\bf \left(\bf H\right)^{-1})}
\label{eq:STD}
\end{equation}

Based on the Gaussian process model of $\chi^2(\vec{gp})$ we determine an estimate of the Hessian matrix by computing all second derivatives of the Gaussian process model of $\chi^2$ at the minimum and can then estimate the error covariance matrix $\left(\bf H\right)^{-1}$ and the parameter confidence interval. 

\section{Results and Discussion}
\subsection{Validation of the optical material parameters}
From the angle-dependent measurement of reflection intensities on a layered system, information about layer thicknesses, densities or even their optical constants can be obtained~\cite{chason_thin_1997}. %,windt_imdsoftware_1998,vignaud_reflex_2019}. 
%The XRR measurements were obtained with a photon energy of $E_i = 680$  $\si{\eV}$ on the Si$_3$N$_4$ layer next to the structured part of the sample. The use of the photon energy identical to that of the GIXRF experiments allows an independent referencing of the optical material parameters. 
Fig.~\ref{fig:corner_XRR} b) shows the experimental data in comparison with the best simulation. The high frequency oscillation visible in the XRR curve, is a clear indication for a multi-layer system. Due to the native oxide layer of the Si substrate and the removal of the photo resist, resulting in an oxidized surface on the Si$_3$N$_4$ layer~\cite{kennedy_oxidation_1999}, we apply a three layer model for the XRR simulation (as shown in the inset of Fig.~\ref{fig:corner_XRR} a)). Since the calculation of the reflectivity for a 1D layer system is several orders of magnitude faster than the FEM based 2D GIXRF modeling, statistical analysis methods of the posterior distributions can be used for a large number of parameters such as layer thickness, roughness and optical constants. We applied the Markow Chain Monte Carlo method (MCMC)~\cite{emcee} to determine the individual parameter uncertainties and to resolve possible inter parameter correlation effects~\cite{Haase2016}. In Fig.~\ref{fig:corner_XRR} a) the posterior distribution determined in this procedure is shown as projections of the refractive index $n(Si_{3}N_{4}) = 1-\delta+i\beta$ and thickness $h$ of the $Si_{3}N_{4}$ layer. The almost perfect gaussian-like shape of the distributions, which is also present in all other parameters, allows the determination of uncertainties directly from the measurements. The relative uncertainties of the experimental data reconstructed with a linear error model ($ax+b$)~\cite{henn_maximum_2012} are with $(0.6\pm 0.2)\%$ exactly in the expected range.

From this modeling we derived optical constants for the top $SiO_2$ ($\delta$ = $(8.73 \pm 0.03) 10^{-4}$, $\beta$ = $(2.58 \pm 0.04) 10^{-4}$) and the $Si_3N_4$ ($\delta$ = $(12.59 \pm 0.05) 10^{-4}$, $\beta$ = $(2.58 \pm 0.02) 10^{-4}$) layers. By comparing the experimentally determined optical constants with tabulated Henke data~\cite{henke_x-ray_1993}, one can estimate the densities of the respective materials and their deviation from the respective bulk densities. For $Si_3N_4$, a relative density of $(0.89 \pm 0.01)$ and for $SiO_2$ a relative density of $(0.79 \pm 0.01)$ was found. This is in line with the already observed material density reduction discussed in Ref.~\cite{V.Soltwisch2018}. The reduced densities as well as the experimental optical constants are used for the GIXRF reconstruction.

\begin{figure}[ht]
\centering
\includegraphics[width=0.45\textwidth]{pic/paperplot_XRR_MCMC.pdf}
	\caption{a) The posterior distributions for relevant parameters $\delta_{Si_3N_4}$, $\beta_{Si_3N_4}$ and the $Si_3N_4$ thickness $h$ obtained from the MCMC sampling. The red line marks the mean of the distribution and the dotted black lines in the histogram indicates a 3$\sigma$ interval. In the top right corner, a sketch of the used layer stack is shown.\\
	b) Comparison of the experimental data (black stars) and the model calculation (red line) as obtained by the MCMC.}
\label{fig:corner_XRR}
\end{figure}

%\begin{table}
%\caption{Comparison of the optical constants obtained from MCMC to values from the Henke database \cite{henke_x-ray_1993} for a reduced density.}
%\textcolor{red}{Die Tabelle muss auch im Text diskutiert werden, aber brauchen wir die überhaupt? Die Schichtdicken sind nur bedingt vergleichbar wegen der Waferuniformity. Da verwirren wir den Leser nur unnötig. Das Fehlermodel wird vorher nirgendwo erklärt und warum sind die Fehlerparameter so unterschiedlich? Die optischen Konstanten kann man zeigen denk ich, da es um die ja hier geht... Aber bitte wieso passen die auf einmal zu Henke??? Dann fehlt auch noch ein Kommentar zur Dichte die jetzt letzten endes genommen wird und wie die bestimmt wurde... War das nicht 0.8 x bulk?}}
%\begin{tabular}{c|c}
%parameter& fitparameter \\ 
%\hline
%$t_t$&  $4.25 \pm 0.02$ $\si{\nm}$\\
%$h$ &  $93.1 \pm 0.1$ $\si{\nm}$\\
%$t_s$ & $1.3 \pm 0.2$ $\si{\nm}$ \\
%rough 1 & $0.666 \pm 0.007$ $\si{\nm}$ \\
%rough 2 & $0.31 \pm 0.06$ $\si{\nm}$\\
%rough 3 & $0.67 \pm 0.05$ $\si{\nm}$ \\
%$a$ & $(0.6 \pm 0.2)e-2$  \\

%$b$ & $(6.6 \pm 0.7)e-6$  \\

%\end{tabular}%
%\begin{tabular}{c|c|c}
%parameter& Fit & Henke \\ 
%\hline
%$\delta_{SiO_2}$ & $(8.73 \pm 0.03)e-4$ & $8.59e-4$   \\
%$\beta_{SiO_2}$ & $(2.58 \pm 0.04)e-4$ & $2.62e-4$ \\
%$\delta_{Si_3N_4}$ & $(12.59 \pm 0.05)e-4$ & $12.36e-4$  \\
%$\beta_{Si_3N_4}$ & $(2.58 \pm 0.02)e-4$ & $2.61e-4$\\
%\end{tabular}
%\label{tab:results_XRR}
%\end{table}


\subsection{GIXRF reconstruction results}
\subsubsection{Virtual Experiment}
Before we apply the reconstruction model to real experimental data, we apply it to an artificial dataset in order to test the reconstruction method and to study, whether an increased incident photon energy, capable of exciting also oxygen fluorescence signal, is beneficial. In our previous study~\cite{V.Soltwisch2018}, measurement data at $E_i = 520$~$\si{\eV}$ was analyzed and an indirect sensitivity to the surface oxide layer was found even though no fluorescence signal originating from it was used for the reconstruction. The indirect sensitivity was merely due to the attenuation behavior of the oxide layer and thus, we expect an increased sensitivity if also a direct signal originating from it is used. For this purpose, 
%As stated before, the calculation of the fluorescence intensity with the FEM Maxwell-solver is orders of magnitude more time consuming than calculating the reflectivity, therefore MCMC is not feasible here. In ~\cite{Andrle_2019, schneider2019benchmarking, schneider2019using} it was shown that the BO reaches good results with less steps and in less time. Additionally it is possible to calculate the error covariance matrix at the minimum of $\chi^2$. 
we generate artificial experimental data by calculating model curves using the reconstruction model for a given set of parameters  and the two incident photon energies of $E_i = 680$~$\si{\eV}$ and $E_i = 520$~$\si{\eV}$. To mimic experimental noise, we apply a Gaussian disturbance with a width of 3\% (see  Tab.~\ref{tab:results_GIXRF_sim}). 
By reconstructing the artificial datasets, we can now analyze the influence of the increased incident photon energy on the reconstruction results and their confidence intervals without the influence of any experimental error contributions.
%Additionally we can verify the error calculation, because the error of the artificial data was chosen to be bigger than the experimental error of the measurement data. \textcolor{red}{Inwiefern lernt man etwas über die Fehlerrechnung bzw. Modellierungsfehlerabschätzung wenn man Datensätze mit unterschiedlichen Unsicherheiten modelliert? versteh ich nich - für den Fit hab ich ein error von 5\% angenommen, die daten habe ich aber nür mit 3\% gestört}
In Fig.~\ref{fig:GIXRF_simu} the corresponding artificial GIXRF curves and reconstruction results are displayed. They match the artificial data well for both photon energies and characteristic features, e.g. the first local maxima are very well retrieved. From the BO reconstruction, we are able to calculate the confidence intervals of the reconstructed parameters and, as shown in Tab.~\ref{tab:results_GIXRF_sim}, they agree well with the initial parameters within the derived confidence interval.

From a comparison of the determined confidence intervals for the two different configurations (Configuration A, $E_i = 520$~$\si{\eV}$, only the nitrogen signal is modeled and Configuration B, $E_i = 680$~$\si{\eV}$, both nitrogen and oxygen signals are modeled, see Tab.~\ref{tab:results_GIXRF_sim}), the positive influence of also considering the oxygen fluorescence signal is obvious. Especially for the height and the groove oxide thickness, the achieved confidence intervals are significantly smaller for configuration B. Nevertheless, also for configuration A, the angle-dependent nitrogen fluorescence contains all relevant information about the dimensional properties of the nanostructure and even the surface oxide layer, as already pointed out in our earlier work~\cite{V.Soltwisch2018}.  

\begin{table}
\caption{The values of the geometrical parameters of the synthetic data from the GIXRF BO reconstruction with the model parameter confidence intervals for $E_i = 520$~$\si{\eV}$ (Configuration A, only the nitrogen signal is modeled) and $E_i = 680$~$\si{\eV}$ (Configuration B, both nitrogen and oxygen signals are modeled). The pitch was set to $p = 50$~$\si{\nm}$. (height $h$, width $w$, sidewall angle $swa$, oxide layer in the groove $t_g$ and oxide layer on the grating line $t_t$)}
\begin{tabular}{c|c|c|c|c}
Parameter& Intial & \multicolumn{2}{c}{Config.} & Conf. Interval  \\ 
Name & Value& A & B & Ratio $\frac{B}{A}$\\%\hline
%$h/\si{\nm}$  & $90$ &   $89.4(5)$   & $89.5(7)$  \\
%$w/\si{\nm}$   &   $50$ &   $49.87(8)$    & $50.1(1)$  \\
%$swa/^{\circ}$  &  $83$ &    $82.9(2)$      & $83.0(1)$ \\
%$t_t/\si{\nm}$ &    $2.5$&    $2.48(7)$     & $2.52(3)$   \\
%$t_g/\si{\nm}$ &$5$&      $4.8(4)$       & $5.0(1)$   \\
%$\epsilon_N$      &$0.95$&     $0.95(1)$             & $0.949(8)$  \\
%$\epsilon_O$      &$1.05$&     -   & $1.05(1)$ \\
\hline
$h/\si{\nm}$  & $90$ &   $89.4(6)$   & $90.3(4)$  & 0.67\\
$w/\si{\nm}$   &   $25$ &   $24.87(7)$    & $25.08(6)$ & 0.85 \\
$swa/^{\circ}$  &  $88$ &    $88.1(1)$      & $87.9(1)$ & 1.0\\
$t_t/\si{\nm}$ &    $3$&    $3.13(6)$     & $3.02(5)$  & 0.83 \\
$t_g/\si{\nm}$ &$5$&      $5.3(6)$       & $5.0(1)$  & 0.17 \\
$\epsilon_N$      &$1$&     $1.02(1)$      & $1.00(1)$ & 1\\
$\epsilon_O$      &$1$&     -             & $0.99(1)$&  
    
\label{tab:results_GIXRF_sim}
\end{tabular}
\end{table}

\subsubsection{Real experimental data}
%As noted before, we are using the optical constant data and densities as derived from the XRR modeling for the FEM based reconstruction in order to reduce the degrees of freedom and thus the necessary computation effort. 

Using the same model and methodologies, also the real experimental data, measured according to configuration B, was modeled. A  comparison of the two experimental datasets and the resulting modeled data is shown in Fig.~\ref{fig:GIXRF}. The corresponding optimal parameters and confidence intervals are summarized in Tab.~\ref{tab:results_GIXRF}. Again, the confidence intervals of the structure parameters derived from the BO posterior distribution are very similar to those determined in the virtual experiment.

%\textcolor{red}{Sollten wir vereinheitlichen: modeling error zu confidence interval da sonst verwirrend mit $\epsilon_N$}
Similarly as already for the virtual experiment, a higher sensitivity for the line width is observed as compared to the height. This is expected to be a result of the relatively large line height with respect to the achieveable information depth in the soft X-ray regime. Thus, the nitrogen fluorescence radiation from the very bottom of the grating line does not contribute significantly to the overall observed signal. Nevertheless all calculated confidence intervals are in the sub-nm regime.

It should also be noted that the two modeling error parameters $\epsilon_N$ and $\epsilon_O$ deviate from unity within a range of 10~\%. This is the same magnitude one would expect the relative uncertainty of the employed fluorescence production cross sections (product of fluorescence yield and photo ionization cross section) to be in.

%\textcolor{red}{streichen? - To compare the calculated error with a statistical error we measured the GIXRF profile at $\varphi=0^{\circ}$ at the same sample position ten times and applied the reconstruction for every single measurement. We calculated the standard deviation of all fitting parameters and compared them to the errors. We found that the standard deviation is in the similar regime as the calculated errors. Therefore the calculated error seems to indicate the statistical error of the reconstruction.} 
Systematic errors not taken into account may increase the final uncertainties. This problem is often called model error and refers to the whole physical model or virtual experiment that is applied and is not limited to the finite element model. The next section shows that these modeling uncertainties can have a significant impact on the reconstruction parameters. 
\begin{table}
\caption{The values of the geometrical parameters of the nanostructures from the GIXRF BO reconstruction with the model parameter confidence intervals (one sigma). The parameters are height $h$, width $w$, sidewall angle $swa$, oxide layer in the groove $t_g$ and oxide layer on the grating line $t_t$.
}

\begin{tabular}{c|c}
Parameter& Reconstructed   \\ 
Name & Value\\
\hline
$h/\si{\nm}$    & $97.5(5)$     \\
$w/\si{\nm}$    & $49.77(7)$     \\
$swa/^{\circ}$  & $83.54(9)$    \\
$t_t/\si{\nm}$  & $2.84(3)$      \\
$t_g/\si{\nm}$  & $5.82(9)$       \\
$\epsilon_N$       & $0.918(6)$     \\
$\epsilon_O$       & $1.059(7)$    

    
\label{tab:results_GIXRF}
\end{tabular}
\end{table}
\begin{figure}[tbp]
\centering
\includegraphics[width=0.49\textwidth]{pic/paperplot_GIXRF_simulation_all.pdf}
	\caption{Comparison of the expected artificial disturbed simulated N-K$\alpha$ (green points) or O-K$\alpha$ (blue points) fluorescence intensities for the different excitation energies and the corresponding BO reconstruction. Clearly visible is how the first peak in the nitrogen signal shifts with increasing energy to smaller incident angles.}
\label{fig:GIXRF_simu}
\end{figure}

\begin{figure}[tbp]
\centering
\includegraphics[width=0.45\textwidth]{pic/allefits_edit_01.pdf}
	\caption{Comparison of the measured and simulated fluorescence maps for N-K a) and O-K b) based on the reconstructed parameter set.  
	c) Comparison of the experimental N-K$\alpha$ (green) or O-K$\alpha$ (blue points) fluorescence intensities for $\varphi = 0^\circ$ to the reconstructions from the Bayesian optimization (red lines).}
\label{fig:GIXRF}
\end{figure}

\subsubsection{Contamination}
In addition to oxygen and nitrogen signals in the fluorescence spectra, also carbon fluorescence was observed. A presence of carbon on the sample surface is likely as the sample is stored under normal ambient conditions. A lateral scan of the sample (Fig.~\ref{fig:GIXRF_PrX} a)) at a fixed incident angle $\theta = 15^{\circ}$ reveals that this carbonaceous contamination is not homogeneously distributed over the patterned area. In the center of the grating area ($x=-0.15$~$\si{\mm}$) a strong increase of the carbon signal and a slight increase of the oxygen signal  can be observed, whereas the nitrogen signal is practically constant.
In an earlier benchmark study, the sample under investigation was measured in various scatterometers and electron microscopes around the world. A punctual contamination of the grating surface by these techniques can therefore not be excluded. Here, we take advantage of this artificially created contamination layer to demonstrate the sensitivity and the influence of model errors.

At each lateral position shown in the figure, we performed a GIXRF angular scan (at $\varphi$ = 0$^\circ$) and performed the reconstruction including the confidence interval calculation without considering any contamination. 
Fig.~\ref{fig:GIXRF_PrX}~b) shows the obtained differences between the reconstructed model parameters at each position to the reference position at $x=0$  $\si{\mm}$ (position where the data shown in Fig.~\ref{fig:GIXRF} was taken). The model parameters at $-0.15$~$\si{\mm}$, which is the position with maximal carbon and oxygen contamination, differ clearly with respect to less contaminated areas. The difference is larger than the calculated confidence intervals from the reconstruction and they are also much larger than the expected lateral inhomogeneities of the sample. In addition, the nearly constant nitrogen fluorescence signal in X-direction clearly indicates a homogeneous overall amount of $Si_3N_4$, which is in contradiction to the larger cross-sectional area of the grating determined by the reconstruction from the GIXRF model. The reconstructed heights and widths increase by more than $4$~$\si{\nm}$. 

This behavior can be explained considering the XSW near field distribution inside the grooves: The slight increase of the oxygen due to the contamination signal can only be incorporated by increasing the oxide layer thicknesses. However, an increase of the oxide layer thickness weakens the penetrating field inside the $Si_3N_4$ and thus the emitted nitrogen fluorescence. To compensate for this, a larger grating cross section is reconstructed. One may think, that the reconstruction algorithm could circumvent this by simply increasing only the groove oxide layer thickness, which does not affect the nitrogen signal so much. But as shown in part c) of the figure, where the angular oxygen fluorescence signal contributions from the different parts in the structure model are shown, the groove oxide has a significantly different angular behavior as compared to the oxide on the grating line surface. Especially the features at about $1^\circ$ and $2.7^\circ$ are very distinct. For this reason, the reconstruction algorithm must increase both in order to account for the higher oxygen signal in the contaminated area throughout the angular range.

This shows how sensitive the GIXRF method is, but also how carefully the models have to be developed for a realistic uncertainty estimation. However, even if the model is not accurate enough, a spacial resolved reconstruction can reveal flaws of the model.


%\textcolor{red}{rewritten, can be removed - A weakening of the penetrating field by the contamination can only be achieved within the framework of the geometrical model by increasing the etching depth (or line height) and reducing the grooves width. Interesting is also the observation that the optimization process increases the SiO$_2$ layer thickness in the grooves much more compared to the SiO$_2$ layer thickness on the line structure. This behavior can be explained by considering the possible oxygen containing domains of the FEM model individually in their GIXRF intensities. This is shown in Fig.~\ref{fig:GIXRF_PrX} c). The O-K$\alpha$ emission from the line (violet line) is dominated by the XSW which cause strong modulations with increasing incidence angle. The groove signal (green line) is dominated by a large peak around the critical angle of total external reflection and has no sensitivity for the line shape. It is similar to a fluorescent signal what one would expect from a pure layer system. This leads to results with significant deviation from the nominal values, which do not match even within the scope of the uncertainties. The line shape model error thus becomes the leading error in the uncertainty calculation. This shows how sensitive the GIXRF method is, but also how carefully the models have to be developed for a realistic uncertainty estimation. A determination of the model errors or the development of a suitable error model which can be included in the BO optimization need to be investigated in future studies.}

\begin{figure}[tbp]
\centering
\includegraphics[width=0.45\textwidth]{pic/paperplot_carbon.pdf}
	\caption{a) Here the C-K$\alpha$, N-K$\alpha$ and O-K$\alpha$ fluorescence intensity at $\theta=15^\circ$ where no XSW needs to be considered from different positions on the sample are compared. \\
	b) The reconstruction results for the width, the height, the thickness of the oxide in the groove and the thickness of oxide around the line  for the different position are plotted. \\
	c) The various contributions from the oxide from the line, the groove and the oxide layer of the silicon wafer to the total oxygen fluorescence are compared.
	}
\label{fig:GIXRF_PrX}
\end{figure}

\subsection{Comparison with SEM and AFM}
For a validation of the dimensional and compositional parameters as derived from the GIXRF modeling without the thick carbon contamination, we have performed AFM measurements on the sample and use also SEM (on a witness sample). As AFM is an established method to map the surface topology of nanostructures with sensitivities down to the $\si{\nm}$ regime, we can use an AFM to verify the GIXRF reconstructed total line heights (difference between top surface and groove surface). From the AFM data, we determined a total line height of $98.4$~$\si{\nm}$. This is consistent with the GIXRF reconstructions within the uncertainties. Here, it should be noted that the AFM measurement is only representative for the small area of the grating where it was performed whereas the GIXRF result is averaged over a much larger area due to the elongated beam footprint. Due to the interplay of the tip shape with the nanostructure, other dimensional parameters as e.g.~line width or sidewall angle are not straightforward to be deduced~\cite{doi:10.1063/1.111578}.  

In Fig.~\ref{fig:AFM} the GIXRF-reconstructed shape of the sample as well as the AFM profile is overlayed onto the SEM cross section. Therefore the GIXRF line profile and the AFM were scaled to the SEM image in order to match the line pitch while keeping the aspect ratios constant. Also here, the agreement with respect to line height, sidewall angle, line width and even the oxide layer thicknesses (assuming the bright areas in the SEM to be the oxide) is very good. The reconstructed thicker groove oxide can also be seen in the SEM picture. 


\begin{figure}[tbp]
\centering
\includegraphics[width=0.45\textwidth]{pic/SEM_vergleich_04.png}
	\caption{Comparison of the AFM data with the result of the GIXRF reconstruction and a SEM picture from a witness sample.}
\label{fig:AFM}
\end{figure}


%%%% LESEMARKE Philipp %%%%

\section{Conclusion}
Here, we have demonstrated how the GIXRF based methodology for a dimensional and compositional characterization of regular nanostructures can be enhanced with respect to the achieveable sensitivities by incorporating fluorescence signals of different elements from within the nanostructure. In addition, the incorporation of supporting experiments as e.g. XRR for optical constant verification and machine learning techniques such as Bayesian optimization decrease the necessary computational effort of the FEM based reconstruction. The BO allows for an intelligent and fast scanning of the parameter space as compared to other optimizer approaches.

Initial steps towards determining a reliable uncertainty budget for the reconstructed parameter set were taken by deriving confidence intervals for the parameters from the Gaussian process model. We have shown, how the incorporation of the oxygen signal shifts the achievable sensitivities well into the sub-$\si{\nm}$ regime. The obtained GIXRF reconstruction results agree very well with results from SEM and AFM indicating the validity of the methodology.

In addition, we have shown that the methodology is also somewhat sensitive towards unexpected effects on the nanostructure using the example of the carbon contamination. Especially the element sensitivity of X-ray fluorescence but also the behavior of the reconstruction results indicate if unexpected effects are present on the nanostructure. 

By developing more sophisticated techniques to quantify the corresponding model error influences to the final parameter uncertainties this can be a promising technique for nanostructure characterization. In fact, by combining it with techniques such as soft X-ray GISAXS one may even enhance the obtainable sensitivities and even learn about important quality parameters e.g. line roughnesses~\cite{FernandezHerrero2020}.

%In this work, it was shown for the first time that the dimensional reconstruction of nanostructures, including a first uncertainty evaluation, can be carried out by an element sensitive analysis based on GIXRF. The method is very sensitive to the spatial distributions of the elements. For the reconstruction of the nanostructure, which requires a high numerical effort, approaches based on machine learning are very promising. A Bayesian optimizer was used for the intelligent and fast scanning of the parameter space. The uncertainty estimation was performed by inverting the Hessian matrix of the error function and leads to uncertainties in the range of sub-$\si{\nm}$, assuming that the experimental errors are leading and not the model errors. The GIXRF reconstruction results agree very well with the results of SEM or AFM. This element sensitive GIXRF analysis of nano structured surfaces is very promising as a new metrological measurement system and can deliver results with an accuracy in the sub-nm regime.

%We have shown that errors of the model are not displayed in the calculated errors and therefore a method to estimate the model error is needed.
%Additionally systematical errors are not investigated here. 
%Nevertheless the method is promising and can provide plausible results with an accuracy in the sub-nm regime.

\section{Acknowledgements}
This project has received funding from the Electronic Component Systems for European Leadership Joint Undertaking under grant agreement No 826589 — MADEin4. This Joint Undertaking receives support from the European Union's Horizon 2020 research and innovation programme and Netherlands, France, Belgium, Germany, Czech Republic, Austria, Hungary, Israel.

JCMwave acknowledges support by the Central Innovation Programm of the Federal Ministry for Economic Affairs and Energy on a basis of a decision by the German Bundestag (project QUPUS, grant no. ZF4450901RR7).

The authors would like to thank Jürgen Probst for producing the samples.

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  (\bibinfo{year}{2012}) \bibinfo{pages}{12771}.
%Type = Article
\bibitem[{Chason and Mayer(1997)}]{chason_thin_1997}
\bibinfo{author}{E.~Chason}, \bibinfo{author}{T.~M. Mayer},
\newblock \bibinfo{title}{Thin film and surface characterization by specular
  {X}-ray reflectivity},
\newblock \bibinfo{journal}{Critical Reviews in Solid State and Materials
  Sciences} \bibinfo{volume}{22} (\bibinfo{year}{1997}) \bibinfo{pages}{1--67}.
%Type = Article
\bibitem[{Kennedy et~al.(1999)Kennedy, Buiu, and
  Taylor}]{kennedy_oxidation_1999}
\bibinfo{author}{G.~P. Kennedy}, \bibinfo{author}{O.~Buiu},
  \bibinfo{author}{S.~Taylor},
\newblock \bibinfo{title}{Oxidation of silicon nitride films in an oxygen
  plasma},
\newblock \bibinfo{journal}{Journal of Applied Physics} \bibinfo{volume}{85}
  (\bibinfo{year}{1999}) \bibinfo{pages}{3319--3326}.
%Type = Article
\bibitem[{{Foreman-Mackey} et~al.(2013){Foreman-Mackey}, {Hogg}, {Lang}, and
  {Goodman}}]{emcee}
\bibinfo{author}{D.~{Foreman-Mackey}}, \bibinfo{author}{D.~W. {Hogg}},
  \bibinfo{author}{D.~{Lang}}, \bibinfo{author}{J.~{Goodman}},
\newblock \bibinfo{title}{emcee: The mcmc hammer},
\newblock \bibinfo{journal}{PASP} \bibinfo{volume}{125} (\bibinfo{year}{2013})
  \bibinfo{pages}{306--312}.
%Type = Article
\bibitem[{Haase et~al.(2016)Haase, Bajt, H{\"{o}}nicke, Soltwisch, and
  Scholze}]{Haase2016}
\bibinfo{author}{A.~Haase}, \bibinfo{author}{S.~Bajt},
  \bibinfo{author}{P.~H{\"{o}}nicke}, \bibinfo{author}{V.~Soltwisch},
  \bibinfo{author}{F.~Scholze},
\newblock \bibinfo{title}{{Multiparameter characterization of subnanometre
  Cr/Sc multilayers based on complementary measurements}},
\newblock \bibinfo{journal}{Journal of Applied Crystallography}
  \bibinfo{volume}{49} (\bibinfo{year}{2016}) \bibinfo{pages}{2161--2171}.
%Type = Article
\bibitem[{Henke et~al.(1993)Henke, Gullikson, and Davis}]{henke_x-ray_1993}
\bibinfo{author}{B.~L. Henke}, \bibinfo{author}{E.~M. Gullikson},
  \bibinfo{author}{J.~C. Davis},
\newblock \bibinfo{title}{X-{Ray} {Interactions}: {Photoabsorption},
  {Scattering}, {Transmission}, and {Reflection} at {E} = 50-30,000 {eV}, {Z} =
  1-92},
\newblock \bibinfo{journal}{Atomic Data and Nuclear Data Tables}
  \bibinfo{volume}{54} (\bibinfo{year}{1993}) \bibinfo{pages}{181 -- 342}.
%Type = Article
\bibitem[{Martin and Wickramasinghe(1994)}]{doi:10.1063/1.111578}
\bibinfo{author}{Y.~Martin}, \bibinfo{author}{H.~K. Wickramasinghe},
\newblock \bibinfo{title}{Method for imaging sidewalls by atomic force
  microscopy},
\newblock \bibinfo{journal}{Applied Physics Letters} \bibinfo{volume}{64}
  (\bibinfo{year}{1994}) \bibinfo{pages}{2498--2500}.

\end{thebibliography}

sample.bib
% Encoding: UTF-8
@article{andrle_anisotropy_2020,
	title = {The anisotropy in the optical constants of quartz crystals for soft {X}-rays},
	url = {http://arxiv.org/abs/2010.09436},
	abstract = {The refractive index of a y-cut SiO\$\_2\$ crystal surface is reconstructed from polarization dependent soft X-ray reflectometry measurements in the energy range from 45 eV to 620 eV. Due to the anisotropy of the crystal structure in the (100) and (001) directions, we observe a significant deviation of the measured reflectance at the Si-L\$\_\{2,3\}\$ and O-K absorption edges. The anisotropy in the optical constants reconstructed from these data is also confirmed by ab initio Bethe-Salpeter Equation calculations of the O-K edge. This new experimental dataset expands the existing literature data for quartz optical constants significantly, particularly in the near-edge regions.},
	language = {en},
	urldate = {2021-02-12},
	journal = {arXiv:2010.09436 [cond-mat, physics:physics]},
	author = {Andrle, A. and Hönicke, P. and Vinson, J. and Quintanilha, R. and Saadeh, Q. and Heidenreich, S. and Scholze, F. and Soltwisch, V.},
	month = oct,
	year = {2020},
	note = {arXiv: 2010.09436},
	keywords = {Condensed Matter - Materials Science, Physics - Optics},
	file = {Andrle et al. - 2020 - The anisotropy in the optical constants of quartz .pdf:/home/andrle01/Zotero/storage/KEEII89L/Andrle et al. - 2020 - The anisotropy in the optical constants of quartz .pdf:application/pdf}
}

@misc{jcm_web:accuracy_2020,
    author = {{JCMwave GmbH}},
    year = {2020},
    title = {Paramter Reference},
    subtitle = {Accuracy},
   url = {https://docs.jcmwave.com/JCMsuite/html/ParameterReference/index.html?version=4.0.3},
    note = {\url{https://docs.jcmwave.com/JCMsuite/html/ParameterReference/index.html?version=4.0.3};
visited on 2020-09-17}
}


@article{FernandezHerrero2020,
author = {Anal\'{i}a Fern\'{a}ndez Herrero and Mika Pfl\"{u}ger and J\"{u}rgen Probst and Frank Scholze and Victor Soltwisch},
journal = {Opt. Express},
keywords = {Atomic force microscopy; Conical diffraction; Diffraction efficiency; Finite element method; Line shapes; Scanning electron microscopy},
number = {22},
pages = {32490--32507},
publisher = {OSA},
title = {Applicability of the Debye-Waller damping factor for the determination of the line-edge roughness of lamellar gratings},
volume = {27},
month = {Oct},
year = {2019},
doi = {10.1364/OE.27.032490},
abstract = {Periodic nanostructures are fundamental elements in optical instrumentation as well as basis structures in integrated electronic circuits. Decreasing sizes and increasing complexity of nanostructures have made roughness a limiting parameter to the performance. Grazing-incidence small-angle X-ray scattering is a characterization method that is sensitive to three-dimensional structures and their imperfections. To quantify line-edge roughness, a Debye-Waller factor (DWF), which is derived for binary gratings, is usually used. In this work, we systematically analyze the effect of roughness on the diffracted intensities. Two different limits to the application of the DWF are found depending on whether the roughness is normally distributed or not.},
}
@ARTICLE{more_1965,

  author={G. E. {Moore}},

  journal={IEEE Solid-State Circuits Society Newsletter}, 

  title={Cramming more components onto integrated circuits, Reprinted from Electronics, volume 38, number 8, April 19, 1965, pp.114 ff.}, 

  year={2006},

  volume={11},

  number={3},

  pages={33-35},}
  
 @article{pfluger_extracting_2020,
	title = {Extracting dimensional parameters of gratings produced with self-aligned multiple patterning using grazing-incidence small-angle x-ray scattering},
	volume = {19},
	copyright = {All rights reserved},
	issn = {1932-5150},
	url = {https://www.spiedigitallibrary.org/journals/journal-of-micro-nanolithography-mems-and-moems/volume-19/issue-01/014001/Extracting-dimensional-parameters-of-gratings-produced-with-self-aligned-multiple/10.1117/1.JMM.19.1.014001.full},
	doi = {10.1117/1.JMM.19.1.014001},
	language = {en},
	number = {01},
	urldate = {2020-01-28},
	journal = {Journal of Micro/Nanolithography, MEMS, and MOEMS},
	author = {Pflüger, Mika and Kline, R. Joseph and Fernández Herrero, Analía and Hammerschmidt, Martin and Soltwisch, Victor and Krumrey, Michael},
	month = jan,
	year = {2020},
	keywords = {GISAXS, lithography},
	pages = {1},
	file = {Pflüger et al. - 2020 - Extracting dimensional parameters of gratings prod.pdf:/home/andrle01/Zotero/storage/9XZ3HPGK/Pflüger et al. - 2020 - Extracting dimensional parameters of gratings prod.pdf:application/pdf}
}



@article{pfluger_distortion_2019,
	title = {Distortion analysis of crystalline and locally quasicrystalline {2D} photonic structures with grazing-incidence small-angle {X}-ray scattering},
	volume = {52},
	issn = {1600-5767},
	url = {http://scripts.iucr.org/cgi-bin/paper?S1600576719001080},
	doi = {10.1107/S1600576719001080},
	language = {en},
	number = {2},
	urldate = {2019-03-14},
	journal = {Journal of Applied Crystallography},
	author = {Pflüger, Mika and Soltwisch, Victor and Xavier, Jolly and Probst, Jürgen and Scholze, Frank and Becker, Christiane and Krumrey, Michael},
	month = apr,
	year = {2019},
	file = {Pflüger et al. - 2019 - Distortion analysis of crystalline and locally qua.pdf:/home/andrle01/Zotero/storage/NY8GAKHC/Pflüger et al. - 2019 - Distortion analysis of crystalline and locally qua.pdf:application/pdf;Pﬂüger et al. - Supporting Information GISAXS calibration procedur.pdf:/home/andrle01/Zotero/storage/IRRMJJAP/Pﬂüger et al. - Supporting Information GISAXS calibration procedur.pdf:application/pdf}
}

@article{pfluger_grazing-incidence_2017,
	title = {Grazing-incidence small-angle {X}-ray scattering ({GISAXS}) on small periodic targets using large beams},
	volume = {4},
	copyright = {http://creativecommons.org/licenses/by/2.0/uk},
	issn = {2052-2525},
	url = {http://scripts.iucr.org/cgi-bin/paper?hf5342},
	doi = {10.1107/S2052252517006297},
	language = {en},
	number = {4},
	urldate = {2017-07-24},
	journal = {IUCrJ},
	author = {Pflüger, M. and Soltwisch, V. and Probst, J. and Scholze, F. and Krumrey, M.},
	month = jul,
	year = {2017},
	keywords = {GISAXS, gratings, Lithography, scattering},
	pages = {431--438},
	file = {hf5342sup1.pdf:/home/andrle01/Zotero/storage/INUKQ9YT/hf5342sup1.pdf:application/pdf;Pflüger et al. - 2017 - Grazing-incidence small-angle X-ray scattering (GI.pdf:/home/andrle01/Zotero/storage/FJVWZFRD/Pflüger et al. - 2017 - Grazing-incidence small-angle X-ray scattering (GI.pdf:application/pdf;Snapshot:/home/andrle01/Zotero/storage/S5M79E9H/index.html:text/html}
}
@article{kline_x-ray_2017,
	title = {X-ray scattering critical dimensional metrology using a compact x-ray source for next generation semiconductor devices},
	volume = {16},
	issn = {1932-5150, 1932-5134},
	url = {https://www.spiedigitallibrary.org/journals/Journal-of-MicroNanolithography-MEMS-and-MOEMS/volume-16/issue-1/014001/X-ray-scattering-critical-dimensional-metrology-using-a-compact-x/10.1117/1.JMM.16.1.014001.short},
	doi = {10.1117/1.JMM.16.1.014001},
	number = {1},
	urldate = {2018-03-09},
	journal = {Journal of Micro/Nanolithography, MEMS, and MOEMS},
	author = {Kline, R. Joseph and Sunday, Daniel F. and Windover, Donald and Bunday, Benjamin D.},
	month = feb,
	year = {2017},
	keywords = {exp methods, gratings, lithography, scattering},
	pages = {014001},
	file = {Kline et al. - 2017 - X-ray scattering critical dimensional metrology us.pdf:/home/andrle01/Zotero/storage/QLCUP2AC/Kline et al. - 2017 - X-ray scattering critical dimensional metrology us.pdf:application/pdf;Snapshot:/home/andrle01/Zotero/storage/INDKDD47/1.JMM.16.1.014001.html:text/html}
}

@article{ferreras_paz_solving_2012,
	title = {Solving the inverse grating problem by white light interference {Fourier} scatterometry},
	volume = {1},
	issn = {2047-7538},
	url = {http://www.nature.com/articles/lsa201236},
	doi = {10.1038/lsa.2012.36},
	language = {en},
	number = {11},
	urldate = {2020-10-29},
	journal = {Light: Science \& Applications},
	author = {Ferreras Paz, Valeriano and Peterhänsel, Sandy and Frenner, Karsten and Osten, Wolfgang},
	month = nov,
	year = {2012},
	pages = {e36--e36},
	file = {Ferreras Paz et al. - 2012 - Solving the inverse grating problem by white light.pdf:/home/andrle01/Zotero/storage/JHYFQE35/Ferreras Paz et al. - 2012 - Solving the inverse grating problem by white light.pdf:application/pdf}
}

@inproceedings{silver_fundamental_2007,
	address = {San Jose, CA},
	title = {Fundamental limits of optical critical dimension metrology: a simulation study},
	shorttitle = {Fundamental limits of optical critical dimension metrology},
	url = {http://proceedings.spiedigitallibrary.org/proceeding.aspx?doi=10.1117/12.716604},
	doi = {10.1117/12.716604},
	language = {en},
	urldate = {2020-10-29},
	author = {Silver, Richard and Germer, Thomas and Attota, Ravikiran and Barnes, Bryan M. and Bunday, Benjamin and Allgair, John and Marx, Egon and Jun, Jay},
	editor = {Archie, Chas N.},
	month = {mar},
	year = {2007},
	pages = {65180U},
	file = {Silver et al. - 2007 - Fundamental limits of optical critical dimension m.pdf:/home/andrle01/Zotero/storage/AJLT6FGS/Silver et al. - 2007 - Fundamental limits of optical critical dimension m.pdf:application/pdf}
}

@article{erni_atomic-resolution_2009,
	title = {Atomic-{Resolution} {Imaging} with a {Sub}-50-pm {Electron} {Probe}},
	volume = {102},
	issn = {0031-9007, 1079-7114},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.102.096101},
	doi = {10.1103/PhysRevLett.102.096101},
	language = {en},
	number = {9},
	urldate = {2020-11-03},
	journal = {Physical Review Letters},
	author = {Erni, Rolf and Rossell, Marta D. and Kisielowski, Christian and Dahmen, Ulrich},
	month = {mar},
	year = {2009},
	pages = {096101},
	file = {Erni et al. - 2009 - Atomic-Resolution Imaging with a Sub-50-pm Electro.pdf:/home/andrle01/Zotero/storage/2QZSU2ME/Erni et al. - 2009 - Atomic-Resolution Imaging with a Sub-50-pm Electro.pdf:application/pdf}
}

@inproceedings{mertens_vertically_2017,
	address = {San Francisco, CA, USA},
	title = {Vertically stacked gate-all-around {Si} nanowire transistors: {Key} {Process} {Optimizations} and {Ring} {Oscillator} {Demonstration}},
	isbn = {978-1-5386-3559-9},
	shorttitle = {Vertically stacked gate-all-around {Si} nanowire transistors},
	url = {http://ieeexplore.ieee.org/document/8268511/},
	doi = {10.1109/IEDM.2017.8268511},
	abstract = {We report on CMOS-integrated vertically stacked gate-all-around (GAA) Si nanowire (NW) MOSFETs with insitu doped source-drain stressors and dual work function metal gates. We demonstrate that oxidation-induced SiGe/Si fin deformation by STI densification is effectively suppressed by a SiN liner. This SiN fin protection improves the controllability of nanowire formation. In addition, highly-selective Si nanowire release and inner spacer cavity formation without Si reflow are demonstrated. Finally, for the first time we report functional ring oscillators based on stacked Si NW-FETs.},
	language = {en},
	urldate = {2020-11-03},
	booktitle = {2017 {IEEE} {International} {Electron} {Devices} {Meeting} ({IEDM})},
	publisher = {IEEE},
	author = {Mertens, H. and Ritzenthaler, R. and Pena, V. and Santoro, G. and Kenis, K. and Schulze, A. and Litta, E. D. and Chew, S. A. and Devriendt, K. and Chiarella, r. and Demuynck, S. and Yakimets, D. and Jang, D. and Spessot, A. and Eneman, G. and Dangol, A. and Lagrain, P. and Bender, H. and Sun, S. and Korolik, M. and Kioussis, D. and Kim, M. and Bu, K-.H. and Chen, S. C. and Cogorno, M. and Devrajan, J. and Machillot, J. and Yoshida, N. and Kim, N. and Barla, K. and Mocuta, D. and Horiguchi, N.},
	month = dec,
	year = {2017},
	pages = {37.4.1--37.4.4},
	file = {Mertens et al. - 2017 - Vertically stacked gate-all-around Si nanowire tra.pdf:/home/andrle01/Zotero/storage/P76ZCP33/Mertens et al. - 2017 - Vertically stacked gate-all-around Si nanowire tra.pdf:application/pdf}
}
@article{zhang_thickness-dependence_2012,
	title = {Thickness-dependence of optical constants for {Ta2O5} ultrathin films},
	volume = {108},
	issn = {0947-8396, 1432-0630},
	url = {http://link.springer.com/10.1007/s00339-012-7007-2},
	doi = {10.1007/s00339-012-7007-2},
	abstract = {An effective method for determining the optical constants of Ta2O5 thin ﬁlms deposited on crystal silicon (c-Si) using spectroscopic ellipsometry (SE) measurement with a two-ﬁlm model (ambient–oxide–interlayer–substrate) was presented. Ta2O5 thin ﬁlms with thickness range of 1–400 nm have been prepared by the electron beam evaporation (EBE) method. We ﬁnd that the refractive indices of Ta2O5 ultrathin ﬁlms less than 40 nm drop with the decreasing thickness, while the other ones are close to those of bulk Ta2O5. This phenomenon was due to the existence of an interfacial oxide region and the surface roughness of the ﬁlm, which was conﬁrmed by the measurement of atomic force microscopy (AFM). Optical properties of ultrathin ﬁlm varying with the thickness are useful for the design and manufacture of nano-scaled thin-ﬁlm devices.},
	language = {en},
	number = {4},
	urldate = {2020-12-01},
	journal = {Applied Physics A},
	author = {Zhang, Dong-Xu and Zheng, Yu-Xiang and Cai, Qing-Yuan and Lin, Wei and Wu, Kang-Ning and Mao, Peng-Hui and Zhang, Rong-Jun and Zhao, Hai-bin and Chen, Liang-Yao},
	month = sep,
	year = {2012},
	pages = {975--979},
	file = {Zhang et al. - 2012 - Thickness-dependence of optical constants for Ta2O.pdf:/home/andrle01/Zotero/storage/WRCX6Q3T/Zhang et al. - 2012 - Thickness-dependence of optical constants for Ta2O.pdf:application/pdf}
}
@article{doi:10.1063/1.111578,
author = {Martin,Yves  and Wickramasinghe,H. Kumar },
title = {Method for imaging sidewalls by atomic force microscopy},
journal = {Applied Physics Letters},
volume = {64},
number = {19},
pages = {2498-2500},
year = {1994},
doi = {10.1063/1.111578},

URL = { 
        https://doi.org/10.1063/1.111578
    
},
eprint = { 
        https://doi.org/10.1063/1.111578
    
}

}
@article{chason_thin_1997,
	title = {Thin film and surface characterization by specular {X}-ray reflectivity},
	volume = {22},
	issn = {1040-8436, 1547-6561},
	url = {https://www.tandfonline.com/doi/full/10.1080/10408439708241258},
	doi = {10.1080/10408439708241258},
	abstract = {We review the use of specular X-ray reflectivity (XRR) for the characterization of thin-film and surface structures. Specular X-ray scattering at small scattering vectors allows characterization of electron density profiles perpendicular to the surface on the length scale of 0. I to 100 nm. This allows measurement of surface morphology, thin films, multilayer structures, and buried interfaces. The technique is nondestructive and can be applied in sifii in a variety of processing environments. In the first half of the article, we review the theory and methods of XRR, including analysis of XRR spectra by a multilayer optical approach and a discussion of surface roughness measurements by XRR and other techniques. In the second half, we present a wide range of examples of XRR applications in thin-film structures, dynamic processes, liquid surfaces. and macromolecular structures.},
	language = {en},
	number = {1},
	urldate = {2021-01-07},
	journal = {Critical Reviews in Solid State and Materials Sciences},
	author = {Chason, E. and Mayer, T. M.},
	month = mar,
	year = {1997},
	pages = {1--67},
	file = {Chason und Mayer - 1997 - Thin film and surface characterization by specular.pdf:/home/andrle01/Zotero/storage/KSG8UPMK/Chason und Mayer - 1997 - Thin film and surface characterization by specular.pdf:application/pdf}
}


@inproceedings{raymond_sub-nanometer_2011,
	location = {San Jose, California, {USA}},
	title = {Sub-nanometer line width and line profile measurement for {CD}-{SEM} calibration by using {STEM}},
	url = {http://proceedings.spiedigitallibrary.org/proceeding.aspx?doi=10.1117/12.879036},
	doi = {10.1117/12.879036},
	abstract = {The novel method of sub-nanometer accuracy (uncertainty) for the line width and line profile measurement using {STEM} (Scanning Transmission Electron Microscope) images is proposed to calibrate {CD}-{SEM} line width measurement. In accordance with the proposed method, the traceability and reference metrology of line width measurements are established using Si lattice structures. First, we define two interfaces of Si-{SiO}2 and Si-Air. The interface of Si-{SiO}2 is defined as the end of Si lattice structure, and the interface of {SiO}2-Air is defined using image intensity of {STEM} image after metal coating. Second, an image magnification is calculated using 2D Fourier analysis of a {STEM} image. Third, the edge positions of the line are detected by Si lattice patterns and image intensity. Using the proposed method, the estimated accuracy less than 0.5 nm for the line width of 50 nm is established.},
	eventtitle = {{SPIE} Advanced Lithography},
	pages = {797108},
	author = {Takamasu, Kiyoshi and Okitou, Haruki and Takahashi, Satoru and Konno, Mitsuru and Inoue, Osamu and Kawada, Hiroki},
	editor = {Raymond, Christopher J.},
	urldate = {2020-05-25},
	date = {2011-03-17},
	year = {2011},
	langid = {english},
	file = {Takamasu et al. - 2011 - Sub-nanometer line width and line profile measurem.pdf:C\:\\Users\\Anna\\Zotero\\storage\\XHHT8PQQ\\Takamasu et al. - 2011 - Sub-nanometer line width and line profile measurem.pdf:application/pdf}
}
@article{Garcia-Santiago2018,
abstract = {Optimizing free-from shapes of photonic nanostructures is a high-dimensional problem. We present a Bayesian optimization algorithm with a hyper-parameter learning routine. We apply the algorithm for optimizing the shape of a reflecting meta-surface. The algorithm exhibits efficient performance.},
author = {Garcia-Santiago, X. and Schneider, P. I. and Rockstuhl, C. and Burger, S.},
doi = {10.1088/1742-6596/963/1/012003},
file = {:home/andrle01/Daten/2019/201906{\_}SPIE{\_}M{\"{u}}nchen/Paper/Literatur/Garcia-Santiago{\_}2018{\_}J.{\_}Phys.{\_}{\_}Conf.{\_}Ser.{\_}963{\_}012003.pdf:pdf},
issn = {17426596},
journal = {Journal of Physics: Conference Series},
number = {1},
title = {{Shape design of a reflecting surface using Bayesian Optimization}},
volume = {963},
year = {2018}
}
@article{Schneider2018,
abstract = {Numerical optimization is an important tool in the field of computational physics in general and in nano-optics in specific. It has attracted attention with the increase in complexity of structures that can be realized with nowadays nano-fabrication technologies for which a rational design is no longer feasible. Also, numerical resources are available to enable the computational photonic material design and to identify structures that meet predefined optical properties for specific applications. However, the optimization objective function is in general non-convex and its computation remains resource demanding such that the right choice for the optimization method is crucial to obtain excellent results. Here, we benchmark five global optimization methods for three typical nano-optical optimization problems from the field of shape optimization and parameter reconstruction: downhill simplex optimization, the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, particle swarm optimization, differential evolution, and Bayesian optimization. In these examples, Bayesian optimization, mainly known from machine learning applications, obtains significantly better results in a fraction of the run times of the other optimization methods.},
archivePrefix = {arXiv},
arxivId = {1809.06674},
author = {Schneider, Philipp-Immanuel and Santiago, Xavier Garcia and Soltwisch, Victor and Hammerschmidt, Martin and Burger, Sven and Rockstuhl, Carsten},
eprint = {1809.06674},
month = {sep},
title = {{Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction}},
url = {http://arxiv.org/abs/1809.06674},
year = {2018}
}
@article{schneider2019benchmarking,
  title={Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction},
  author={Schneider, Philipp-Immanuel and Garcia Santiago, Xavier and Soltwisch, Victor and Hammerschmidt, Martin and Burger, Sven and Rockstuhl, Carsten},
  journal={ACS Photonics},
  volume={6},
  number={11},
  pages={2726--2733},
  year={2019},
  publisher={ACS Publications}
}
@article{schneider2019using,
  title={Using {G}aussian process regression for efficient parameter reconstruction},
  author={Schneider, Philipp-Immanuel and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven},
  volume={10959},
  pages={1095911},
  year={2019},
  journal={Proc. SPIE}
}
@article{henn_maximum_2012,
	title = {A maximum likelihood approach to the inverse problem of scatterometry},
	volume = {20},
	issn = {1094-4087},
	url = {https://www.osapublishing.org/oe/abstract.cfm?uri=oe-20-12-12771},
	doi = {10.1364/OE.20.012771},
	abstract = {Scatterometry is frequently used as a non-imaging indirect optical method to reconstruct the critical dimensions (CD) of periodic nanostructures. A particular promising direction is EUV scatterometry with wavelengths in the range of 13 - 14 nm. The conventional approach to determine CDs is the minimization of a least squares function (LSQ). In this paper, we introduce an alternative method based on the maximum likelihood estimation (MLE) that determines the statistical error model parameters directly from measurement data. By using simulation data, we show that the MLE method is able to correct the systematic errors present in LSQ results and improves the accuracy of scatterometry. In a second step, the MLE approach is applied to measurement data from both extreme ultraviolet (EUV) and deep ultraviolet (DUV) scatterometry. Using MLE removes the systematic disagreement of EUV with other methods such as scanning electron microscopy and gives consistent results for DUV.},
	language = {en},
	number = {12},
	urldate = {2020-06-04},
	journal = {Optics Express},
	author = {Henn, Mark-Alexander and Gross, Hermann and Scholze, Frank and Wurm, Matthias and Elster, Clemens and Bär, Markus},
	month = jun,
	year = {2012},
	pages = {12771},
	file = {Henn et al. - 2012 - A maximum likelihood approach to the inverse probl.pdf:/home/andrle01/Zotero/storage/FWGYPBNH/Henn et al. - 2012 - A maximum likelihood approach to the inverse probl.pdf:application/pdf}
}
@article{vignaud_reflex_2019,
	title = {\textit{{REFLEX}} : a program for the analysis of specular {X}-ray and neutron reflectivity data},
	volume = {52},
	issn = {1600-5767},
	shorttitle = {\textit{{REFLEX}}},
	url = {http://scripts.iucr.org/cgi-bin/paper?S1600576718018186},
	doi = {10.1107/S1600576718018186},
	abstract = {The use of X-ray and neutron reflectivity has been generalized worldwide for scientists who want to determine specific physical properties (such as electron-density profile, scattering-length density, roughness and thickness) of films less than 200 nm thick deposited on a substrate. This paper describes a freeware program named
              REFLEX
              , which is a standalone program dedicated to the simulation and analysis of X-ray and neutron reflectivity from multilayers. This program was first written two decades ago and has been constantly improved since, but never published until now. The latest version of
              REFLEX
              covers generalized types of calculation of reflectivity curves including both neutron and X-ray reflectivity. In the case of X-rays, the program can deal with both s and p polarization, which is quite important in the soft X-ray region where the two polarizations can yield different results. Neutron reflectivity is calculated within the framework of non-spin-polarized neutrons.
              REFLEX
              has also been designed to include any type of fluid (such as supercritical CO
              2
              ) on top of the analysed film and includes corrections of the footprint effect for analysis on an absolute scale.},
	language = {en},
	number = {1},
	urldate = {2020-07-13},
	journal = {Journal of Applied Crystallography},
	author = {Vignaud, Guillaume and Gibaud, Alain},
	month = feb,
	year = {2019},
	pages = {201--213},
	file = {Vignaud und Gibaud - 2019 - REFLEX  a program for the analysis of spec.pdf:/home/andrle01/Zotero/storage/6QN7IS23/Vignaud und Gibaud - 2019 - REFLEX  a program for the analysis of spec.pdf:application/pdf}
}
@inproceedings{ukraintsev_role_2005,
	location = {San Jose, {CA}},
	title = {The role of {AFM} in semiconductor technology development: the 65 nm technology node and beyond},
	url = {http://proceedings.spiedigitallibrary.org/proceeding.aspx?doi=10.1117/12.602758},
	doi = {10.1117/12.602758},
	shorttitle = {The role of {AFM} in semiconductor technology development},
	abstract = {The International Technology Roadmap for Semiconductors ({ITRS}) predicts that atomic force microscopy ({AFM}) will become an in-line metrology tool starting at the 65 nm technology node. Others argue that {AFM} is not suitable beyond the 65 nm node due to probe size limitations [1]. This presentation examines the current state of {AFM} in semiconductor technology development and manufacturing. The following {AFM} applications are reviewed: post chemical mechanical polishing (post-{CMP}) and post reactive ion etching (post-{RIE}) topography measurements, critical dimension ({CD}) scanning electron microscopy ({SEM}) and optical scatterometry ({OCD}) calibration and long-term accuracy monitoring, across integrated circuit ({IC}) {CD} bias measurements ({OCD} lines vs. real circuit), optical proximity correction ({OPC}) modeling verification, non-destructive 3D metrology (resist, gate, sidewall offsets, holes and trenches). This current state is contrasted with upcoming requirements, benefits and limitations of metrology tools. The topics include the following: an application specific analysis of {AFM} limitations, the merits and limitations of transmission electron microscopy ({TEM}) as reference technique for {AFM}, {CD} {SEM} and {OCD}, the impact of sample-to-sample bias variation on total measurement uncertainty of {TEM}, {CD} {SEM}, {OCD} and {AFM}, the unique role of {AFM} in establishing across {CD} metrology correlation and accuracy, and need for a new type of intelligent in-line {CD} metrology tools, which would combine the merits of {OCD}, {CD} {SEM} and {AFM}.},
	eventtitle = {Microlithography 2005},
	pages = {127},
	author = {Ukraintsev, Vladimir A. and Baum, Christopher and Zhang, Gary and Hall, Craig L.},
	editor = {Silver, Richard M.},
	urldate = {2020-05-25},
	date = {2005-05-10},
	year = {2005},
	langid = {english},
	file = {Ukraintsev et al. - 2005 - The role of AFM in semiconductor technology develo.pdf:C\:\\Users\\Anna\\Zotero\\storage\\X7IJA5F2\\Ukraintsev et al. - 2005 - The role of AFM in semiconductor technology develo.pdf:application/pdf}
}
@article{vandervorst_dopantcarrier_2014,
	title = {Dopant/carrier profiling for 3D-structures: Dopant/carrier profiling for 3D-structures},
	volume = {11},
	issn = {18626351},
	url = {http://doi.wiley.com/10.1002/pssc.201300329},
	doi = {10.1002/pssc.201300329},
	shorttitle = {Dopant/carrier profiling for 3D-structures},
	pages = {121--129},
	number = {1},
	journaltitle = {physica status solidi (c)},
	shortjournal = {Phys. Status Solidi C},
	author = {Vandervorst, Wilfried and Schulze, Andreas and Kambham, Ajay Kumar and Mody, Jay and Gilbert, Matthieu and Eyben, Pierre},
	urldate = {2020-05-29},
	date = {2014-01},
	year = {2014},
	langid = {english},
	file = {Vandervorst et al. - 2014 - Dopantcarrier profiling for 3D-structures Dopant.pdf:C\:\\Users\\Anna\\Zotero\\storage\\7WMWWYL3\\Vandervorst et al. - 2014 - Dopantcarrier profiling for 3D-structures Dopant.pdf:application/pdf}
}
@article{siewert_gratings_2018,
	title = {Gratings for synchrotron and {FEL} beamlines: a project for the manufacture of ultra-precise gratings at {Helmholtz} {Zentrum} {Berlin}},
	volume = {25},
	issn = {1600-5775},
	shorttitle = {Gratings for synchrotron and {FEL} beamlines},
	url = {http://scripts.iucr.org/cgi-bin/paper?S1600577517015600},
	doi = {10.1107/S1600577517015600},
	abstract = {Blazed gratings are of dedicated interest for the monochromatization of synchrotron radiation when a high photon flux is required, such as, for example, in resonant inelastic X-ray scattering experiments or when the use of laminar gratings is excluded due to too high flux densities and expected damage, for example at free-electron laser beamlines. Their availability became a bottleneck since the decommissioning of the grating manufacture facility at Carl Zeiss in Oberkochen. To resolve this situation a new technological laboratory was established at the Helmholtz Zentrum Berlin, including instrumentation from Carl Zeiss. Besides the upgraded ZEISS equipment, an advanced grating production line has been developed, including a new ultra-precise ruling machine, ion etching technology as well as laser interference lithography. While the old ZEISS ruling machine GTM-6 allows ruling for a grating length up to 170 mm, the new GTM-24 will have the capacity for 600 mm (24 inch) gratings with groove densities between 50 lines mm
              −1
              and 1200 lines mm
              −1
              . A new ion etching machine with a scanning radiofrequency excited ion beam (HF) source allows gratings to be etched into substrates of up to 500 mm length. For a final at-wavelength characterization, a new reflectometer at a new Optics beamline at the BESSY-II storage ring is under operation. This paper reports on the status of the grating fabrication, the measured quality of fabricated items by
              ex situ
              and
              in situ
              metrology, and future development goals.},
	language = {en},
	number = {1},
	urldate = {2020-07-06},
	journal = {Journal of Synchrotron Radiation},
	author = {Siewert, F. and Löchel, B. and Buchheim, J. and Eggenstein, F. and Firsov, A. and Gwalt, G. and Kutz, O. and Lemke, St. and Nelles, B. and Rudolph, I. and Schäfers, F. and Seliger, T. and Senf, F. and Sokolov, A. and Waberski, Ch. and Wolf, J. and Zeschke, T. and Zizak, I. and Follath, R. and Arnold, T. and Frost, F. and Pietag, F. and Erko, A.},
	month = jan,
	year = {2018},
	pages = {91--99},
	file = {Siewert et al. - 2018 - Gratings for synchrotron and FEL beamlines a proj.pdf:/home/andrle01/Zotero/storage/ABLANMQE/Siewert et al. - 2018 - Gratings for synchrotron and FEL beamlines a proj.pdf:application/pdf}
}
@article{shahriari2016taking,
  title={Taking the human out of the loop: A review of {B}ayesian optimization},
  author={Shahriari, Bobak and Swersky, Kevin and Wang, Ziyu and Adams, Ryan P and De Freitas, Nando},
  journal={Proceedings of the IEEE},
  volume={104},
  number={1},
  pages={148--175},
  year={2016},
  publisher={IEEE}
}
@Article{P.Hoenicke2015,
  author    = {P. H{\"{o}}nicke and B. Detlefs and M. M{\"{u}}ller and E. Darlatt and E. Nolot and H. Grampeix and B. Beckhoff},
  title     = {Reference-free, depth-dependent characterization of nanolayers and gradient systems with advanced grazing incidence X-ray fluorescence analysis},
  journal   = {Physica Status Solidi (A)},
  year      = {2015},
  volume    = {212(3)},
  pages     = {523-528},
  doi       = {10.1002/pssa.201400204},
  owner     = {wh07021956},
  timestamp = {2014.11.08},
}
@Article{Sunday_2015,
  author    = {Daniel F. Sunday and Scott List and Jasmeet S. Chawla and R. Joseph Kline},
  journal   = {Journal of Applied Crystallography},
  title     = {Determining the shape and periodicity of nanostructures using small-angle X-ray scattering},
  year      = {2015},
  month     = {aug},
  number    = {5},
  pages     = {1355--1363},
  volume    = {48},
  doi       = {10.1107/S1600576715013369},
  file      = {:sunday2015.pdf:PDF},
  groups    = {3DNanotech},
  publisher = {International Union of Crystallography ({IUCr})},
  timestamp = {2020-03-30},
}
@Article{Kenslea_2018,
  author    = {Anne Kenslea and Chris Hakala and Zhenxin Zhong and Yinggang Lu and John Fretwell and Jack Hager and Chris Kang and Haiyan Tan and Weihao Weng and Laurent Dumas and Irene Brooks},
  title     = {{CD}-{TEM}: Characterizing impact of {TEM} sample preparation on {CD} metrology},
  year      = {2018},
  month     = {apr},
  booktitle = {2018 29th Annual {SEMI} Advanced Semiconductor Manufacturing Conference ({ASMC})},
  doi       = {10.1109/ASMC.2018.8373170},
  groups    = {3DNanotech},
  publisher = {{IEEE}},
}
@Article{Mack_2018,
  author    = {Chris A. Mack and Benjamin D. Bunday},
  title     = {{CD}-{SEM} algorithm optimization for line roughness metrology (Conference Presentation)},
  year      = {2018},
  month     = {mar},
  booktitle = {Metrology, Inspection, and Process Control for Microlithography {XXXII}},
  doi       = {10.1117/12.2297426},
  editor    = {Ofer Adan and Vladimir A. Ukraintsev},
  groups    = {3DNanotech},
  publisher = {{SPIE}},
}
@Article{Orji_2018,
  author    = {N. G. Orji and M. Badaroglu and B. M. Barnes and C. Beitia and B. D. Bunday and U. Celano and R. J. Kline and M. Neisser and Y. Obeng and A. E. Vladar},
  title     = {Metrology for the next generation of semiconductor devices},
  journal   = {Nature Electronics},
  year      = {2018},
  volume    = {1},
  number    = {10},
  pages     = {532--547},
  month     = {oct},
  doi       = {10.1038/s41928-018-0150-9},
  file      = {:orji2018.pdf:PDF},
  groups    = {Reviews, 3DNanotech, nano_XRF},
  publisher = {Springer Nature},
}
@Article{Kizu_2018,
  author    = {Ryosuke Kizu and Ichiko Misumi and Akiko Hirai and Kazuto Kinoshita and Satoshi Gonda},
  journal   = {Measurement Science and Technology},
  title     = {Development of a metrological atomic force microscope with a tip-tilting mechanism for 3D nanometrology},
  year      = {2018},
  month     = {may},
  number    = {7},
  pages     = {075005},
  volume    = {29},
  doi       = {10.1088/1361-6501/aabe1a},
  groups    = {3DNanotech},
  publisher = {{IOP} Publishing},
}
@Article{A.Singh2017,
  author    = {A. Singh and K. Luening and S. Brennan and T. Homma and N. Kubo and S.H. Nowak and P. Pianetta},
  title     = {Determination of copper nanoparticle size distributions with total reflection X-ray fluorescence spectroscopy},
  journal   = {J. Synchrotron Rad.},
  year      = {2017},
  volume    = {24},
  pages     = {283-287},
  doi       = {10.1107/S1600577516015484},
  file      = {:fv5058.pdf:PDF},
  groups    = {Applications, GIXRF},
  owner     = {wh07021956},
  timestamp = {2016.11.30},
}

@Article{Hoenicke2019,
  author    = {P. H\"{o}nicke and B. Detlefs and E. Nolot and Y. Kayser and U. M\"{u}hle and B. Pollakowski and B. Beckhoff},
  title     = {Reference-free grazing incidence X-ray fluorescence and reflectometry as a methodology for independent validation of X-ray reflectometry on ultrathin layer stacks and a depth-dependent characterization},
  journal   = {J. Vac. Sci. Technol., A},
  year      = {2019},
  volume    = {37},
  number    = {4},
  pages     = {041502},
  month     = {jul},
  doi       = {10.1116/1.5094891},
  file      = {:1.5094891.pdf:PDF},
  groups    = {meine Paper, 7.24 Paper, XRRcomGIXRF, GIXRF},
  publisher = {American Vacuum Society},
  timestamp = {2019-03-21},
}
@Article{Unterumsberger_2020,
  author    = {Rainer Unterumsberger and Philipp Hönicke and Yves Kayser and Beatrix Pollakowski and Saeed Gholhaki and Quanmin Guo and Richard Edward Palmer and Burkhard Beckhoff},
  journal   = {Journal of Analytical Atomic Spectrometry},
  title     = {Interaction of nanoparticle properties and X-ray analytical techniques},
  year      = {2020},
  doi       = {10.1039/D0JA00049C},
  file      = {:D0JA00049C.pdf:PDF},
  groups    = {7.24 Paper, meine Paper},
  publisher = {Royal Society of Chemistry ({RSC})},
}
@Article{Pfl_ger_2020,
  author    = {Mika Pflüger and R. Joseph Kline and Anal{\'{\i}}a Fern{\'{a}}ndez Herrero and Martin Hammerschmidt and Victor Soltwisch and Michael Krumrey},
  journal   = {Journal of Micro/Nanolithography, {MEMS}, and {MOEMS}},
  title     = {Extracting dimensional parameters of gratings produced with self-aligned multiple patterning using grazing-incidence small-angle x-ray scattering},
  year      = {2020},
  month     = {jan},
  number    = {01},
  pages     = {1},
  volume    = {19},
  doi       = {10.1117/1.JMM.19.1.014001},
  file      = {:014001_1.pdf:PDF},
  groups    = {3DNanotech},
  publisher = {{SPIE}-Intl Soc Optical Eng},
}
@Article{Kline_2017,
  author    = {R. Joseph Kline and Daniel F. Sunday and Donald Windover and Benjamin D. Bunday},
  journal   = {Journal of Micro/Nanolithography, {MEMS}, and {MOEMS}},
  title     = {X-ray scattering critical dimensional metrology using a compact x-ray source for next generation semiconductor devices},
  year      = {2017},
  month     = {feb},
  number    = {1},
  pages     = {014001},
  volume    = {16},
  doi       = {10.1117/1.JMM.16.1.014001},
  groups    = {3DNanotech},
  publisher = {{SPIE}-Intl Soc Optical Eng},
  timestamp = {2020-03-30},
}
@Article{Zheng_2016,
  author    = {Xiaoyu Zheng and William Smith and Julie Jackson and Bryan Moran and Huachen Cui and Da Chen and Jianchao Ye and Nicholas Fang and Nicholas Rodriguez and Todd Weisgraber and Christopher M. Spadaccini},
  title     = {Multiscale metallic metamaterials},
  journal   = {Nat. Mater.},
  year      = {2016},
  volume    = {15},
  number    = {10},
  pages     = {1100--1106},
  month     = {jul},
  doi       = {10.1038/nmat4694},
  file      = {:zheng2016.pdf:PDF},
  groups    = {otherApplications},
  publisher = {Springer Science and Business Media {LLC}},
  timestamp = {2019-12-22},
}
@book{Bbeckhoff_2006,
  Author = {B. Beckhoff and B. Kanngießer and N. Langhoff and R. Wedell and H. Wolff},
  Title = {Handbook of Practical X-Ray Fluorescence Analysis},
  Publisher = {Springer},
  Year = {2006},
  ISBN = {3662496011}
 }
@Article{Andrle_2019,
  title       = {Grazing incidence x-ray fluorescence based characterization of nanostructures for element sensitive profile reconstruction},
  year        = {2019},
  publisher   = {{SPIE}},
  month       = {jun},
  journal   = {Proc. SPIE - Modeling Aspects in Optical Metrology VII},
  pages = {110570M},
   volume    = {11057},
 author      = {A. Andrle and P. Hönicke and P.-I. Schneider and Y. Kayser and M. Hammerschmidt and S. Burger and F. Scholze and B. Beckhoff and V. Soltwisch},
  booktitle   = {Modeling Aspects in Optical Metrology {VII}},
  doi         = {10.1117/12.2526082},
  file        = {:110570M.pdf:PDF},
  genehmigung = {1},
  groups      = {meine Paper},
  timestamp   = {2019-06-27},
}
@Article{Pollakowski,
  author      = {B. Pollakowski and B. Beckhoff},
  title       = {Nondestructive Speciation Depth Profiling of complex TiOx Nanolayer Structures by Grazing Incidence X‑ray Fluorescence Analysis and Near Edge X‑ray Absorption Fine Structure Spectroscopy},
  journal     = {Anal. Chem.},
  year        = {2015},
  volume    = {87(15)},
  pages     = {7705 - 7711},
  doi         = {10.1021/acs.analchem.5b01172},
}
@Article{Krumrey1998,
  author    = {M. Krumrey},
  title     = {Design of a Four-Crystal Monochromator Beamline for Radiometry at BESSY II},
  journal   = {Journal of Synchrotron Radiation},
  year      = {1998},
  volume    = {5(1)},
  pages     = {6-9},
  doi       = {10.1107/S0909049597011825},
  file      = {S0909049597011825.pdf:S0909049597011825.pdf:PDF},
  groups    = {Beamlines},
  owner     = {wh07021956},
  timestamp = {2015.03.19},
}
@Article{M.Dialameh2017,
  author    = {M. Dialameh and F. Ferrarese Lupi and P. H\"{o}nicke and Y. Kayser and B. Beckhoff and T. Weimann and C. Fleischmann and W. Vandervorst and P. Dubcek and B. Pivac and M. Perego and G. Seguini and N. De Leo and L. Boarino},
  title     = {Development and synchrotron-based characterization of Al and Cr nanostructures as potential calibration samples for 3D analytical techniques},
  journal   = {Physica Status Solidi A},
  year      = {2017},
  number    = {6},
  pages     = {1700866},
  volume    = {215},
  doi       = {10.1002/pssa.201700866},
  file      = {:Dialameh_et_al-2018.pdf:PDF},
  groups    = {7.24 Paper, meine Paper},
  owner     = {phoenick},
  timestamp = {2017-08-01},
} 
@Article{F.Reinhardt2014,
  author    = {F. Reinhardt and S.H. Nowak and B. Beckhoff and J.-C. Dousse and M. Schoengen},
  title     = {Grazing Incidence X-ray Fluorescence of periodic structures – a comparison between X-ray Standing Waves and Geometrical Optics calculations},
  journal   = {J. Anal. At. Spectrom.},
  year      = {2014},
  volume    = {29},
  pages     = {1778-1784},
  doi       = {10.1039/C4JA00164H},
  file      = {FReinhardt_JAAS_2014.pdf:FReinhardt_JAAS_2014.pdf:PDF},
  groups    = {7.24 Paper, Applications, XSW, GIXRF},
  owner     = {wh07021956},
  timestamp = {2014.07.09},
}

@article{Golovchenko1982,
  title = {Solution to the Surface Registration Problem Using X-Ray Standing Waves},
  author = {Golovchenko, J. A. and Patel, J. R. and Kaplan, D. R. and Cowan, P. L. and Bedzyk, M. J.},
  journal = {Phys. Rev. Lett.},
  volume = {49},
  issue = {8},
  pages = {560--563},
  numpages = {0},
  year = {1982},
  month = {Aug},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.49.560},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.49.560}
}

@article{Haase2016,
author = "Haase, Anton and Bajt, Sa{\v{s}}a and H{\"{o}}nicke, Philipp and Soltwisch, Victor and Scholze, Frank",
title = "{Multiparameter characterization of subnanometre Cr/Sc multilayers based on complementary measurements}",
journal = "Journal of Applied Crystallography",
year = "2016",
volume = "49",
number = "6",
pages = "2161--2171",
month = "Dec",
doi = {10.1107/S1600576716015776},
url = {https://doi.org/10.1107/S1600576716015776},
abstract = {Cr/Sc multilayer systems can be used as near-normal incidence mirrors for the water window spectral range. It is shown that a detailed characterization of these multilayer systems with 400 bilayers of Cr and Sc, each with individual layer thicknesses <1nm, is attainable by the combination of several analytical techniques. EUV and X-ray reflectance measurements, resonant EUV reflectance across the Sc {\it L} edge, and X-ray standing wave fluorescence measurements were used. The parameters of the multilayer model were determined {\it via} a particle-swarm optimizer and validated using a Markov chain Monte Carlo maximum-likelihood approach. For the determination of the interface roughness, diffuse scattering measurements were conducted.},
keywords = {multilayers, water window, metrology, roughness, interdiffusion},
}

@Article{Kennedy_1999,
  author  = {G. P. Kennedy and O. Buiu and S. Taylor},
  journal = {Journal of Applied Physics},
  title   = {Oxidation of silicon nitride films in an oxygen plasma},
  year    = {1999},
  number  = {6},
  pages   = {3319-3326},
  volume  = {85},
  doi     = {10.1063/1.369678},
  eprint  = {http://dx.doi.org/10.1063/1.369678},
  url     = {http://dx.doi.org/10.1063/1.369678},
}

@Article{Pollakowski_2015,
  author  = {Pollakowski, Beatrix and Beckhoff, Burkhard},
  journal = {Analytical Chemistry},
  title   = {Nondestructive Speciation Depth Profiling of Complex TiOx Nanolayer Structures by Grazing Incidence X-ray Fluorescence Analysis and Near Edge X-ray Absorption Fine Structure Spectroscopy},
  year    = {2015},
  note    = {PMID: 26153035},
  number  = {15},
  pages   = {7705-7711},
  volume  = {87},
  doi     = {10.1021/acs.analchem.5b01172},
  eprint  = {http://dx.doi.org/10.1021/acs.analchem.5b01172},
  url     = {http://dx.doi.org/10.1021/acs.analchem.5b01172},
}

@Article{Malerba2015,
author={Malerba, Mario
and Alabastri, Alessandro
and Miele, Ermanno
and Zilio, Pierfrancesco
and Patrini, Maddalena
and Bajoni, Daniele
and Messina, Gabriele C.
and Dipalo, Michele
and Toma, Andrea
and Proietti Zaccaria, Remo
and De Angelis, Francesco},
title={3D vertical nanostructures for enhanced infrared plasmonics},
year={2015},
month={Nov},
day={10},
publisher={The Author(s) SN  -},
volume={5},
pages={16436 EP  -},
note={Article},
url={http://dx.doi.org/10.1038/srep16436}
}

@Article{Fletcher_2015,
  author  = {Patrick C. Fletcher and Vengadesh Kumara R. Mangalam and Lane W. Martin and William P. King},
  journal = {Journal of Vacuum Science \& Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena},
  title   = {Field emission from nanometer-scale tips of crystalline PbZrxTi1-xO3},
  year    = {2013},
  number  = {2},
  pages   = {021805},
  volume  = {31},
  doi     = {10.1116/1.4793219},
  eprint  = {http://dx.doi.org/10.1116/1.4793219},
  url     = {http://dx.doi.org/10.1116/1.4793219},
}
@article{Bedzyk_1989,
  title = {X-ray standing waves at a reflecting mirror surface},
  author = {Bedzyk, M. J. and Bommarito, G. M. and Schildkraut, J. S.},
  journal = {Phys. Rev. Lett.},
  volume = {62},
  issue = {12},
  pages = {1376--1379},
  numpages = {0},
  year = {1989},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.62.1376},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.62.1376}
}

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@Article{P.Hoenicke2016a,
  author      = {P. H\"onicke and M. Kolbe and M. Krumrey and R. Unterumsberger and B. Beckhoff},
  title       = {Experimental determination of the oxygen K-shell fluorescence yield using thin SiO2 and Al2O3 foils},
  journal     = {Spectrochim. Acta B},
  year        = {2016},
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  file        = {:000S0584854716301732-main.pdf:PDF},
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  pages     = {94-98},
  genehmigung = {1},
  groups      = {7.24 Paper, meine Paper},
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  timestamp   = {2016.08.23},
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@Article{Soltwisch2017,
author = "Soltwisch, Victor and Fern{\'{a}}ndez Herrero, Anal{\'\i}a and Pfl{\"{u}}ger, Mika and Haase, Anton and Probst, J{\"{u}}rgen and Laubis, Christian and Krumrey, Michael and Scholze, Frank",
title = "{Reconstructing detailed line profiles of lamellar gratings from GISAXS patterns with a Maxwell solver}",
journal = "Journal of Applied Crystallography",
year = "2017",
volume = "50",
number = "5",
pages = "1524--1532",
month = "Oct",
doi = {10.1107/S1600576717012742},
url = {https://doi.org/10.1107/S1600576717012742},
abstract = {Laterally periodic nanostructures have been investigated with grazing-incidence small-angle X-ray scattering (GISAXS) by using the diffraction patterns to reconstruct the surface shape. To model visible light scattering, rigorous calculations of the near and far field by numerical solution of Maxwell's equations with a finite-element method are well established. The application of this technique to X-rays is still challenging, owing to the discrepancy between the incident wavelength and the finite-element size. This drawback vanishes for GISAXS because of the small angles of incidence, the conical scattering geometry and the periodicity of the surface structures, which allows a rigorous computation of the diffraction efficiencies with sufficient numerical precision. To develop metrology tools based on GISAXS, lamellar gratings with line widths down to 55nm were produced by state-of-the-art electron-beam lithography and then etched into silicon. The high surface sensitivity of GISAXS in conjunction with a Maxwell solver allows the detailed reconstruction of the grating line shape for thick non-homogeneous substrates as well. The reconstructed geometric line-shape models are statistically validated by applying a Markov chain Monte Carlo sampling technique which reveals that GISAXS is able to reconstruct critical parameters like the widths of the lines with sub-nanometre uncertainty.},
keywords = {line profiles, lamellar gratings, grazing-incidence small-angle X-ray scattering, GISAXS, Maxwell solvers, finite-element method, Markov chain Monte Carlo technique, reconstruction, metrology},
}

@Article{barth_2017,
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}


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	copyright = {Copyright © 2007 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim},
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	doi = {10.1002/pssb.200743192},
	abstract = {We discuss realization, properties and performance of the adaptive finite element approach to the design of nano-photonic components. Central issues are the construction of vectorial finite elements and the embedding of bounded components into the unbounded and possibly heterogeneous exterior. We apply the finite element method to the optimization of the design of a hollow core photonic crystal fiber. Thereby we look at the convergence of the method and discuss automatic and adaptive grid refinement and the performance of higher order elements. (© 2007 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim)},
	language = {en},
	number = {10},
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	author = {Pomplun, Jan and Burger, Sven and Zschiedrich, Lin and Schmidt, Frank},
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	keywords = {07.05.Tp, 42.70.Qs, 42.81.Qb, 78.20.Bh},
	pages = {3419--3434}
}

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@article{Chourou:nb5076,
author = "Chourou, Slim T. and Sarje, Abhinav and Li, Xiaoye S. and Chan, Elaine R. and Hexemer, Alexander",
title = "{{\it HipGISAXS}: a high-performance computing code for simulating grazing-incidence X-ray scattering data}",
journal = "Journal of Applied Crystallography",
year = "2013",
volume = "46",
number = "6",
pages = "1781--1795",
month = "Dec",
doi = {10.1107/S0021889813025843},
url = {http://dx.doi.org/10.1107/S0021889813025843},
abstract = {This article describes the development of a flexible grazing-incidence small-angle X-ray scattering (GISAXS) simulation code in the framework of the distorted wave Born approximation that effectively utilizes the parallel processing power provided by graphics processors and multicore processors. The code, entitled {\it High-Performance GISAXS}, computes the GISAXS image for any given superposition of user-defined custom shapes or morphologies in a material and for various grazing-incidence angles and sample orientations. These capabilities permit treatment of a wide range of possible sample structures, including multilayered polymer films and nanoparticles on top of or embedded in a substrate or polymer film layers. In cases where the material displays regions of significant refractive index contrast, an algorithm has been implemented to perform a slicing of the sample and compute the averaged refractive index profile to be used as the reference geometry of the unperturbed system. A number of case studies are presented, which demonstrate good agreement with the experimental data for a variety of polymer and hybrid polymer/nanoparticle composite materials. The parallelized simulation code is well suited for addressing the analysis efforts required by the increasing amounts of GISAXS data being produced by high-speed detectors and ultrafast light sources.},
keywords = {grazing-incidence X-ray scattering, simulation, block copolymers, thin films, nanocomposites, high-performance computing, GPUs, computer programs},
}

@article {JCR2:JCR2RG5106,
author = {Suh, Hyo Seon and Chen, Xuanxuan and Rincon-Delgadillo, Paulina A. and Jiang, Zhang and Strzalka, Joseph and Wang, Jin and Chen, Wei and Gronheid, Roel and de Pablo, Juan J. and Ferrier, Nicola and Doxastakis, Manolis and Nealey, Paul F.},
title = {Characterization of the shape and line-edge roughness of polymer gratings with grazing incidence small-angle X-ray scattering and atomic force microscopy},
journal = {Journal of Applied Crystallography},
publisher = {International Union of Crystallography},
issn = {1600-5767},
url = {http://dx.doi.org/10.1107/S1600576716004453},
doi = {10.1107/S1600576716004453},
pages = {n/a--n/a},
keywords = {grazing-incidence small-angle X-ray scattering, GISAXS, polymer gratings, line-edge roughness, grating truncation rods},
year = {2016},
}
@article{Kato:12, 
author = {Akiko Kato and Sven Burger and Frank Scholze}, 
journal = {Appl. Opt.}, 
number = {27}, 
pages = {6457--6464}, 
publisher = {OSA},
title = {Analytical modeling and three-dimensional finite element simulation of line edge roughness in scatterometry}, 
volume = {51}, 
month = {Sep},
year = {2012},
url = {http://ao.osa.org/abstract.cfm?URI=ao-51-27-6457},
doi = {10.1364/AO.51.006457},
}


@article{Auguie:2008,
  title = {Collective Resonances in Gold Nanoparticle Arrays},
  author = {Augui\'e, Baptiste and Barnes, William L.},
  journal = {Phys. Rev. Lett.},
  volume = {101},
  issue = {14},
  pages = {143902},
  numpages = {4},
  year = {2008},
  month = {Sep},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.101.143902},
  url = {http://link.aps.org/doi/10.1103/PhysRevLett.101.143902}
}

@article{Narayanan:2004,
  title = {Dynamical Self-Assembly of Nanocrystal Superlattices during Colloidal Droplet Evaporation by     \textit{in situ}   Small Angle X-Ray Scattering},
  author = {Narayanan, Suresh and Wang, Jin and Lin, Xiao-Min},
  journal = {Phys. Rev. Lett.},
  volume = {93},
  issue = {13},
  pages = {135503},
  numpages = {4},
  year = {2004},
  month = {Sep},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.93.135503},
  url = {http://link.aps.org/doi/10.1103/PhysRevLett.93.135503}
}

@article{Weinhausen:2014,
  title = {Scanning X-Ray Nanodiffraction on Living Eukaryotic Cells in Microfluidic Environments},
  author = {Weinhausen, Britta and Saldanha, Oliva and Wilke, Robin N. and Dammann, Christian and Priebe, Marius and Burghammer, Manfred and Sprung, Michael and K\"oster, Sarah},
  journal = {Phys. Rev. Lett.},
  volume = {112},
  issue = {8},
  pages = {088102},
  numpages = {5},
  year = {2014},
  month = {Feb},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.112.088102},
  url = {http://link.aps.org/doi/10.1103/PhysRevLett.112.088102}
}

@article{PhysRevLett.94.145504,
  title = {Real-Time Evolution of the Distribution of Nanoparticles in an Ultrathin-Polymer-Film-Based Waveguide},
  author = {Narayanan, Suresh and Lee, Dong Ryeol and Guico, Rodney S. and Sinha, Sunil K. and Wang, Jin},
  journal = {Phys. Rev. Lett.},
  volume = {94},
  issue = {14},
  pages = {145504},
  numpages = {4},
  year = {2005},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.94.145504},
}


@article{Barke:2015uq,
	Abstract = {The diversity of nanoparticle shapes generated by condensation from gaseous matter reflects the fundamental competition between thermodynamic equilibration and the persistence of metastable configurations during growth. In the kinetically limited regime, intermediate geometries that are favoured only in early formation stages can be imprinted in the finally observed ensemble of differently structured specimens. Here we demonstrate that single-shot wide-angle scattering of femtosecond soft X-ray free-electron laser pulses allows three-dimensional characterization of the resulting metastable nanoparticle structures. For individual free silver particles, which can be considered frozen in space for the duration of photon exposure, both shape and orientation are uncovered from measured scattering images. We identify regular shapes, including species with fivefold symmetry and surprisingly large aspect ratio up to particle radii of the order of 100 nm. Our approach includes scattering effects beyond Born's approximation and is remarkably efficient---opening up new routes in ultrafast nanophysics and free-electron laser science.},
	Annote = {Supplementary information available for this article at http://www.nature.com/ncomms/2015/150204/ncomms7187/suppinfo/ncomms7187{\_}S1.html},
	Author = {Barke, Ingo and Hartmann, Hannes and Rupp, Daniela and Fl{\"u}ckiger, Leonie and Sauppe, Mario and Adolph, Marcus and Schorb, Sebastian and Bostedt, Christoph and Treusch, Rolf and Peltz, Christian and others},
	Date = {2015/02/04/online},
	Date-Added = {2015-06-02 14:10:16 +0000},
	Date-Modified = {2015-06-02 14:13:21 +0000},
	Day = {04},
	Journal = {Nat. Commun.},
	L3 = {10.1038/ncomms7187},
	M3 = {Article},
	Month = {02},
	Publisher = {Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
	Title = {The 3D-architecture of individual free silver nanoparticles captured by X-ray scattering},
	Ty = {JOUR},
	Volume = {6},
	Year = {2015},
	Bdsk-Url-1 = {http://dx.doi.org/10.1038/ncomms7187}}
	
	@article{Sun_2012fk,
		Annote = {10.1038/nphoton.2012.178},
		Author = {Sun, Tao and Jiang, Zhang and Strzalka, Joseph and Ocola, Leonidas and Wang, Jin},
		Date = {2012/09//print},
		Date-Added = {2015-06-02 12:28:43 +0000},
		Date-Modified = {2015-06-02 12:28:43 +0000},
		Isbn = {1749-4885},
		Journal = {Nat. Photon.},
		L3 = {http://www.nature.com/nphoton/journal/v6/n9/abs/nphoton.2012.178.html#supplementary-information},
		M3 = {10.1038/nphoton.2012.178},
		Month = {09},
		Number = {9},
		Pages = {586--590},
		Publisher = {Nature Publishing Group},
		Title = {Three-dimensional coherent X-ray surface scattering imaging near total external reflection},
		Ty = {JOUR},
		Volume = {6},
		Year = {2012},
		Bdsk-Url-1 = {http://dx.doi.org/10.1038/nphoton.2012.178}}
@article{goesmann_nanoparticulate_2010,
	title = {Nanoparticulate {Functional} {Materials}},
	volume = {49},
	issn = {14337851},
	doi = {10.1002/anie.200903053},
	language = {en},
	number = {8},
	urldate = {2015-01-07},
	journal = {Angewandte Chemie International Edition},
	author = {Goesmann, Helmut and Feldmann, Claus},
	month = feb,
	year = {2010},
	pages = {1362--1395},
	file = {Nanoparticulate Functional Materials - Goesmann - 2010 - Angewandte Chemie International Edition - Wiley Online Library:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/TPD59EVT/anie.html:text/html}
}

@article{yan_intersection_2007,
	title = {On the intersection of grating truncation rods with the {Ewald} sphere studied by grazing-incidence small-angle {X}-ray scattering},
	volume = {40},
	issn = {0021-8898},
	doi = {10.1107/S0021889807044482},
	number = {6},
	urldate = {2014-11-03},
	journal = {J. Appl. Cryst.},
	author = {Yan, Minhao and Gibaud, Alain},
	month = dec,
	year = {2007},
	pages = {1050--1055},
	file = {Attachment:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/EFHECDNB/paper.html:text/html}
}

@article{levine_grazing-incidence_1989,
	title = {Grazing-incidence small-angle {X}-ray scattering: new tool for studying thin film growth},
	volume = {22},
	issn = {00218898},
	shorttitle = {Grazing-incidence small-angle {X}-ray scattering},
	doi = {10.1107/S002188988900717X},
	number = {6},
	urldate = {2015-01-07},
	journal = {J. Appl. Cryst.},
	author = {Levine, J. R. and Cohen, J. B. and Chung, Y. W. and Georgopoulos, P.},
	month = dec,
	year = {1989},
	pages = {528--532},
	file = {:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/HDTDNFHX/paper.html:text/html}
}

@inproceedings{scholze_high-accuracy_2001,
	title = {High-accuracy {EUV} metrology of {PTB} using synchrotron radiation},
	volume = {4344},
	doi = {10.1117/12.436766},
	abstract = {The development of EUV lithography, has made high-accuracy at-wavelength metrology necessary. Radiometry using synchrotron radiation has been performed by the German national metrology institute, the Physikalisch-Technische Bundesanstalt (PTB), for almost 20 years. Recently, PTB has set up four new beamlines for EUV metrology at the electron storage ring BESSY II. At a bending magnet, a monochromator for soft X-ray radiometry is routinely used for reflectometry and detector characterisation. A reflectometer designed for mirrors up to 550 mm in diameter and 50 kg in mass will be operational in January 2002. Detector characterisation is based on a primary detector standard, a cryogenic electrical substitution radiometer. Measuring tools for EUV source characterisation are calibrated on this basis. Detector testing at irradiation levels comparable to the anticipated conditions in EUV tools is feasible at a plane grating monochromator, installed at an undulator optimised for EUV radiation. A test beamline for EUV optics alignment and system metrology has been installed, using undispersed undulator radiation. Bending magnet radiation is available at a station for irradiation testing. A focusing mirror collects a radiant power of about 10 mW within the multilayer bandwidth and a 1 mmÂ focal spot.},
	urldate = {2014-10-28},
	author = {Scholze, Frank and Beckhoff, Burkhard and Brandt, G. and Fliegauf, R. and Gottwald, Alexander and Klein, Roman and Meyer, Bernd and Schwarz, U. D. and Thornagel, R. and Tuemmler, Johannes and Vogel, Klaus and Weser, J. and Ulm, Gerhard},
	year = {2001},
	pages = {402--413}
}

@article{laue_rontgenstrahlinterferenzen_1913,
	title = {R{\"o}ntgenstrahlinterferenzen},
	volume = {14},
	number = {22/23},
	journal = {Physikalische Zeitschrift},
	author = {Laue, Max von},
	year = {1913},
	pages = {1075--1079}
}

@book{_nanoscience_2004,
	title = {Nanoscience and {Nanotechnologies}: {Opportunities} and {Uncertainties}},
	isbn = {9780854036042},
	shorttitle = {Nanoscience and {Nanotechnologies}},
	abstract = {Report on the current state of scientific knowledge about nanotechnologies, how they might be used in the future, and potential health, safety, environmental, ethical and societal implications.},
	language = {en},
	publisher = {Royal Society},
	year = {2004}
}

@article{rontgen_new_1896,
	title = {On a {New} {Kind} of {Rays}},
	volume = {3},
	issn = {0036-8075, 1095-9203},
	doi = {10.1126/science.3.59.227},
	language = {en},
	number = {59},
	urldate = {2015-05-27},
	journal = {Science},
	author = {R\"ontgen, W. C.},
	month = feb,
	year = {1896},
	pmid = {17769966},
	pages = {227--231}
}

@inproceedings{kennedy_particle_1995,
	title = {Particle swarm optimization},
	volume = {4},
	doi = {10.1109/ICNN.1995.488968},
	abstract = {A concept for the optimization of nonlinear functions using particle swarm methodology is introduced. The evolution of several paradigms is outlined, and an implementation of one of the paradigms is discussed. Benchmark testing of the paradigm is described, and applications, including nonlinear function optimization and neural network training, are proposed. The relationships between particle swarm optimization and both artificial life and genetic algorithms are described},
	booktitle = {, {IEEE} {International} {Conference} on {Neural} {Networks}, 1995. {Proceedings}},
	author = {Kennedy, J. and Eberhart, R.},
	month = nov,
	year = {1995},
	keywords = {artificial intelligence, artificial life, Artificial neural networks, Birds, Educational institutions, evolution, genetic algorithms, Humans, Marine animals, multidimensional search, neural nets, neural network, nonlinear functions, optimization, Optimization methods, particle swarm, Particle swarm optimization, Performance evaluation, search problems, simulation, social metaphor, Testing},
	pages = {1942--1948 vol.4},
	file = {IEEE Xplore Abstract Record:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/MP6IRT9T/articleDetails.html:text/html;IEEE Xplore Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/72SBHMEV/Kennedy und Eberhart - 1995 - Particle swarm optimization.pdf:application/pdf}
}

@article{rontgen_new_1896-1,
	title = {On a {New} {Kind} of {Rays}},
	volume = {3},
	issn = {0036-8075, 1095-9203},
	doi = {10.1126/science.3.59.227},
	language = {en},
	number = {59},
	urldate = {2015-05-27},
	journal = {Science},
	author = {R\"ontgen, W. C.},
	month = feb,
	year = {1896},
	pmid = {17769966},
	pages = {227--231},
	file = {Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/27G6DD2E/227.html:text/html}
}

@article{thostenson_advances_2001,
	title = {Advances in the science and technology of carbon nanotubes and their composites: a review},
	volume = {61},
	issn = {0266-3538},
	shorttitle = {Advances in the science and technology of carbon nanotubes and their composites},
	doi = {10.1016/S0266-3538(01)00094-X},
	abstract = {Since their first observation nearly a decade ago by Iijima (Iijima S. Helical microtubules of graphitic carbon Nature. 1991; 354:56–8), carbon nanotubes have been the focus of considerable research. Numerous investigators have since reported remarkable physical and mechanical properties for this new form of carbon. From unique electronic properties and a thermal conductivity higher than diamond to mechanical properties where the stiffness, strength and resilience exceeds any current material, carbon nanotubes offer tremendous opportunities for the development of fundamentally new material systems. In particular, the exceptional mechanical properties of carbon nanotubes, combined with their low density, offer scope for the development of nanotube-reinforced composite materials. The potential for nanocomposites reinforced with carbon tubes having extraordinary specific stiffness and strength represent tremendous opportunity for application in the 21st century. This paper provides a concise review of recent advances in carbon nanotubes and their composites. We examine the research work reported in the literature on the structure and processing of carbon nanotubes, as well as characterization and property modeling of carbon nanotubes and their composites.},
	number = {13},
	urldate = {2015-01-07},
	journal = {Composites Science and Technology},
	author = {Thostenson, Erik T and Ren, Zhifeng and Chou, Tsu-Wei},
	month = oct,
	year = {2001},
	pages = {1899--1912},
	file = {ScienceDirect Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/3JXK3SKM/Thostenson et al. - 2001 - Advances in the science and technology of carbon n.pdf:application/pdf;ScienceDirect Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/56IESM4U/S026635380100094X.html:text/html}
}

@article{lee_nanoimprint_2005,
	title = {Nanoimprint pattern transfer quality from specular x-ray reflectivity},
	volume = {87},
	issn = {0003-6951, 1077-3118},
	doi = {10.1063/1.2158512},
	abstract = {Specular x-rayreflectivity is used for high precision measurements of the pattern height, residual layer thickness, and the line-to-space ratio for parallel line and space patterns fabricated with nanoimprint lithography. The line-to-space ratio is profiled vertically to reveal relative linewidth variations as a function of the feature height. These relative linewidth variations are quantified through an external measure of the average pitch to fully define the line shape profile or cross section. An excellent fidelity of the nanoimprint pattern transfer process is quantified by comparing the line shape profiles of the mold to the imprinted pattern.},
	number = {26},
	urldate = {2015-05-29},
	journal = {Appl. Phys. Lett.},
	author = {Lee, Hae-Jeong and Soles, Christopher L. and Ro, Hyun Wook and Jones, Ronald L. and Lin, Eric K. and Wu, Wen-li and Hines, Daniel R.},
	month = dec,
	year = {2005},
	keywords = {Linewidths, Nanolithography, Nanopatterning, Reflectivity, Surface patterning},
	pages = {263111},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/EA4KC5I4/Lee et al. - 2005 - Nanoimprint pattern transfer quality from specular.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/DWHDU429/1.html:text/html}
}

@inproceedings{foucher_manufacturing_2013,
	title = {Manufacturing and advanced characterization of sub-25nm diameter {CD}-{AFM} probes with sub-10nm tip edges radius},
	volume = {8681},
	doi = {10.1117/12.2011451},
	abstract = {Atomic force microscopy (AFM) is increasingly used in the semiconductor industry as a versatile monitoring tool for highly critical lithography and etching process steps. Applications range from the inspection of the surface roughness of new materials, over accurate depth measurements to the determination of critical dimension structures. The aim to address the rapidly growing demands on measurement uncertainty and throughput more and more shifts the focus of attention to the AFM tip, which represents the crucial link between AFM tool and the sample to be monitored. Consequently, in order to reach the AFM tool’s full potential, the performance of the AFM tip has to be considered as a determining parameter. Currently available AFM tips made from silicon are generally limited by their diameter, radius, and sharpness, considerably restricting the AFM measurement capabilities on sub-30nm spaces. In addition to that, there’s lack of adequate characterization structures to accurately characterize sub-25nm tip diameters. Here, we present and discuss a recently introduced AFM tip design (T-shape like design) with precise tip diameters down to 15nm and tip radii down to 5nm fabricated from amorphous, high density diamond-like carbon (HDC/DLC) using electron beam induced processing (EBIP). In addition to that advanced design, we propose a new characterizer structure, which allows for accurate characterization and design control of sub-25nm tip diameters and sub-10nm tip edges radii. We demonstrate the potential advantages of combining a small tip shape design, i.e. tip diameter and tip edge radius, and an advanced tip characterizer for the semiconductor industry by the measurement of advanced lithography patterns.},
	urldate = {2014-11-14},
	author = {Foucher, Johann and Filippov, Pavel and Penzkofer, Christian and Irmer, Bernd and Schmidt, Sebastian W.},
	year = {2013},
	pages = {86811I--86811I--6}
}

@article{windt_imdsoftware_1998,
	title = {{IMD}—{Software} for modeling the optical properties of multilayer films},
	volume = {12},
	issn = {0894-1866},
	doi = {10.1063/1.168689},
	abstract = {A computer program called IMD is described. IMD is used for modeling the optical properties (reflectance, transmittance, electric-field intensities, etc.) of multilayer films, i.e., films consisting of any number of layers of any thickness. IMD includes a full graphical user interface and affords modeling with up to eight simultaneous independent variables, as well as parameter estimation (including confidence interval generation) using nonlinear, least-squares curve fitting to user-supplied experimental optical data. The computation methods and user interface are described, and numerous examples are presented that illustrate some of IMD's unique modeling, fitting, and visualization capabilities. {\textbackslash}copyright 1998 American Institute of Physics.},
	number = {4},
	urldate = {2015-05-22},
	journal = {Computers in Physics},
	author = {Windt, David L.},
	month = jul,
	year = {1998},
	keywords = {Computational methods, Computer modeling, Multilayers, Optical properties, User interfaces},
	pages = {360--370},
	file = {Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/DSCMZ4VR/1.html:text/html}
}

@article{rauscher_small-angle_1995,
	title = {Small-angle x-ray scattering under grazing incidence: {The} cross section in the distorted-wave {Born} approximation},
	volume = {52},
	shorttitle = {Small-angle x-ray scattering under grazing incidence},
	doi = {10.1103/PhysRevB.52.16855},
	abstract = {The specular and nonspecular intensity of x rays scattered from a rough surface with fluctuations in the electron density is calculated in the distorted-wave Born approximation. The contributions to the nonspecular intensity of roughness and density fluctuations can be separated. The structure factor is given by a convolution integral of the Fourier transform of the density correlation function. Special geometries of density fluctuations are discussed.},
	number = {23},
	urldate = {2015-01-07},
	journal = {Phys. Rev. B},
	author = {Rauscher, M. and Salditt, T. and Spohn, H.},
	month = dec,
	year = {1995},
	pages = {16855--16863},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/G6CT3XQN/PhysRevB.52.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/QNN7WZHV/Rauscher et al. - 1995 - Small-angle x-ray scattering under grazing inciden.pdf:application/pdf}
}

@article{laue_rontgenstrahlinterferenzen_1913-1,
	title = {R\"ontgenstrahlinterferenzen},
	volume = {14},
	number = {22/23},
	journal = {Physikalische Zeitschrift},
	author = {Laue, Max von},
	year = {1913},
	pages = {1075--1079}
}

@article{hofmann_grazing_2009,
	title = {Grazing incident small angle x-ray scattering: {A} metrology to probe nanopatterned surfaces},
	volume = {27},
	issn = {2166-2746, 2166-2754},
	shorttitle = {Grazing incident small angle x-ray scattering},
	doi = {10.1116/1.3253608},
	number = {6},
	urldate = {2014-11-17},
	journal = {J. Vac. Sci. Technol. B},
	author = {Hofmann, T. and Dobisz, E. and Ocko, B. M.},
	month = nov,
	year = {2009},
	keywords = {Form factors, Scanning electron microscopy, Surface patterning, Surface scattering, X-ray scattering},
	pages = {3238--3243},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/XAKSZU7G/Hofmann et al. - 2009 - Grazing incident small angle x-ray scattering A m.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/98NINQHN/1.html:text/html}
}

@article{ash_super-resolution_1972,
	title = {Super-resolution {Aperture} {Scanning} {Microscope}},
	volume = {237},
	copyright = {\copyright 1972 Nature Publishing Group},
	doi = {10.1038/237510a0},
	language = {en},
	number = {5357},
	urldate = {2015-01-07},
	journal = {Nature},
	author = {Ash, E. A. and Nicholls, G.},
	month = jun,
	year = {1972},
	pages = {510--512},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/WZVJ9AZR/Ash und Nicholls - 1972 - Super-resolution Aperture Scanning Microscope.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/A78VNERC/237510a0.html:text/html}
}

@article{feng_x-ray_1993,
	title = {X-ray flux enhancement in thin-film waveguides using resonant beam couplers},
	volume = {71},
	doi = {10.1103/PhysRevLett.71.537},
	abstract = {We present experimental evidence for achieving significant x-ray flux enhancement by coupling a highly collimated and monochromatic synchrotron x-ray beam into a Si/polyimide/SiO2 thin-film waveguide. The observed 20-fold flux increase agrees with theoretical predictions and was limited only by absorption of the 1 {\textbackslash}AA x rays in the waveguide structure.},
	number = {4},
	urldate = {2015-03-04},
	journal = {Phys. Rev. Lett.},
	author = {Feng, Y. P. and Sinha, S. K. and Deckman, H. W. and Hastings, J. B. and Siddons, D. P.},
	month = jul,
	year = {1993},
	pages = {537--540},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/ICV7P6T3/PhysRevLett.71.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/EXS5I323/Feng et al. - 1993 - X-ray flux enhancement in thin-film waveguides usi.pdf:application/pdf}
}

@article{yoneda_anomalous_1963,
	title = {Anomalous {Surface} {Reflection} of {X} {Rays}},
	volume = {131},
	doi = {10.1103/PhysRev.131.2010},
	abstract = {An asymmetric surface reflection of x rays was found. It was experimentally determined that this anomalously reflected wave has almost the same wavelength as the incident wave. The angle of this reflection changes only slightly with the incident angle and the crystal structure of the sample in the measured angular range. The glancing angle of this reflection increases with the wavelength of the incident x rays. According to measurements on evaporated surfaces of metallic elements, these reflection angles were found to have an important relation to the periodic system of the elements.},
	number = {5},
	urldate = {2014-11-20},
	journal = {Phys. Rev.},
	author = {Yoneda, Y.},
	month = sep,
	year = {1963},
	pages = {2010--2013},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/J2MHN32W/PhysRev.131.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/FU8RIRH9/Yoneda - 1963 - Anomalous Surface Reflection of X Rays.pdf:application/pdf}
}

@article{krumrey_thickness_2004,
	title = {Thickness determination for {SiO}2 films on {Si} by {X}-ray reflectometry at the {Si} {K} edge},
	volume = {459},
	issn = {0040-6090},
	doi = {10.1016/j.tsf.2003.12.100},
	number = {1–2},
	urldate = {2014-10-28},
	journal = {Thin Solid Films},
	author = {Krumrey, M and Hoffmann, M and Ulm, G and Hasche, K and Thomsen-Schmidt, P},
	month = jul,
	year = {2004},
	keywords = {silicon, Silicon oxide, X-ray reflectometry},
	pages = {241--244},
	file = {ScienceDirect Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/PIN6ZKJ8/S004060900302042X.html:text/html}
}

@article{hlaing_nanoimprint-induced_2011,
	title = {Nanoimprint-{Induced} {Molecular} {Orientation} in {Semiconducting} {Polymer} {Nanostructures}},
	volume = {5},
	issn = {1936-0851},
	doi = {10.1021/nn202515z},
	number = {9},
	urldate = {2015-05-29},
	journal = {ACS Nano},
	author = {Hlaing, Htay and Lu, Xinhui and Hofmann, Tommy and Yager, Kevin G. and Black, Charles T. and Ocko, Benjamin M.},
	month = sep,
	year = {2011},
	pages = {7532--7538},
	file = {ACS Full Text PDF w/ Links:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/55MIAA8I/Hlaing et al. - 2011 - Nanoimprint-Induced Molecular Orientation in Semic.pdf:application/pdf;ACS Full Text Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/44RI2DUP/nn202515z.html:text/html}
}

@article{albert_self-assembly_2010,
	title = {Self-assembly of block copolymer thin films},
	volume = {13},
	issn = {1369-7021},
	doi = {10.1016/S1369-7021(10)70106-1},
	number = {6},
	urldate = {2015-01-07},
	journal = {Materials Today},
	author = {Albert, Julie N. L. and Epps III, Thomas H.},
	month = jun,
	year = {2010},
	pages = {24--33},
	file = {ScienceDirect Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/77A5EUD9/Albert und Epps III - 2010 - Self-assembly of block copolymer thin films.pdf:application/pdf;ScienceDirect Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/2XHB2ER7/S1369702110701061.html:text/html}
}

@article{windt_imdsoftware_1998-1,
	title = {{IMD}—{Software} for modeling the optical properties of multilayer films},
	volume = {12},
	issn = {0894-1866},
	doi = {10.1063/1.168689},
	number = {4},
	urldate = {2015-05-22},
	journal = {Computers in Physics},
	author = {Windt, David L.},
	month = jul,
	year = {1998},
	keywords = {Computational methods, Computer modeling, Multilayers, Optical properties, User interfaces},
	pages = {360--370},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/68JXB3DT/Windt - 1998 - IMD—Software for modeling the optical properties o.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/2K47UH4S/1.html:text/html}
}

@article{goesmann_nanoparticulate_2010-1,
	title = {Nanoparticulate {Functional} {Materials}},
	volume = {49},
	issn = {14337851},
	doi = {10.1002/anie.200903053},
	language = {en},
	number = {8},
	urldate = {2015-01-07},
	journal = {Angewandte Chemie International Edition},
	author = {Goesmann, Helmut and Feldmann, Claus},
	month = feb,
	year = {2010},
	pages = {1362--1395},
	file = {Nanoparticulate Functional Materials - Goesmann - 2010 - Angewandte Chemie International Edition - Wiley Online Library:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/P4CIPHV2/anie.html:text/html}
}

@article{renaud_probing_2009,
	title = {Probing surface and interface morphology with {Grazing} {Incidence} {Small} {Angle} {X}-{Ray} {Scattering}},
	volume = {64},
	issn = {0167-5729},
	doi = {10.1016/j.surfrep.2009.07.002},
	number = {8},
	urldate = {2015-01-07},
	journal = {Surf. Sci.},
	author = {Renaud, Gilles and Lazzari, R\'emi and Leroy, Fr\'ed\'eric},
	month = aug,
	year = {2009},
	pages = {255--380},
	file = {ScienceDirect Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/94HF2NNG/S0167572909000399.html:text/html}
}

@article{barke_3d-architecture_2015,
	title = {The 3D-architecture of individual free silver nanoparticles captured by {X}-ray scattering},
	volume = {6},
	journal = {Nat Commun},
	author = {Barke, Ingo and Hartmann, Hannes and Rupp, Daniela and Fl{\"u}ckiger, Leonie and Sauppe, Mario and Adolph, Marcus and Schorb, Sebastian and Bostedt, Christoph and Treusch, Rolf and Peltz, Christian and Bartling, Stephan and Fennel, Thomas and Meiwes-Broer, Karl-Heinz and M{\"o}ller, Thomas},
	year = {2015}
}

@article{sun_three-dimensional_2012,
	title = {Three-dimensional coherent {X}-ray surface scattering imaging near total external reflection},
	volume = {6},
	number = {9},
	journal = {Nat. Photon.},
	author = {Sun, Tao and Jiang, Zhang and Strzalka, Joseph and Ocola, Leonidas and Wang, Jin},
	year = {2012},
	pages = {586--590}
}

@article{ash_super-resolution_1972-1,
	title = {Super-resolution {Aperture} {Scanning} {Microscope}},
	volume = {237},
	copyright = {© 1972 Nature Publishing Group},
	doi = {10.1038/237510a0},
	language = {en},
	number = {5357},
	urldate = {2015-01-07},
	journal = {Nature},
	author = {Ash, E. A. and Nicholls, G.},
	month = jun,
	year = {1972},
	pages = {510--512},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/93TMWHUR/Ash und Nicholls - 1972 - Super-resolution Aperture Scanning Microscope.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/BBA6I2QN/237510a0.html:text/html}
}

@article{guinier_diffraction_1939,
	Author = {Guinier, Andr\'e},
	Journal = {Ann. de. Phy. (Paris)},
	Pages = {161},
	Title = {La {Diffraction} des {Rayons} {X} aux {Tr}\`es {Faibles} {Angles}: {Applications} \`a l'{Etude} des {Ph}\'enom{\`e}nes {Ultra}-microscopiques},
	Volume = {12},
	Year = {1939}}

@article{hu_small_2004,
	title = {Small angle x-ray scattering metrology for sidewall angle and cross section of nanometer scale line gratings},
	volume = {96},
	issn = {0021-8979, 1089-7550},
	doi = {10.1063/1.1773376},
	abstract = {High-volume fabrication of nanostructures requires nondestructive metrologies capable of measuring not only the pattern size but also the pattern shape profile. Measurement tool requirements will become more stringent as the feature size approaches 50 nm and tolerances of pattern shape will reach a few nanometers. A small angle x-ray scattering (SAXS) based technique has been demonstrated to have the capability of characterizing the average pitch size and pattern width to subnanometer precision. In this study, we report a simple, modeling-free protocol to extract cross-section information such as the average sidewall angle and the pattern height of line gratingpatterns from the SAXS data. Diffraction peak intensities and reciprocal space positions are measured while the sample is rotated around the axis perpendicular to the grating direction. Linear extrapolations of peak positions in reciprocal space allow a precise determination of both the sidewall angle and the pattern height.},
	number = {4},
	urldate = {2015-05-29},
	journal = {J. Appl. Phys.},
	author = {Hu, Tengjiao and Jones, Ronald L. and Wu, Wen-li and Lin, Eric K. and Lin, Qinghuang and Keane, Denis and Weigand, Steve and Quintana, John},
	month = aug,
	year = {2004},
	keywords = {Diffraction gratings, Metrology, Nanopatterning, X-ray diffraction, X-ray scattering},
	pages = {1983--1987},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/U2RPZVDQ/Hu et al. - 2004 - Small angle x-ray scattering metrology for sidewal.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/TTW3TPJT/1.html:text/html}
}

@article{carlisle_off--shelf_2001,
	title = {An {Off}-{The}-{Shelf} {PSO}},
	number = {1-6},
	journal = {Proceedings of the 2001 Workshop on Particle Swarm Optimization},
	author = {Carlisle, A. and Dozier, G.},
	year = {2001}
}

@article{chapman_femtosecond_2011,
	title = {Femtosecond {X}-ray protein nanocrystallography},
	volume = {470},
	copyright = {{\textbackslash}copyright 2011 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
	issn = {0028-0836},
	doi = {10.1038/nature09750},
	abstract = {X-ray crystallography provides the vast majority of macromolecular structures, but the success of the method relies on growing crystals of sufficient size. In conventional measurements, the necessary increase in X-ray dose to record data from crystals that are too small leads to extensive damage before a diffraction signal can be recorded. It is particularly challenging to obtain large, well-diffracting crystals of membrane proteins, for which fewer than 300 unique structures have been determined despite their importance in all living cells. Here we present a method for structure determination where single-crystal X-ray diffraction `snapshots' are collected from a fully hydrated stream of nanocrystals using femtosecond pulses from a hard-X-ray free-electron laser, the Linac Coherent Light Source. We prove this concept with nanocrystals of photosystem I, one of the largest membrane protein complexes. More than 3,000,000 diffraction patterns were collected in this study, and a three-dimensional data set was assembled from individual photosystem I nanocrystals ({\textbackslash}textasciitilde200 nm to 2 μm in size). We mitigate the problem of radiation damage in crystallography by using pulses briefer than the timescale of most damage processes. This offers a new approach to structure determination of macromolecules that do not yield crystals of sufficient size for studies using conventional radiation sources or are particularly sensitive to radiation damage.},
	language = {en},
	number = {7332},
	urldate = {2015-06-01},
	journal = {Nature},
	author = {Chapman, Henry N. and Fromme, Petra and Barty, Anton and White, Thomas A. and Kirian, Richard A. and Aquila, Andrew and Hunter, Mark S. and Schulz, Joachim and DePonte, Daniel P. and Weierstall, Uwe and others},
	month = feb,
	year = {2011},
	keywords = {Applied physics and engineering, Physics, Structural biology},
	pages = {73--77},
	file = {Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/BBRZ3869/nature09750.html:text/html}
}

@article{renaud_probing_2009-1,
	title = {Probing surface and interface morphology with {Grazing} {Incidence} {Small} {Angle} {X}-{Ray} {Scattering}},
	volume = {64},
	issn = {0167-5729},
	doi = {10.1016/j.surfrep.2009.07.002},
	abstract = {Nanoscience and nanotechnology are tremendously increasing fields of research that aim at producing, characterizing and understanding nanoobjects and assemblies of nanoobjects. Their new physical or chemical properties, which arise from confinement effects, intimately depend on their morphological properties, i.e. their shapes, their sizes and their spatial organization. This calls for dedicated morphological characterization tools, among which is the Grazing Incidence Small Angle X-Ray Scattering (GISAXS). This reciprocal space technique has emerged in the last two decades as a powerful tool that allows investigating in a non-destructive way the morphological properties from one to billions of nanoparticles, either on a surface, or embedded in a matrix, with sizes ranging from 1 nm to several microns. The advantages of the technique are that it is non-destructive; it yields statistical information averaged on a large number of nanoparticles; it allows probing both the surface or deep below it, by changing the incident angle of the X-ray beam; it can be used in very different sample environments, in particular in situ in the course of a given process such as growth, annealing, gas exposure; and it may be given chemical sensitivity by use of anomalous scattering. This report presents a review of the GISAXS technique, from experimental issues to the theories underlying the data analysis, with a wealth of examples. The physical morphological information contained in GISAXS data and its analysis are presented in simple terms, introducing the notions of particle form factor and interference function, together with the different cases encountered according to the size/shape dispersion. The theoretical background of X-ray diffuse scattering under grazing incidence is presented in a general way, and then applied to the particular case of grazing incidence small angle X-ray scattering from assemblies of particles either on a substrate, or buried below it. Most of the GISAXS measurements published to date are reported, covering the fields of ex situ studies of embedded metallic nanoparticles, granular multilayered systems, implanted systems, embedded or stacked or deposited semi-conductor nanostructures, porous materials and copolymer thin films. A special emphasis is brought on in situ experiments, performed either in ultra-high vacuum during nanoparticle growth by molecular beam epitaxy, or in gas-reactors during catalytic reactions. This covers a very broad field, from (i) the 3D island (Volmer–Weber) growth of metals on oxides surfaces to (ii) the organized growth of metals on surfaces that are nanopatterned either by surface reconstruction or by underlying dislocation networks or by deposit-induced nanofacetting, to (iii) the in situ investigation of the self-organized Stranski–Krastanow hetero-epitaxial growth of semi-conductor quantum dots on semi-conductor surfaces, or (iv) the in situ surface nanopatterning by ion bombardment. Many examples are discussed in detail, to illustrate the large diversity of systems and morphologies that can be addressed as well as the different analysis issues and the conclusions of the technique in terms of growth mode.},
	number = {8},
	urldate = {2015-01-07},
	journal = {Surf. Sci.},
	author = {Renaud, Gilles and Lazzari, R{\'e}mi and Leroy, Fr\'ed\'eric},
	month = aug,
	year = {2009},
	keywords = {Assemblies of nanoparticles, Catalysis, Decoupling Approximation, Distorted Wave Born Approximation, DWBA, Form factor, GISAXS, Grazing incidence, Grazing Incidence Small Angle X-Ray Scattering, Growth laws, Growth modes, In situ, Interference function, Local Monodispersed Approximation, Metal on oxide surfaces, Metal surfaces, Molecular beam epitaxy, Nano-particles, Nano-structures, Patterned substrates, Polymers, Quantum dots, Reconstructions, Scaling Approximation, Self- organized growth, Semi-conductors, Size-Spacing Correlation Approximation, Synchrotron X-rays, Theory of X-ray scattering, Ultra-high-vacuum, X-ray scattering},
	pages = {255--380},
	file = {ScienceDirect Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/W2E3QBAM/S0167572909000399.html:text/html}
}

@article{baumbach_grazing_1999,
	title = {Grazing incidence diffraction by laterally patterned semiconductor nanostructures},
	volume = {32},
	issn = {0022-3727},
	doi = {10.1088/0022-3727/32/6/020},
	abstract = {A theoretical study of grazing incidence diffraction by laterally patterned epitaxial nanostructures is presented and successfully applied to experimental findings of pseudomorphic multilayer gratings. Numerical results from a distorted wave Born approximation are given. The grating structure generates a fine structure around the reciprocal lattice points consisting of grating truncation rods, which are similar to the crystal truncation rod of a planar crystal surface. We show the influence of the grating shape, the compositional profile and the lattice strain on the intensity pattern along the grating truncation rods. The effect of lattice strain will be discussed by comparing the fully strained state (tetragonal lattice distortion), uniform strain relaxation and graduated strain relaxation in the surface grating. Our theoretical treatment allows us to interpret grazing incidence diffraction measurements obtained from strained layer gratings and superlattice gratings.},
	language = {en},
	number = {6},
	urldate = {2015-04-09},
	journal = {J. Phys. D},
	author = {Baumbach, T. and L\"ubbert, D.},
	month = mar,
	year = {1999},
	pages = {726},
	file = {Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/FWQEVTUZ/020.html:text/html}
}

@article{mikulik_coplanar_2001,
	title = {Coplanar and non-coplanar x-ray reflectivity characterization of lateral {W}/{Si} multilayer gratings},
	volume = {34},
	issn = {0022-3727},
	doi = {10.1088/0022-3727/34/10A/339},
	abstract = {Structural characterization of a fully etched amorphous W/Si multilayer grating with a lateral periodicity of 800 nm is performed by x-ray reflectivity in the coplanar and non-coplanar modes using a scintillation detector and a two-dimensional gas-filled detector, respectively. Three-dimensional reciprocal space constructions were used to explain the scattering features recorded in both geometries. Coplanar coherent grating truncation rods were fitted by a dynamical theory for rough gratings. Comparison of the reflectivity from the reference planar multilayer completes the study.},
	language = {en},
	number = {10A},
	urldate = {2014-11-17},
	journal = {J. Phys. D},
	author = {Mikul\'ik, P. and Jergel, M. and Baumbach, T. and Majkov\'a, E. and Pinc\'ik, E. and Luby, S. and Ortega, L. and Tucoulou, R. and Hudek, P. and Kostic, I.},
	month = may,
	year = {2001},
	pages = {A188},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/DFHEIBNZ/Mikulík et al. - 2001 - Coplanar and non-coplanar x-ray reflectivity chara.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/Z5D3P479/339.html:text/html}
}

@article{lee_nanoimprint_2005-1,
	title = {Nanoimprint pattern transfer quality from specular x-ray reflectivity},
	volume = {87},
	issn = {0003-6951, 1077-3118},
	doi = {10.1063/1.2158512},
	abstract = {Specular x-rayreflectivity is used for high precision measurements of the pattern height, residual layer thickness, and the line-to-space ratio for parallel line and space patterns fabricated with nanoimprint lithography. The line-to-space ratio is profiled vertically to reveal relative linewidth variations as a function of the feature height. These relative linewidth variations are quantified through an external measure of the average pitch to fully define the line shape profile or cross section. An excellent fidelity of the nanoimprint pattern transfer process is quantified by comparing the line shape profiles of the mold to the imprinted pattern.},
	number = {26},
	urldate = {2015-05-29},
	journal = {Appl. Phys. Lett.},
	author = {Lee, Hae-Jeong and Soles, Christopher L. and Ro, Hyun Wook and Jones, Ronald L. and Lin, Eric K. and Wu, Wen-li and Hines, Daniel R.},
	month = dec,
	year = {2005},
	keywords = {Linewidths, Nanolithography, Nanopatterning, Reflectivity, Surface patterning},
	pages = {263111},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/8U77K3B5/Lee et al. - 2005 - Nanoimprint pattern transfer quality from specular.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/FJGXRHB9/1.html:text/html}
}

@article{pomplun_adaptive_2007,
	title = {Adaptive finite element method for simulation of optical nano structures},
	volume = {244},
	copyright = {Copyright © 2007 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim},
	issn = {1521-3951},
	doi = {10.1002/pssb.200743192},
	abstract = {We discuss realization, properties and performance of the adaptive finite element approach to the design of nano-photonic components. Central issues are the construction of vectorial finite elements and the embedding of bounded components into the unbounded and possibly heterogeneous exterior. We apply the finite element method to the optimization of the design of a hollow core photonic crystal fiber. Thereby we look at the convergence of the method and discuss automatic and adaptive grid refinement and the performance of higher order elements. (© 2007 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim)},
	language = {en},
	number = {10},
	urldate = {2015-07-07},
	journal = {Phys. Status Solidi B},
	author = {Pomplun, Jan and Burger, Sven and Zschiedrich, Lin and Schmidt, Frank},
	month = oct,
	year = {2007},
	keywords = {07.05.Tp, 42.70.Qs, 42.81.Qb, 78.20.Bh},
	pages = {3419--3434},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/UT9JHAZ3/Pomplun et al. - 2007 - Adaptive finite element method for simulation of o.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/AEHIV6I5/abstract.html:text/html}
}

@article{kendrew_three-dimensional_1958,
	title = {A {Three}-{Dimensional} {Model} of the {Myoglobin} {Molecule} {Obtained} by {X}-{Ray} {Analysis}},
	volume = {181},
	copyright = {{\textbackslash}copyright 1958 Nature Publishing Group},
	doi = {10.1038/181662a0},
	language = {en},
	number = {4610},
	urldate = {2015-05-27},
	journal = {Nature},
	author = {Kendrew, J. C. and Bodo, G. and Dintzis, H. M. and Parrish, R. G. and Wyckoff, H. and Phillips, D. C.},
	month = mar,
	year = {1958},
	pages = {662--666},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/N263IIUK/Kendrew et al. - 1958 - A Three-Dimensional Model of the Myoglobin Molecul.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/SKIJSNQ6/181662a0.html:text/html}
}

@article{wernecke_characterization_2014,
	title = {Characterization of an in-vacuum {PILATUS} {1M} detector},
	volume = {21},
	issn = {1600-5775},
	doi = {10.1107/S160057751400294X},
	number = {3},
	urldate = {2014-10-28},
	journal = {J. Sync. Rad.},
	author = {Wernecke, Jan and Gollwitzer, Christian and Mueller, Peter and Krumrey, Michael},
	month = may,
	year = {2014},
	pages = {529--536},
	file = {Attachment:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/K6KTM74I/paper.html:text/html}
}

@article{klein_radiometry_2002,
	title = {Radiometry with synchrotron radiation at the {PTB} laboratory at {Bessy} ii},
	volume = {15},
	issn = {0894-0886},
	doi = {10.1080/08940880208602929},
	number = {1},
	urldate = {2014-10-28},
	journal = {Sync. Rad. News},
	author = {Klein, R. and Krumrey, M. and Richter, M. and Scholze, F. and Thornagel, R. and Ulm, G.},
	month = jan,
	year = {2002},
	pages = {23--29},
	file = {Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/C6ZU4AIH/08940880208602929.html:text/html}
}

@article{ardenne_elektronen-rastermikroskop_1938,
	title = {Das {Elektronen}-{Rastermikroskop}},
	volume = {109},
	issn = {0044-3328},
	doi = {10.1007/BF01341584},
	abstract = {Das Prinzip des Elektronen-Rastermikroskops. Herstellung der Elektronensonde. Herstellung des Rasters. Die verschiedenen Beleuchtungsarten. Untersuchung von Objekten in Luft. Die Grenzen für das Aufl{\"o}sungsverm{\"o}gen des Rastermikroskops. IntensitÄtsfragen und Aufl{\"o}sungsverm{\"o}gen. Zusammenfassung.},
	language = {de},
	number = {9-10},
	urldate = {2015-01-07},
	journal = {Zeitschrift f{\"u}r Physik},
	author = {Ardenne, Manfred von},
	month = sep,
	year = {1938},
	keywords = {Elementary Particles and Nuclei, Hadrons, Heavy Ions, Nuclear Fusion, Nuclear Physics},
	pages = {553--572},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/B3PVWCK2/Ardenne - 1938 - Das Elektronen-Rastermikroskop.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/77FRBWNZ/10.html:text/html}
}

@book{pietsch_high-resolution_2004,
	title = {High-{Resolution} {X}-{Ray} {Scattering}: {From} {Thin} {Films} to {Lateral} {Nanostructures}},
	isbn = {9780387400921},
	shorttitle = {High-{Resolution} {X}-{Ray} {Scattering}},
	abstract = {During the last 20 years interest in high-resolution x-ray diffractometry and reflectivity has grown as a result of the development of the semiconductor industry and the increasing interest in material research of thin layers of magnetic, organic, and other materials. For example, optoelectronics requires a subsequent epitaxy of thin layers of different semiconductor materials. Here, the individuallayer thicknesses are scaled down to a few atomic layers in order to exploit quantum effects. For reasons of electronic and optical confinement, these thin layers are embedded within much thicker cladding layers or stacks of multilayers of slightly different chemical composition. It is evident that the interface quality of those quantum weHs is quite important for the function of devices. Thin metallic layers often show magnetic properties which do not ap pear for thick layers or in bulk material. The investigation of the mutual interaction of magnetic and non-magnetic layers leads to the discovery of colossal magnetoresistance, for example. This property is strongly related to the thickness and interface roughness of covered layers.},
	language = {en},
	publisher = {Springer Science \& Business Media},
	author = {Pietsch, Ullrich and Holy, Vaclav and Baumbach, Tilo},
	month = aug,
	year = {2004},
	keywords = {Technology \& Engineering / Electronics / General, Technology \& Engineering / Manufacturing, Technology \& Engineering / Materials Science, Technology \& Engineering / Nanotechnology \& MEMS, Technology \& Engineering / Optics}
}

@article{levine_grazing-incidence_1989-1,
	title = {Grazing-incidence small-angle {X}-ray scattering: new tool for studying thin film growth},
	volume = {22},
	issn = {00218898},
	shorttitle = {Grazing-incidence small-angle {X}-ray scattering},
	doi = {10.1107/S002188988900717X},
	number = {6},
	urldate = {2015-01-07},
	journal = {Journal of Applied Crystallography},
	author = {Levine, J. R. and Cohen, J. B. and Chung, Y. W. and Georgopoulos, P.},
	month = dec,
	year = {1989},
	pages = {528--532},
	file = {Attachment:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/NCFSFNU4/paper.html:text/html}
}

@article{kato_effect_2010,
	title = {Effect of line roughness on the diffraction intensities in angular resolved scatterometry},
	volume = {49},
	doi = {10.1364/AO.49.006102},
	abstract = {Scatterometry is a common technique for the characterization of nanostructured surfaces. With shrinking dimensions, fewer and fewer propagating diffraction orders exist, and structure roughness becomes more important. Recent investigations suggest that roughness has to be taken into account for structure reconstruction. The short wavelength of the extreme UV (EUV) is advantageous, since it provides more propagating diffraction orders as compared to UV and visible radiation and increases the sensitivity to small structural features, particularly roughness. We present a method to numerically estimate changes in measured diffraction intensities in angular resolved EUV scatterometry induced by line roughness. The model can be used to include the estimation of the roughness into the structure reconstruction algorithm.},
	number = {31},
	urldate = {2014-11-17},
	journal = {Applied Optics},
	author = {Kato, Akiko and Scholze, Frank},
	month = nov,
	year = {2010},
	keywords = {Scattering measurements, Scattering theory, Surface measurements, roughness},
	pages = {6102--6110},
	file = {Appl. Opt. Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/W6NQSEEU/abstract.html:text/html}
}

@article{kaganer_bragg_1995,
	title = {Bragg diffraction peaks in x-ray diffuse scattering from multilayers with rough interfaces},
	volume = {52},
	doi = {10.1103/PhysRevB.52.16369},
	abstract = {The peaks in x-ray diffuse scattering appearing due to diffraction of incident or scattered waves on a periodically layered structure are sensitive to the perfection of multilayers. These peaks are investigated analytically and compared with numerical calculations. It is shown that, if the roughness of periodic interfaces is not correlated, the peaks follow the intensity of the x-ray standing wave on the interfaces. Interference effects due to correlated interfacial roughness can change the sense of the peak (sequence of maximum and minimum). The factors controlling the peak sense are derived and applied to explain the results of numerical calculations.},
	number = {23},
	urldate = {2015-03-03},
	journal = {Phys. Rev. B},
	author = {Kaganer, V. M. and Stepanov, S. A. and Koehler, R.},
	month = dec,
	year = {1995},
	pages = {16369--16372},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/T3ZI2AMI/PhysRevB.52.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/RQ6W626R/Kaganer et al. - 1995 - Bragg diffraction peaks in x-ray diffuse scatterin.pdf:application/pdf}
}

@article{feng_x-ray_1993-1,
	title = {X-ray flux enhancement in thin-film waveguides using resonant beam couplers},
	volume = {71},
	doi = {10.1103/PhysRevLett.71.537},
	abstract = {We present experimental evidence for achieving significant x-ray flux enhancement by coupling a highly collimated and monochromatic synchrotron x-ray beam into a Si/polyimide/SiO2 thin-film waveguide. The observed 20-fold flux increase agrees with theoretical predictions and was limited only by absorption of the 1 Å x rays in the waveguide structure.},
	number = {4},
	urldate = {2015-03-04},
	journal = {Physical Review Letters},
	author = {Feng, Y. P. and Sinha, S. K. and Deckman, H. W. and Hastings, J. B. and Siddons, D. P.},
	month = jul,
	year = {1993},
	pages = {537--540},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/DETPGV8K/PhysRevLett.71.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/3UX75JTB/Feng et al. - 1993 - X-ray flux enhancement in thin-film waveguides usi.pdf:application/pdf}
}

@article{wang_characterization_2007,
	title = {Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering},
	volume = {102},
	issn = {0021-8979, 1089-7550},
	doi = {10.1063/1.2753588},
	abstract = {To meet the challenges in dimensional metrology as the minimum feature size in semiconductor devices approaches sub-35 nm length scales, we have been developing a nondestructive method using x rays termed critical dimension small angle x-ray scattering (SAXS). Its capacity to quantify the dimension of linewidth, pitch, line height, and sidewall angle of line gratings has been demonstrated. In this work, we have further extended its capabilities to quantify the correlated line-edge roughness (LER) and linewidthroughness (LWR). Model line grating patterns with controlled LER and LWR were prepared and measured using x ray, their results were analyzed with model calculations. The magnitude of LER/LWR deduced from x-ray results compares favorably with the scanning electron microscopy results obtained from the same samples. An apparent Debye–Waller factor, which can be deduced from the SAXS data without any detailed model-based calculations, is found to be a convenient parameter to quantify the amplitude of LER/LWR.},
	number = {2},
	urldate = {2015-04-23},
	journal = {Journal of Applied Physics},
	author = {Wang, Chengqing and Jones, Ronald L. and Lin, Eric K. and Wu, Wen-Li and Rice, Bryan J. and Choi, Kwang-Woo and Thompson, George and Weigand, Steven J. and Keane, Denis T.},
	month = jul,
	year = {2007},
	keywords = {Diffraction gratings, Linewidths, Photoresistors, Scanning electron microscopy, X-ray scattering},
	pages = {024901},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/DBR53M98/Wang et al. - 2007 - Characterization of correlated line edge roughness.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/VW666RVT/1.html:text/html}
}

@article{rosei_nanostructured_2004,
	title = {Nanostructured surfaces: challenges and frontiers in nanotechnology},
	volume = {16},
	issn = {0953-8984},
	shorttitle = {Nanostructured surfaces},
	doi = {10.1088/0953-8984/16/17/001},
	abstract = {Nanostructured surfaces can be broadly defined as substrates in which the typical features have dimensions in the range 1–100 nm (although the upper limit of 100 nm may be relaxed to greater sizes in some cases, depending on the material and the specific property being investigated). The recent surge of interest in these systems stems from the remarkable effects that may arise from the critical size reduction. Interesting novel properties (catalytic, magnetic, ferroelectric, mechanical, optical and electronic) occur as we reduce the dimensions from a practically infinite (and periodic) solid crystal to a system composed of a relatively small number of atoms. So far, nanostructured materials or nanomaterials are perhaps the only sub-field of nanoscience that has made the transition from fundamental science to real world applications, thus becoming a technology (a good example of this are nanostructured surface coatings). This paper describes some selected examples of recent progress in the study of nanostructured surfaces. Surface reconstructions, which occur either naturally or as a consequence of the interaction with adsorbates, are discussed because of their importance in model chemical reactions and for their potential use as templates for the ordered growth of nanostructures. Supramolecular assemblies and molecular nanostructures, resulting from the balance between molecule–molecule and molecule–surface interactions, are described because of their fundamental interest and their potential use in nanoelectronic devices. Recent progress in the growth of semiconductor nanostructures, in particular Ge–Si and InAs–GaAs, is briefly reviewed. A few selected examples of nanostructured functional materials, such as ferroelectric and magnetic nanostructures, are discussed in view of their potential for applications in future data storage devices. Nanostructured materials used in catalysis and gas sensor applications are briefly described. Finally, perspectives and future challenges in this emerging field of research are also discussed.},
	language = {en},
	number = {17},
	urldate = {2014-11-14},
	journal = {Journal of Physics: Condensed Matter},
	author = {Rosei, Federico},
	month = may,
	year = {2004},
	pages = {S1373},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/AGBECGNB/Rosei - 2004 - Nanostructured surfaces challenges and frontiers .pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/6XQ8K5WC/001.html:text/html}
}

@article{smith_microlithography:_2007,
	title = {Microlithography: Science and Technology, Second Edition},
	isbn = {9781420051537},
	shorttitle = {Microlithography},
	abstract = {This new edition of the bestselling Microlithography: Science and Technology provides a balanced treatment of theoretical and operational considerations, from elementary concepts to advanced aspects of modern submicron microlithography. Each chapter reflects the current research and practices from the world's leading academic and industrial laboratories detailed by a stellar panel of international experts.New in the Second EditionIn addition to updated information on existing material, this new edition features coverage of technologies developed over the last decade since the first edition appeared, including: Immersion Lithography 157nm Lithography Electron Projection Lithography (EPL) Extreme Ultraviolet (EUV) Lithography Imprint Lithography Photoresists for 193nm and Immersion Lithography Scatterometry Microlithography: Science and Technology, Second Edition authoritatively covers the physics, chemistry, optics, metrology tools and techniques, resist processing and materials, and fabrication methods involved in the latest generations of microlithography such as immersion lithography and extreme ultraviolet (EUV) lithography. It also looks ahead to the possible future systems and technologies that will bring the next generations to fruition.Loaded with illustrations, equations, tables, and time-saving references to the most current literature, this book is the most comprehensive and reliable source for anyone, from student to seasoned professional, looking to achieve robust, accurate, and cost-effective microlithography processes and systems.},
	language = {en},
	publisher = {CRC Press},
	author = {Smith, Bruce W. and Suzuki, Kazuaki},
	month = may,
	year = {2007},
	keywords = {Science / Physics / Optics \& Light, Technology \& Engineering / Electronics / General, Technology \& Engineering / Electronics / Microelectronics, Technology \& Engineering / Lasers \& Photonics}
}

@article{Goodman10,
   author = {Jonathan Goodman and Jonathan Weare},
    title = {Ensemble samplers with affine invariance},
  journal = {Comm. App. Math. Com. Sc.},
     year = 2010,
   volume = 5,
    pages = {65-80},
      doi = {10.2140/camcos.2010.5.65}
}
@article{emcee,
   author = {{Foreman-Mackey}, D. and {Hogg}, D.~W. and {Lang}, D. and {Goodman}, J.},
    title = {emcee: The MCMC Hammer},
  journal = {PASP},
     year = 2013,
   volume = 125,
    pages = {306-312},
   eprint = {1202.3665},
      doi = {10.1086/670067}
}
@inproceedings{burger_jcmsuite:_2008,
	title = {{JCMsuite}: {An} {Adaptive} {FEM} {Solver} or {Precise} {Simulations} in {Nano}-{Optics}},
	shorttitle = {{JCMsuite}},
	doi = {10.1364/IPNRA.2008.ITuE4},
	urldate = {2014-10-28},
	journal = {Integrated {Photonics} and {Nanophotonics} {Research} and {Applications}},
	publisher = {Optical Society of America},
	author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank},
	month = jul,
	year = {2008},
	keywords = {Nanophotonics and photonic crystals, Numerical approximation and analysis, Other areas of optics},
	pages = {ITuE4},
	file = {IPNRA Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/USZA5FH3/abstract.html:text/html}
}

@article{tsunoda_spectroscopic_2003,
	title = {Spectroscopic characterization of naturally and chemically oxidized silicon surfaces},
	volume = {94},
	issn = {0021-8979},
	doi = {10.1063/1.1613792},
	abstract = {We have determined the thicknesses of naturally and chemically grown oxides on HF-cleaned silicon surfaces in ambient air and in NH4OH/H2O2/H2O solution, respectively, using spectroscopic ellipsometry. The naturally grown oxide thickness versus air-exposure time plots yield a rate constant of 3.5\${\textbackslash}pm\$0.5 {\textbackslash}AA/decade in ambient air. Chemical oxidation occurs immediately upon immersing the sample in the chemical solution and leaves the sample surface terminated with ∼6 {\textbackslash}AA of a chemical oxide. Photoreflectance intensity is found to be strongly dependent on such surface processing, and results are explained by the different degree of surface (interface) states. {\textbackslash}copyright 2003 American Institute of Physics.},
	number = {9},
	journal = {Journal of Applied Physics},
	author = {Tsunoda, Kazuaki and Ohashi, Emiko and Adachi, Sadao},
	month = nov,
	year = {2003},
	keywords = {6847Fg, 7320At, 7868+m, 8165Mq, elemental semiconductors, ellipsometry, oxidation, photoreflectance, silicon, surface cleaning, surface states},
	pages = {5613--5616},
	file = {IEEE Xplore Abstract Record:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/A7TIGDP7/freeabs_all.html:text/html}
}

@article{raman_new_1928,
	title = {A new radiation},
	number = {2},
	journal = {Indian Journal of physics},
	author = {Raman, Chandrasekhara Venkata},
	year = {1928},
	pages = {387--398}
}

@book{smith_microlithography:_2007-1,
	title = {Microlithography: {Science} and {Technology}, {Second} {Edition}},
	isbn = {9781420051537},
	shorttitle = {Microlithography},
	abstract = {This new edition of the bestselling Microlithography: Science and Technology provides a balanced treatment of theoretical and operational considerations, from elementary concepts to advanced aspects of modern submicron microlithography. Each chapter reflects the current research and practices from the world's leading academic and industrial laboratories detailed by a stellar panel of international experts.New in the Second EditionIn addition to updated information on existing material, this new edition features coverage of technologies developed over the last decade since the first edition appeared, including:  Immersion Lithography 157nm Lithography Electron Projection Lithography (EPL) Extreme Ultraviolet (EUV) Lithography Imprint Lithography Photoresists for 193nm and Immersion Lithography Scatterometry Microlithography: Science and Technology, Second Edition authoritatively covers the physics, chemistry, optics, metrology tools and techniques, resist processing and materials, and fabrication methods involved in the latest generations of microlithography such as immersion lithography and extreme ultraviolet (EUV) lithography. It also looks ahead to the possible future systems and technologies that will bring the next generations to fruition.Loaded with illustrations, equations, tables, and time-saving references to the most current literature, this book is the most comprehensive and reliable source for anyone, from student to seasoned professional, looking to achieve robust, accurate, and cost-effective microlithography processes and systems.},
	language = {en},
	publisher = {CRC Press},
	author = {Smith, Bruce W. and Suzuki, Kazuaki},
	month = may,
	year = {2007},
	keywords = {Science / Physics / Optics \& Light, Technology \& Engineering / Electronics / General, Technology \& Engineering / Electronics / Microelectronics, Technology \& Engineering / Lasers \& Photonics}
}

@article{gollmer_fabrication_2014,
	
	title = {Fabrication and characterization of combined metallic nanogratings and {ITO} electrodes for organic photovoltaic cells},
	volume = {119},
	issn = {0167-9317},
	doi = {10.1016/j.mee.2014.03.042},
	abstract = {Organic photovoltaic devices are interesting alternatives to conventional silicon based photovoltaic cells, due to potentially lower material costs and energy consumption during the fabrication process. However, the energy conversion efficiency of organic photovoltaic cells may still be improved. One possible approach is a combination with metallic nanostructures to improve light absorption properties in the active layer. We report on the fabrication and characterization of metallic nanogratings integrated with an indium tin oxide (ITO) electrode to be combined with small-molecule organic photovoltaic cells. With respect to geometry and extinction properties gratings fabricated by two different fabrication methods, conventional electron beam lithography and nanoimprint lithography, are presented. Furthermore, gratings fabricated on top of ITO are compared to gratings integrated both below and within ITO electrodes. Fabricating structures below or within electrodes is advantageous for organic thin film techniques to avoid compromising the crystallinity of the organic thin film and short-circuiting across the thin layer.},
	urldate = {2014-12-01},
	journal = {Micro. Engine.},
	author = {Gollmer, D. A. and Walter, F. and Lorch, C. and Novák, J. and Banerjee, R. and Dieterle, J. and Santoro, G. and Schreiber, F. and Kern, D. P. and Fleischer, M.},
	month = may,
	year = {2014},
	keywords = {Extinction spectroscopy, GISAXS, Nano imprint lithography, Organic photovoltaics, Plasmonic nanogratings, Plasmonic solar cells},
	pages = {122--126},
	file = {ScienceDirect Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/E2TSPHFB/S0167931714001373.html:text/html}
}

@article{chapman_femtosecond_2011-1,
	title = {Femtosecond {X}-ray protein nanocrystallography},
	volume = {470},
	copyright = {© 2011 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
	issn = {0028-0836},
	doi = {10.1038/nature09750},
	abstract = {X-ray crystallography provides the vast majority of macromolecular structures, but the success of the method relies on growing crystals of sufficient size. In conventional measurements, the necessary increase in X-ray dose to record data from crystals that are too small leads to extensive damage before a diffraction signal can be recorded. It is particularly challenging to obtain large, well-diffracting crystals of membrane proteins, for which fewer than 300 unique structures have been determined despite their importance in all living cells. Here we present a method for structure determination where single-crystal X-ray diffraction ‘snapshots’ are collected from a fully hydrated stream of nanocrystals using femtosecond pulses from a hard-X-ray free-electron laser, the Linac Coherent Light Source. We prove this concept with nanocrystals of photosystem I, one of the largest membrane protein complexes. More than 3,000,000 diffraction patterns were collected in this study, and a three-dimensional data set was assembled from individual photosystem I nanocrystals ({\textasciitilde}200 nm to 2 μm in size). We mitigate the problem of radiation damage in crystallography by using pulses briefer than the timescale of most damage processes. This offers a new approach to structure determination of macromolecules that do not yield crystals of sufficient size for studies using conventional radiation sources or are particularly sensitive to radiation damage.},
	language = {en},
	number = {7332},
	urldate = {2015-06-01},
	journal = {Nature},
	author = {Chapman, Henry N. and Fromme, Petra and Barty, Anton and White, Thomas A. and Kirian, Richard A. and Aquila, Andrew and Hunter, Mark S. and Schulz, Joachim and DePonte, Daniel P. and Weierstall, Uwe and others},
	month = feb,
	year = {2011},
	keywords = {Applied physics and engineering, Physics, Structural biology},
	pages = {73--77},
	file = {Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/WVUP4I64/nature09750.html:text/html}
}

@article{soccio_assessment_2014,
	title = {On the assessment by grazing-incidence small-angle {X}-ray scattering of replica quality in polymer gratings fabricated by nanoimprint lithography},
	volume = {47},
	issn = {1600-5767},
	doi = {10.1107/S160057671400168X},
	number = {2},
	urldate = {2015-01-07},
	journal = {Journal of Applied Crystallography},
	author = {Soccio, M. and Alayo, N. and Martín-Fabiani, I. and Rueda, D. R. and García-Gutiérrez, M. C. and Rebollar, E. and Martínez-Tong, D. E. and Pérez-Murano, F. and Ezquerra, T. A.},
	month = apr,
	year = {2014},
	pages = {613--618},
	file = {On the assessment by grazing-incidence small-angle X-ray scattering of replica quality in polymer gratings fabricated by nanoimprint lithography:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/HNMU87XX/paper.html:text/html}
}

@article{rueda_grazing-incidence_2012,
	title = {Grazing-incidence small-angle {X}-ray scattering of soft and hard nanofabricated gratings},
	volume = {45},
	issn = {0021-8898, 1600-5767},
	doi = {10.1107/S0021889812030415},
	number = {5},
	urldate = {2014-11-13},
	journal = {J. Appl. Cryst.},
	author = {Rueda, D. R. and Martín-Fabiani, I. and Soccio, M. and Alayo, N. and Pérez-Murano, F. and Rebollar, E. and García-Gutiérrez, M. C. and Castillejo, M. and Ezquerra, T. A.},
	month = oct,
	year = {2012},
	pages = {1038--1045},
	file = {Attachment:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/J6M8VRA3/paper.html:text/html}
}

@article{jiang_waveguide-enhanced_2011,
	title = {Waveguide-enhanced grazing-incidence small-angle x-ray scattering of buried nanostructures in thin films},
	volume = {84},
	doi = {10.1103/PhysRevB.84.075440},
	abstract = {X-ray standing waves generated by the interference of the scattered x rays from parallel surfaces of a thin film, the so-called waveguide effect, can be used to enhance or reduce the scatterings from certain depths of the film. Used in combination with grazing-incidence small-angle x-ray scattering, this resonance effect provides depth sensitivity to extract buried structures in thin films of polymer and polymer/nanoparticle nanocomposite, which are not readily accessible by most surface techniques, such as scanning probe microscopy. We developed a rigorous theory of the diffuse scattering in the framework of the distorted-wave Born approximation using a discretization method analogous to Parratt’s recursive formalism. In such a case, the distortion of the electric field of the unperturbed state from the nanostructures of interest is considered in a self-consistent manner. This theory allows a quantitative determination of the buried nanostructures when the x-ray waveguide enhancement is present or the size of the nanostructures of interest is comparable to or larger than the spatial frequency of electric-field intensity modulation. A unique capability afforded by this theory is that a nanometer or even subnanometer spatial resolution can be achieved in the depth information of the buried nanostructures, along with the in-plane correlation of the structures.},
	number = {7},
	urldate = {2015-03-04},
	journal = {Phys. Rev. B},
	author = {Jiang, Zhang and Lee, Dong Ryeol and Narayanan, Suresh and Wang, Jin and Sinha, Sunil K.},
	month = aug,
	year = {2011},
	pages = {075440},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/9Z97S9T5/PhysRevB.84.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/5IBK97DI/Jiang et al. - 2011 - Waveguide-enhanced grazing-incidence small-angle x.pdf:application/pdf}
}

@article{holy_nonspecular_1994,
	Abstract = {X-ray reflection from periodical multilayers with randomly rough interfaces has been described within the distorted-wave Born approximation. The method is suitable for calculating both specular x-ray reflection and nonspecular (diffuse) scattering. In this paper, both in-plane and vertical correlations of the roughness profiles have been considered and it has been demonstrated that the vertical roughness correlation substantially affects the nonspecular scattering. The theory can explain resonant effects observed in the beam scattered nonspecularly from a periodical multilayer. The theoretical approach has been used for the study of interfacial roughness in a long-periodic AlAs/GaAs multilayer and good agreement has been achieved between the experimental results and the theory.},
	Author = {Hol\'y, V. and Baumbach, T.},
	Doi = {10.1103/PhysRevB.49.10668},
	File = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/HMRNVI8C/PhysRevB.49.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/ATP8A72H/Hol{\'y} und Baumbach - 1994 - Nonspecular x-ray reflection from rough multilayer.pdf:application/pdf},
	Journal = {Phys. Rev. B},
	Month = apr,
	Number = {15},
	Pages = {10668--10676},
	Title = {Nonspecular x-ray reflection from rough multilayers},
	Urldate = {2015-01-06},
	Volume = {49},
	Year = {1994},
	Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevB.49.10668}}

@inproceedings{foucher_manufacturing_2013-1,
	title = {Manufacturing and advanced characterization of sub-25nm diameter {CD}-{AFM} probes with sub-10nm tip edges radius},
	volume = {8681},
	doi = {10.1117/12.2011451},
	abstract = {Atomic force microscopy (AFM) is increasingly used in the semiconductor industry as a versatile monitoring tool for highly critical lithography and etching process steps. Applications range from the inspection of the surface roughness of new materials, over accurate depth measurements to the determination of critical dimension structures. The aim to address the rapidly growing demands on measurement uncertainty and throughput more and more shifts the focus of attention to the AFM tip, which represents the crucial link between AFM tool and the sample to be monitored. Consequently, in order to reach the AFM tool's full potential, the performance of the AFM tip has to be considered as a determining parameter. Currently available AFM tips made from silicon are generally limited by their diameter, radius, and sharpness, considerably restricting the AFM measurement capabilities on sub-30nm spaces. In addition to that, there's lack of adequate characterization structures to accurately characterize sub-25nm tip diameters. Here, we present and discuss a recently introduced AFM tip design (T-shape like design) with precise tip diameters down to 15nm and tip radii down to 5nm fabricated from amorphous, high density diamond-like carbon (HDC/DLC) using electron beam induced processing (EBIP). In addition to that advanced design, we propose a new characterizer structure, which allows for accurate characterization and design control of sub-25nm tip diameters and sub-10nm tip edges radii. We demonstrate the potential advantages of combining a small tip shape design, i.e. tip diameter and tip edge radius, and an advanced tip characterizer for the semiconductor industry by the measurement of advanced lithography patterns.},
	urldate = {2014-11-14},
	author = {Foucher, Johann and Filippov, Pavel and Penzkofer, Christian and Irmer, Bernd and Schmidt, Sebastian W.},
	year = {2013},
	pages = {86811I--86811I--6}
}

@article{binnig_atomic_1986,
	title = {Atomic {Force} {Microscope}},
	volume = {56},
	doi = {10.1103/PhysRevLett.56.930},
	abstract = {The scanning tunneling microscope is proposed as a method to measure forces as small as 10−18 N. As one application for this concept, we introduce a new type of microscope capable of investigating surfaces of insulators on an atomic scale. The atomic force microscope is a combination of the principles of the scanning tunneling microscope and the stylus profilometer. It incorporates a probe that does not damage the surface. Our preliminary results in air demonstrate a lateral resolution of 30 {\textbackslash}AAA and a vertical resolution less than 1 {\textbackslash}AA.},
	number = {9},
	urldate = {2015-01-07},
	journal = {Physical Review Letters},
	author = {Binnig, G. and Quate, C. F. and Gerber, Ch.},
	month = mar,
	year = {1986},
	pages = {930--933},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/2CCBHMP9/PhysRevLett.56.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/4BH93F5I/Binnig et al. - 1986 - Atomic Force Microscope.pdf:application/pdf}
}

@article{zhang_addressing_2014,
	title = {Addressing {FinFET} metrology challenges in 1× node using tilt-beam critical dimension scanning electron microscope},
	volume = {13},
	issn = {1932-5150},
	doi = {10.1117/1.JMM.13.4.041407},
	language = {en},
	number = {4},
	urldate = {2014-11-26},
	journal = {Journal of Micro/Nanolithography, MEMS, and MOEMS},
	author = {Zhang, Xiaoxiao and Zhou, Hua and Ge, Zhenhua and Vaid, Alok and Konduparthi, Deepasree and Osorio, Carmen and Ventola, Stefano and Meir, Roi and Shoval, Ori and Kris, Roman and Adan, Ofer and Bar-Zvi, Maayan},
	month = oct,
	year = {2014},
	pages = {041407},
	file = {Addressing FinFET metrology challenges in 1× node using tilt-beam critical dimension scanning electron microscope | (2014) | Zhang | Publications | Spie:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/IFIAIKHX/1.JMM.13.4.html:text/html}
}

@article{mikulik_coplanar_2001-1,
	title = {Coplanar and non-coplanar x-ray reflectivity characterization of lateral {W}/{Si} multilayer gratings},
	volume = {34},
	issn = {0022-3727},
	doi = {10.1088/0022-3727/34/10A/339},
	abstract = {Structural characterization of a fully etched amorphous W/Si multilayer grating with a lateral periodicity of 800 nm is performed by x-ray reflectivity in the coplanar and non-coplanar modes using a scintillation detector and a two-dimensional gas-filled detector, respectively. Three-dimensional reciprocal space constructions were used to explain the scattering features recorded in both geometries. Coplanar coherent grating truncation rods were fitted by a dynamical theory for rough gratings. Comparison of the reflectivity from the reference planar multilayer completes the study.},
	language = {en},
	number = {10A},
	urldate = {2014-11-17},
	journal = {Journal of Physics D: Applied Physics},
	author = {Mikul\'ik, P. and Jergel, M. and Baumbach, T. and Majkov\'a, E. and Pinc\'ik, E. and Luby, S. and Ortega, L. and Tucoulou, R. and Hudek, P. and Kostic, I.},
	month = may,
	year = {2001},
	pages = {A188},
	file = {Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/2U5TNPV2/339.html:text/html}
}

@inproceedings{kennedy_particle_1995-1,
	title = {Particle swarm optimization},
	volume = {4},
	doi = {10.1109/ICNN.1995.488968},
	abstract = {A concept for the optimization of nonlinear functions using particle swarm methodology is introduced. The evolution of several paradigms is outlined, and an implementation of one of the paradigms is discussed. Benchmark testing of the paradigm is described, and applications, including nonlinear function optimization and neural network training, are proposed. The relationships between particle swarm optimization and both artificial life and genetic algorithms are described},
	booktitle = {, {IEEE} {International} {Conference} on {Neural} {Networks}, 1995. {Proceedings}},
	author = {Kennedy, J. and Eberhart, R.},
	month = nov,
	year = {1995},
	keywords = {artificial intelligence, artificial life, Artificial neural networks, Birds, Educational institutions, evolution, genetic algorithms, Humans, Marine animals, multidimensional search, neural nets, neural network, nonlinear functions, optimization, Optimization methods, particle swarm, Particle swarm optimization, Performance evaluation, search problems, simulation, social metaphor, Testing},
	pages = {1942--1948 vol.4},
	file = {IEEE Xplore Abstract Record:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/BW5CMXBG/articleDetails.html:text/html;IEEE Xplore Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/239BJKSC/Kennedy und Eberhart - 1995 - Particle swarm optimization.pdf:application/pdf}
}

@article{krumrey_high-accuracy_2001,
	title = {High-accuracy detector calibration at the {PTB} four-crystal monochromator beamline},
	volume = {467–-468},
	issn = {0168-9002},
	doi = {10.1016/S0168-9002(01)00598-8},
	abstract = {A four-crystal monochromator beamline has been installed by the Physikalisch-Technische Bundesanstalt at a bending magnet of the electron storage ring BESSY II. The monochromatic radiation with very high spectral purity and high spectral resolution in the photon energy range from 1.75 to 10 keV is used to calibrate detectors by comparison to a cryogenic electrical substitution radiometer as primary detector standard with relative uncertainties well below 1\%. This is one order of magnitude better than all calibrations of non-energy-dispersive detectors in this spectral range previously performed. The beamline is also used for the characterization of optical components.},
	urldate = {2014-10-28},
	journal = {Nucl. Instrum. Methods},
	author = {Krumrey, M. and Ulm, G.},
	month = jul,
	year = {2001},
	keywords = {Four-crystal monochromator, Semiconductor photodiodes, X-ray detector calibration},
	pages = {1175--1178},
	file = {ScienceDirect Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/IJFKE79C/Krumrey und Ulm - 2001 - High-accuracy detector calibration at the PTB four.pdf:application/pdf;ScienceDirect Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/DS3IC67R/S0168900201005988.html:text/html}
}

@article{wernecke_direct_2012,
	title = {Direct structural characterisation of line gratings with grazing incidence small-angle x-ray scattering},
	volume = {83},
	issn = {0034-6748, 1089-7623},
	doi = {10.1063/1.4758283},
	abstract = {Grazing incidence small-angle x-ray scattering (GISAXS) and x-ray reflectometry (XRR) have been used to investigate structural parameters, especially period length, line width, groove width, and line height, of grating test structures in the sub-micron range. The gratings are e-beam written structures on a quartz substrate with a fixed period length, but different line and groove widths, covered by a layer of ruthenium. A Ru layer thickness of 9.4 nm has been determined with XRR. GISAXS was performed in two orientations, with an incident beam alignment perpendicular and parallel to the grating lines. The scattering patterns in parallel orientation have been analysed without numerical simulation by Fourier transformation. The obtained results for line and groove width are in good agreement with nominal values. The analysis method has been validated by analysing simulated scattering data. A superposition of scattering intensities measured for different azimuthal rotation angles close to parallel alignment was used to determine the line height of a grating of 27.3 nm, which is also close to the nominal value. The Fourier analysis procedure opens up the possibility of traceable structure determination with GISAXS in the nanometre range.},
	number = {10},
	urldate = {2015-01-07},
	journal = {Rev. Sci. Instrum.},
	author = {Wernecke, Jan and Scholze, Frank and Krumrey, Michael},
	month = oct,
	year = {2012},
	keywords = {Diffraction gratings, Multiple scattering, Position sensitive detectors, Surface scattering, X-ray scattering},
	pages = {103906},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/X9KGNHFV/Wernecke et al. - 2012 - Direct structural characterisation of line grating.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/PEZX8EP3/1.html:text/html}
}

@article{albert_self-assembly_2010-1,
	title = {Self-assembly of block copolymer thin films},
	volume = {13},
	issn = {1369-7021},
	doi = {10.1016/S1369-7021(10)70106-1},
	abstract = {Block copolymers self-assemble on nanometer length scales, making them ideal for emerging nanotechnologies. Many applications (e.g., templating, membranes) require the use of block copolymers in thin film geometries (∼100 nm thickness), where self-assembly is strongly influenced by surface energetics. In this review, we discuss the roles of surface and interfacial effects on self-assembly, with a specific focus on confinement, substrate surface modification, and thermal and solvent annealing conditions. Finally, we comment on novel techniques for manipulating and characterizing thin films, motivating the use of gradient and high-throughput methods for gaining a comprehensive picture of self-assembly to enable advanced nanotechnologies.},
	number = {6},
	urldate = {2015-01-07},
	journal = {Materials Today},
	author = {Albert, Julie N. L. and Epps III, Thomas H.},
	month = jun,
	year = {2010},
	pages = {24--33},
	file = {ScienceDirect Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/FJNKZ2UR/Albert und Epps III - 2010 - Self-assembly of block copolymer thin films.pdf:application/pdf;ScienceDirect Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/BZJHPI7X/S1369702110701061.html:text/html}
}

@article{vineyard_grazing-incidence_1982,
	title = {Grazing-incidence diffraction and the distorted-wave approximation for the study of surfaces},
	volume = {26},
	doi = {10.1103/PhysRevB.26.4146},
	abstract = {A method is developed for calculating the scattering of a beam of x rays striking the plane surface of a crystal at an angle below the critical angle for total external reflection. The low penetration under this condition offers the possibility of determining the special structure of the surface layers, as has been pointed out by Marra, Eisenberger, and Cho. A distorted-wave approach is developed whereby the crystal is first taken to be a homogeneous dielectric slab for the purpose of calculating the distorted wave. The distorted wave is considered to illuminate the actual crystal, from which a scattering pattern can then be calculated. The effects of absorption can be taken into account; in some cases absorption may offer the possibility of observing near-surface structures at angles of incidence larger than the critical angle. Such illumination may also be useful for performing fluorescence analysis of the near-surface layers to determine their impurity content. Synchrotron sources offer new opportunities for measurements of these kinds. Thermal neutrons may also be used in place of x rays and offer unique opportunities for studying surface magnetization and, through inelastic scattering, surface phonons and, conceivably, surface magnons.},
	number = {8},
	urldate = {2014-11-20},
	journal = {Phys. Rev. B},
	author = {Vineyard, George H.},
	month = oct,
	year = {1982},
	pages = {4146--4159},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/W2IVJM53/PhysRevB.26.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/CGWI4RAJ/Vineyard - 1982 - Grazing-incidence diffraction and the distorted-wa.pdf:application/pdf}
}

@article{vineyard_grazing-incidence_1982-1,
	title = {Grazing-incidence diffraction and the distorted-wave approximation for the study of surfaces},
	volume = {26},
	doi = {10.1103/PhysRevB.26.4146},
	abstract = {A method is developed for calculating the scattering of a beam of x rays striking the plane surface of a crystal at an angle below the critical angle for total external reflection. The low penetration under this condition offers the possibility of determining the special structure of the surface layers, as has been pointed out by Marra, Eisenberger, and Cho. A distorted-wave approach is developed whereby the crystal is first taken to be a homogeneous dielectric slab for the purpose of calculating the distorted wave. The distorted wave is considered to illuminate the actual crystal, from which a scattering pattern can then be calculated. The effects of absorption can be taken into account; in some cases absorption may offer the possibility of observing near-surface structures at angles of incidence larger than the critical angle. Such illumination may also be useful for performing fluorescence analysis of the near-surface layers to determine their impurity content. Synchrotron sources offer new opportunities for measurements of these kinds. Thermal neutrons may also be used in place of x rays and offer unique opportunities for studying surface magnetization and, through inelastic scattering, surface phonons and, conceivably, surface magnons.},
	number = {8},
	urldate = {2014-11-20},
	journal = {Physical Review B},
	author = {Vineyard, George H.},
	month = oct,
	year = {1982},
	pages = {4146--4159},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/X4TJMJ4A/PhysRevB.26.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/ISIP2JUE/Vineyard - 1982 - Grazing-incidence diffraction and the distorted-wa.pdf:application/pdf}
}

@article{grigorescu_resists_2009,
	title = {Resists for sub-20-nm electron beam lithography with a focus on {HSQ}: state of the art},
	volume = {20},
	issn = {0957-4484},
	shorttitle = {Resists for sub-20-nm electron beam lithography with a focus on {HSQ}},
	doi = {10.1088/0957-4484/20/29/292001},
	abstract = {In the past decade, the feature size in ultra large-scale integration (ULSI) has been continuously decreasing, leading to nanostructure fabrication. Nowadays, various lithographic techniques ranging from conventional methods (e.g. photolithography, x-rays) to unconventional ones (e.g. nanoimprint lithography, self-assembled monolayers) are used to create small features. Among all these, resist-based electron beam lithography (EBL) seems to be the most suitable technique when nanostructures are desired. The achievement of sub-20-nm structures using EBL is a very sensitive process determined by various factors, starting with the choice of resist material and ending with the development process. After a short introduction to nanolithography, a framework for the nanofabrication process is presented. To obtain finer patterns, improvements of the material properties of the resist are very important. The present review gives an overview of the best resolution obtained with several types of both organic and inorganic resists. For each resist, the advantages and disadvantages are presented. Although very small features (2–5 nm) have been obtained with PMMA and inorganic metal halides, for the former resist the low etch resistance and instability of the pattern, and for the latter the delicate handling of the samples and the difficulties encountered in the spinning session, prevent the wider use of these e-beam resists in nanostructure fabrication. A relatively new e-beam resist, hydrogen silsesquioxane (HSQ), is very suitable when aiming for sub-20-nm resolution. The changes that this resist undergoes before, during and after electron beam exposure are discussed and the influence of various parameters (e.g. pre-baking, exposure dose, writing strategy, development process) on the resolution is presented. In general, high resolution can be obtained using ultrathin resist layers and when the exposure is performed at high acceleration voltages. Usually, one of the properties of the resist material is improved to the detriment of another. It has been demonstrated that aging, baking at low temperature, immediate exposure after spin coating, the use of a weak developer and development at a low temperature increase the sensitivity but decrease the contrast. The surface roughness is more pronounced at low exposure doses (high sensitivity) and high baking temperatures. A delay between exposure and development seems to increase both contrast and the sensitivity of samples which are stored in a vacuum after exposure, compared to those stored in air. Due to its relative novelty, the capabilities of HSQ have not been completely explored, hence there is still room for improvement. Applications of this electron beam resist in lithographic techniques other than EBL are also discussed. Finally, conclusions and an outlook are presented.},
	language = {en},
	number = {29},
	urldate = {2014-11-13},
	journal = {Nanotechnology},
	author = {Grigorescu, A. E. and Hagen, C. W.},
	month = jul,
	year = {2009},
	pages = {292001},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/H9UZ8HM7/Grigorescu und Hagen - 2009 - Resists for sub-20-nm electron beam lithography wi.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/CWQVURTX/292001.html:text/html}
}

@article{soltwisch_nanometrology_2014,
	title = {Nanometrology on gratings with {GISAXS}: {FEM} reconstruction and fourier analysis},
	shorttitle = {Nanometrology on gratings with {GISAXS}},
	doi = {10.1117/12.2046212},
	urldate = {2014-11-13},
	journal = {Proc. SPIE 9050},
	author = {Soltwisch, Victor and Wernecke, Jan and Haase, Anton and Probst, J{\"u}rgen and Schoengen, Max and Krumrey, Michael and Scholze, Frank},
	editor = {Cain, Jason P. and Sanchez, Martha I.},
	month = apr,
	year = {2014},
	pages = {905012},
	file = {Nanometrology on gratings with GISAXS\: FEM reconstruction and fourier analysis | (2014) | Soltwisch | Publications | Spie:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/B8Z3EN4B/12.html:text/html}
}

@article{hofmann_grazing_2009-1,
	title = {Grazing incident small angle x-ray scattering: {A} metrology to probe nanopatterned surfaces},
	volume = {27},
	issn = {2166-2746, 2166-2754},
	shorttitle = {Grazing incident small angle x-ray scattering},
	doi = {10.1116/1.3253608},
	abstract = {Grazing incident small angle x-ray scattering (GISAXS) and transmission small angle x-ray scattering studies have been carried out on periodic patterns on silicon substrates in order to determine the average morphology and arrangement of the patterned features. The GISAXS pattern exhibited rods of scattering at Bragg positions, discrete and evenly spaced, in the surface plane. The scattered intensity modulations along each rod have been compared with simulated scattering from simple geometrical patterns to obtain quantitative information on the diameter, width, height, and sidewall inclination of the pillars and gratings. The results are in good agreement with real space images obtained with SEM and demonstrate that GISAXS is a powerful technique for characterizing nanoscale arrays used in patterned media, photonics structures, and electronics structures.},
	number = {6},
	urldate = {2014-11-17},
	journal = {J. Vac. Sci. Technol. B},
	author = {Hofmann, T. and Dobisz, E. and Ocko, B. M.},
	month = nov,
	year = {2009},
	keywords = {Form factors, Scanning electron microscopy, Surface patterning, Surface scattering, X-ray scattering},
	pages = {3238--3243},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/DRRE2UUW/Hofmann et al. - 2009 - Grazing incident small angle x-ray scattering A m.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/NMIRMAHG/1.html:text/html}
}

@article{markov_limits_2014,
	title = {Limits on fundamental limits to computation},
	volume = {512},
	copyright = {© 2014 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
	issn = {0028-0836},
	doi = {10.1038/nature13570},
	abstract = {An indispensable part of our personal and working lives, computing has also become essential to industries and governments. Steady improvements in computer hardware have been supported by periodic doubling of transistor densities in integrated circuits over the past fifty years. Such Moore scaling now requires ever-increasing efforts, stimulating research in alternative hardware and stirring controversy. To help evaluate emerging technologies and increase our understanding of integrated-circuit scaling, here I review fundamental limits to computation in the areas of manufacturing, energy, physical space, design and verification effort, and algorithms. To outline what is achievable in principle and in practice, I recapitulate how some limits were circumvented, and compare loose and tight limits. Engineering difficulties encountered by emerging technologies may indicate yet unknown limits.},
	language = {en},
	number = {7513},
	urldate = {2015-05-28},
	journal = {Nature},
	author = {Markov, Igor L.},
	month = aug,
	year = {2014},
	keywords = {Applied physics, Computer science, Electrical and electronic engineering},
	pages = {147--154},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/GHHUZJ74/Markov - 2014 - Limits on fundamental limits to computation.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/QGZ42ZSN/nature13570.html:text/html}
}

@article{guinier_small-angle_1955,
	title = {Small-angle scattering of {X}-rays},
	language = {en},
	journal = {Wiley},
	author = {Guinier, Andr\'e and Fournet, G\'erard},
	year = {1955},
	keywords = {X-rays}
}

@article{yoneda_anomalous_1963-1,
	title = {Anomalous {Surface} {Reflection} of {X} {Rays}},
	volume = {131},
	doi = {10.1103/PhysRev.131.2010},
	abstract = {An asymmetric surface reflection of x rays was found. It was experimentally determined that this anomalously reflected wave has almost the same wavelength as the incident wave. The angle of this reflection changes only slightly with the incident angle and the crystal structure of the sample in the measured angular range. The glancing angle of this reflection increases with the wavelength of the incident x rays. According to measurements on evaporated surfaces of metallic elements, these reflection angles were found to have an important relation to the periodic system of the elements.},
	number = {5},
	urldate = {2014-11-20},
	journal = {Physical Review},
	author = {Yoneda, Y.},
	month = sep,
	year = {1963},
	pages = {2010--2013},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/K6GIWARN/PhysRev.131.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/U6PFA6JA/Yoneda - 1963 - Anomalous Surface Reflection of X Rays.pdf:application/pdf}
}

@book{guinier_small-angle_1955-1,
	title = {Small-angle scattering of {X}-rays},
	language = {en},
	publisher = {Wiley},
	author = {Guinier, Andr\'e and Fournet, G\'erard},
	year = {1955},
	keywords = {X-rays}
}

@article{henke_x-ray_1993,
	title = {X-{Ray} {Interactions}: {Photoabsorption}, {Scattering}, {Transmission}, and {Reflection} at {E} = 50-30,000 {eV}, {Z} = 1-92},
	volume = {54},
	issn = {0092-640X},
	doi = {http://dx.doi.org/10.1006/adnd.1993.1013},
	number = {2},
	journal = {Atomic Data and Nuclear Data Tables},
	author = {Henke, B. L. and Gullikson, E. M. and Davis, J. C.},
	year = {1993},
	pages = {181 -- 342}
}

@article{gollmer_fabrication_2014-1,
	series = {Micro/{Nano} {Devices} and {Systems} 2013},
	title = {Fabrication and characterization of combined metallic nanogratings and {ITO} electrodes for organic photovoltaic cells},
	volume = {119},
	issn = {0167-9317},
	doi = {10.1016/j.mee.2014.03.042},
	abstract = {Organic photovoltaic devices are interesting alternatives to conventional silicon based photovoltaic cells, due to potentially lower material costs and energy consumption during the fabrication process. However, the energy conversion efficiency of organic photovoltaic cells may still be improved. One possible approach is a combination with metallic nanostructures to improve light absorption properties in the active layer. We report on the fabrication and characterization of metallic nanogratings integrated with an indium tin oxide (ITO) electrode to be combined with small-molecule organic photovoltaic cells. With respect to geometry and extinction properties gratings fabricated by two different fabrication methods, conventional electron beam lithography and nanoimprint lithography, are presented. Furthermore, gratings fabricated on top of ITO are compared to gratings integrated both below and within ITO electrodes. Fabricating structures below or within electrodes is advantageous for organic thin film techniques to avoid compromising the crystallinity of the organic thin film and short-circuiting across the thin layer.},
	urldate = {2014-12-01},
	journal = {Microelectronic Engineering},
	author = {Gollmer, D. A. and Walter, F. and Lorch, C. and Nov\'ak, J. and Banerjee, R. and Dieterle, J. and Santoro, G. and Schreiber, F. and Kern, D. P. and Fleischer, M.},
	month = may,
	year = {2014},
	keywords = {Extinction spectroscopy, GISAXS, Nano imprint lithography, Organic photovoltaics, Plasmonic nanogratings, Plasmonic solar cells},
	pages = {122--126},
	file = {ScienceDirect Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/DVWTNST2/S0167931714001373.html:text/html}
}

@article{binnig_surface_1982,
	title = {Surface {Studies} by {Scanning} {Tunneling} {Microscopy}},
	volume = {49},
	doi = {10.1103/PhysRevLett.49.57},
	abstract = {Surface microscopy using vacuum tunneling is demonstrated for the first time. Topographic pictures of surfaces on an atomic scale have been obtained. Examples of resolved monoatomic steps and surface reconstructions are shown for (110) surfaces of CaIrSn4 and Au.},
	number = {1},
	urldate = {2015-01-07},
	journal = {Physical Review Letters},
	author = {Binnig, G. and Rohrer, H. and Gerber, Ch. and Weibel, E.},
	month = jul,
	year = {1982},
	pages = {57--61},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/2MZC83XT/PhysRevLett.49.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/AIP6N3ER/Binnig et al. - 1982 - Surface Studies by Scanning Tunneling Microscopy.pdf:application/pdf}
}

@article{baumbach_grazing_1999-1,
	title = {Grazing incidence diffraction by laterally patterned semiconductor nanostructures},
	volume = {32},
	issn = {0022-3727},
	doi = {10.1088/0022-3727/32/6/020},
	abstract = {A theoretical study of grazing incidence diffraction by laterally patterned epitaxial nanostructures is presented and successfully applied to experimental findings of pseudomorphic multilayer gratings. Numerical results from a distorted wave Born approximation are given. The grating structure generates a fine structure around the reciprocal lattice points consisting of grating truncation rods, which are similar to the crystal truncation rod of a planar crystal surface. We show the influence of the grating shape, the compositional profile and the lattice strain on the intensity pattern along the grating truncation rods. The effect of lattice strain will be discussed by comparing the fully strained state (tetragonal lattice distortion), uniform strain relaxation and graduated strain relaxation in the surface grating. Our theoretical treatment allows us to interpret grazing incidence diffraction measurements obtained from strained layer gratings and superlattice gratings.},
	language = {en},
	number = {6},
	urldate = {2015-04-09},
	journal = {J. Phys. D},
	author = {Baumbach, T. and L\'ubbert, D.},
	month = mar,
	year = {1999},
	pages = {726},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/CVE3PF6S/Baumbach und Lübbert - 1999 - Grazing incidence diffraction by laterally pattern.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/WI3RPD5Q/020.html:text/html}
}

@article{wang_characterization_2007-1,
	title = {Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering},
	volume = {102},
	issn = {0021-8979, 1089-7550},
	doi = {10.1063/1.2753588},
	abstract = {To meet the challenges in dimensional metrology as the minimum feature size in semiconductor devices approaches sub-35 nm length scales, we have been developing a nondestructive method using x rays termed critical dimension small angle x-ray scattering (SAXS). Its capacity to quantify the dimension of linewidth, pitch, line height, and sidewall angle of line gratings has been demonstrated. In this work, we have further extended its capabilities to quantify the correlated line-edge roughness (LER) and linewidthroughness (LWR). Model line grating patterns with controlled LER and LWR were prepared and measured using x ray, their results were analyzed with model calculations. The magnitude of LER/LWR deduced from x-ray results compares favorably with the scanning electron microscopy results obtained from the same samples. An apparent Debye–Waller factor, which can be deduced from the SAXS data without any detailed model-based calculations, is found to be a convenient parameter to quantify the amplitude of LER/LWR.},
	number = {2},
	urldate = {2015-04-23},
	journal = {Journal of Applied Physics},
	author = {Wang, Chengqing and Jones, Ronald L. and Lin, Eric K. and Wu, Wen-Li and Rice, Bryan J. and Choi, Kwang-Woo and Thompson, George and Weigand, Steven J. and Keane, Denis T.},
	month = jul,
	year = {2007},
	keywords = {Diffraction gratings, Linewidths, Photoresistors, Scanning electron microscopy, X-ray scattering},
	pages = {024901},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/F66ISPEE/Wang et al. - 2007 - Characterization of correlated line edge roughness.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/JVI54D7Z/1.html:text/html}
}

@article{senn_fabrication_2011,
	title = {Fabrication of photonic crystals for applications in the visible range by {Nanoimprint} {Lithography}},
	volume = {9},
	issn = {1569-4410},
	doi = {10.1016/j.photonics.2011.04.007},
	abstract = {The integration of photonic crystals into optical circuits is a decisive factor for further development of photonic crystal applications. The feasibility of these applications depends on fabrication technologies suitable for mass production. In this work, we used Nanoimprint Lithography (NIL) for the fabrication of photonic crystal structures for applications in the visible range. The photonic crystals were integrated into waveguides in order to characterize the created system. The waveguides have dimensions of up to 50 μm whereas the holes in the photonic crystals have dimensions of 80 nm. Due to parameter optimization photonic crystal structures and the corresponding waveguides could be replicated with high accuracy. For the fabrication of the photonic crystal structures a Si substrate with an oxide and a nitride layer was used. A poly-methyl-methacrylate (PMMA) layer was spincoated onto this substrate. A stamp containing the negative structures was fabricated using Electron Beam Lithography (EBL). This stamp was used for imprinting the structures into the PMMA layer. The structures were than transferred into the nitride layer using reactive ion etching (RIE). The underlying oxide layer was used as a sacrificial layer to achieve a nitride membrane. The fabricated structures were characterized by measuring the transmission spectra. The results were compared favorably to a simulation and a photonic band gap (PBG) in the range of 670 nm to 780 nm has been observed.},
	number = {3},
	urldate = {2014-10-28},
	journal = {Photonics and Nanostructures - Fundamentals and Applications},
	author = {Senn, T. and Bischoff, J. and N\"usse, N. and Schoengen, M. and L{\"o}chel, B.},
	month = jul,
	year = {2011},
	keywords = {Nanoimprint Lithography, Photonic crystal, Visible range},
	pages = {248--254},
	file = {ScienceDirect Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/EN8Z6VWQ/S1569441011000459.html:text/html}
}

@article{raman_new_1928-1,
	title = {A new radiation},
	number = {2},
	journal = {Indian Journal of physics},
	author = {Raman, Chandrasekhara Venkata},
	year = {1928},
	pages = {387--398}
}

@article{wang_resonance-enhanced_1992,
	title = {Resonance-enhanced x-rays in thin films: a structure probe for membranes and surface layers},
	volume = {258},
	issn = {0036-8075, 1095-9203},
	shorttitle = {Resonance-enhanced x-rays in thin films},
	doi = {10.1126/science.1439784},
	abstract = {An x-ray resonance effect in an organic thin film on an x-ray reflecting mirror is reported. The resonance effect is the result of interference between reflected and refracted x-rays at the air-organic thin film interface and occurs at incident angles slightly above the critical angle of the film. In excellent agreement with theory, the primary resonant x-ray electric field that is confined in the organic thin film is approximately 20 times as intense as the electric field of the incident beam when measured at a position close to the center of the film. Resonance-enhanced x-rays can be used to characterize the internal structure of Langmuir-Blodgett thin film membranes. This effect may also find use in x-ray-based thin film devices and in the structural analysis of adlayers and surfaces that have thus far proved difficult, if not impossible, to study because of sensitivity limitations.},
	language = {en},
	number = {5083},
	urldate = {2015-04-08},
	journal = {Science},
	author = {Wang, J. and Bedzyk, M. J. and Caffrey, M.},
	month = oct,
	year = {1992},
	pmid = {1439784},
	pages = {775--778},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/SPGP9NDN/Wang et al. - 1992 - Resonance-enhanced x-rays in thin films a structu.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/R7MTPKAR/775.html:text/html}
}

@article{carlisle_off--shelf_2001-1,
	title = {An {Off}-{The}-{Shelf} {PSO}},
	number = {1-6},
	journal = {Proceedings of the 2001 Workshop on Particle Swarm Optimization},
	author = {Carlisle, A. and Dozier, G.},
	year = {2001}
}

@article{hlaing_nanoimprint-induced_2011-1,
	title = {Nanoimprint-{Induced} {Molecular} {Orientation} in {Semiconducting} {Polymer} {Nanostructures}},
	volume = {5},
	issn = {1936-0851},
	doi = {10.1021/nn202515z},
	abstract = {The morphology and orientation of thin films of the polymer poly-3(hexylthiophene)?important parameters influencing electronic and photovoltaic device performance?have been significantly altered through nanoimprinting with 100 nm spaced grooves. Grazing-incidence small-angle X-ray scattering studies demonstrate the excellent fidelity of the pattern transfer, while wide-angle scattering convincingly shows an imprinting-induced π?π reorientation and polymer backbone alignment along the imprinted grooves. Surprisingly, temperature-dependent scattering measurements indicate that the imprinted induced orientation and alignment remain intact even at temperatures where the imprinted topographical features nearly vanish.},
	number = {9},
	urldate = {2015-05-29},
	journal = {ACS Nano},
	author = {Hlaing, Htay and Lu, Xinhui and Hofmann, Tommy and Yager, Kevin G. and Black, Charles T. and Ocko, Benjamin M.},
	month = sep,
	year = {2011},
	pages = {7532--7538},
	file = {ACS Full Text PDF w/ Links:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/Q7E8G8G5/Hlaing et al. - 2011 - Nanoimprint-Induced Molecular Orientation in Semic.pdf:application/pdf;ACS Full Text Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/8PQP4P8B/nn202515z.html:text/html}
}

@article{tolan_x-ray_1995,
	title = {X-ray diffraction from laterally structured surfaces: {Total} external reflection},
	volume = {51},
	shorttitle = {X-ray diffraction from laterally structured surfaces},
	doi = {10.1103/PhysRevB.51.2239},
	abstract = {In this work x-ray-diffraction measurements from GaAs surface gratings are presented. The experiments were performed using a three-crystal diffractometer. Measurements in the region of total external reflection (small incidence angles) for five samples were done and compared with model calculations based on a dynamical scattering theory. The theory is able to explain all experiments quantitatively. Mesoscopic grating parameters as well as microscopic surface roughnesses of the samples were obtained from fits of the data. For three samples scanning-electron-microscope pictures were taken. The analysis of these pictures leads to the same mesoscopic parameters as obtained from x-ray diffraction.},
	number = {4},
	urldate = {2014-11-17},
	journal = {Phys. Rev. B},
	author = {Tolan, M. and Press, W. and Brinkop, F. and Kotthaus, J. P.},
	month = jan,
	year = {1995},
	pages = {2239--2251},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/XQCPSICZ/PhysRevB.51.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/PFFUW3P8/Tolan et al. - 1995 - X-ray diffraction from laterally structured surfac.pdf:application/pdf}
}

@article{ardenne_elektronen-rastermikroskop_1938-1,
	title = {Das {Elektronen}-{Rastermikroskop}},
	volume = {109},
	issn = {0044-3328},
	doi = {10.1007/BF01341584},
	language = {de},
	number = {9-10},
	urldate = {2015-01-07},
	journal = {Zeitschrift f{\"u}r Physik},
	author = {Ardenne, Manfred von},
	month = sep,
	year = {1938},
	keywords = {Elementary Particles and Nuclei, Nuclear Fusion, Nuclear Physics, Heavy Ions, Hadrons},
	pages = {553--572},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/54SKNN6Z/Ardenne - 1938 - Das Elektronen-Rastermikroskop.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/PD3ISI8T/10.html:text/html}
}

@article{thostenson_advances_2001-1,
	title = {Advances in the science and technology of carbon nanotubes and their composites: a review},
	volume = {61},
	issn = {0266-3538},
	shorttitle = {Advances in the science and technology of carbon nanotubes and their composites},
	doi = {10.1016/S0266-3538(01)00094-X},
	number = {13},
	urldate = {2015-01-07},
	journal = {Composites Science and Technology},
	author = {Thostenson, Erik T and Ren, Zhifeng and Chou, Tsu-Wei},
	month = oct,
	year = {2001},
	pages = {1899--1912}
}

@book{_nanoscience_2004-1,
	title = {Nanoscience and {Nanotechnologies}: {Opportunities} and {Uncertainties}},
	isbn = {9780854036042},
	shorttitle = {Nanoscience and {Nanotechnologies}},
	abstract = {Report on the current state of scientific knowledge about nanotechnologies, how they might be used in the future, and potential health, safety, environmental, ethical and societal implications.},
	language = {en},
	publisher = {Royal Society},
	year = {2004}
}

@book{pietsch_high-resolution_2004-1,
	title = {High-{Resolution} {X}-{Ray} {Scattering}: {From} {Thin} {Films} to {Lateral} {Nanostructures}},
	isbn = {9780387400921},
	shorttitle = {High-{Resolution} {X}-{Ray} {Scattering}},
	abstract = {During the last 20 years interest in high-resolution x-ray diffractometry and reflectivity has grown as a result of the development of the semiconductor industry and the increasing interest in material research of thin layers of magnetic, organic, and other materials. For example, optoelectronics requires a subsequent epitaxy of thin layers of different semiconductor materials. Here, the individuallayer thicknesses are scaled down to a few atomic layers in order to exploit quantum effects. For reasons of electronic and optical confinement, these thin layers are embedded within much thicker cladding layers or stacks of multilayers of slightly different chemical composition. It is evident that the interface quality of those quantum weHs is quite important for the function of devices. Thin metallic layers often show magnetic properties which do not ap pear for thick layers or in bulk material. The investigation of the mutual interaction of magnetic and non-magnetic layers leads to the discovery of colossal magnetoresistance, for example. This property is strongly related to the thickness and interface roughness of covered layers.},
	language = {en},
	publisher = {Springer Science \& Business Media},
	author = {Pietsch, Ullrich and Hol\'y, Vaclav and Baumbach, Tilo},
	month = aug,
	year = {2004},
	keywords = {Technology \& Engineering / Electronics / General, Technology \& Engineering / Manufacturing, Technology \& Engineering / Materials Science, Technology \& Engineering / Nanotechnology \& MEMS, Technology \& Engineering / Optics}
}

@article{markov_limits_2014-1,
	title = {Limits on fundamental limits to computation},
	volume = {512},
	copyright = {{\textbackslash}copyright 2014 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
	issn = {0028-0836},
	doi = {10.1038/nature13570},
	abstract = {An indispensable part of our personal and working lives, computing has also become essential to industries and governments. Steady improvements in computer hardware have been supported by periodic doubling of transistor densities in integrated circuits over the past fifty years. Such Moore scaling now requires ever-increasing efforts, stimulating research in alternative hardware and stirring controversy. To help evaluate emerging technologies and increase our understanding of integrated-circuit scaling, here I review fundamental limits to computation in the areas of manufacturing, energy, physical space, design and verification effort, and algorithms. To outline what is achievable in principle and in practice, I recapitulate how some limits were circumvented, and compare loose and tight limits. Engineering difficulties encountered by emerging technologies may indicate yet unknown limits.},
	language = {en},
	number = {7513},
	urldate = {2015-05-28},
	journal = {Nature},
	author = {Markov, Igor L.},
	month = aug,
	year = {2014},
	keywords = {Applied physics, Computer science, Electrical and electronic engineering},
	pages = {147--154},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/4XZXDFU8/Markov - 2014 - Limits on fundamental limits to computation.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/3FJ85I4T/nature13570.html:text/html}
}

@article{tolan_x-ray_1995-1,
	title = {X-ray diffraction from laterally structured surfaces: {Total} external reflection},
	volume = {51},
	shorttitle = {X-ray diffraction from laterally structured surfaces},
	doi = {10.1103/PhysRevB.51.2239},
	abstract = {In this work x-ray-diffraction measurements from GaAs surface gratings are presented. The experiments were performed using a three-crystal diffractometer. Measurements in the region of total external reflection (small incidence angles) for five samples were done and compared with model calculations based on a dynamical scattering theory. The theory is able to explain all experiments quantitatively. Mesoscopic grating parameters as well as microscopic surface roughnesses of the samples were obtained from fits of the data. For three samples scanning-electron-microscope pictures were taken. The analysis of these pictures leads to the same mesoscopic parameters as obtained from x-ray diffraction.},
	number = {4},
	urldate = {2014-11-17},
	journal = {Physical Review B},
	author = {Tolan, M. and Press, W. and Brinkop, F. and Kotthaus, J. P.},
	month = jan,
	year = {1995},
	pages = {2239--2251},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/CKJSFXBG/PhysRevB.51.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/E2EHF6XE/Tolan et al. - 1995 - X-ray diffraction from laterally structured surfac.pdf:application/pdf}
}

@article{jiang_waveguide-enhanced_2011-1,
	title = {Waveguide-enhanced grazing-incidence small-angle x-ray scattering of buried nanostructures in thin films},
	volume = {84},
	doi = {10.1103/PhysRevB.84.075440},
	abstract = {X-ray standing waves generated by the interference of the scattered x rays from parallel surfaces of a thin film, the so-called waveguide effect, can be used to enhance or reduce the scatterings from certain depths of the film. Used in combination with grazing-incidence small-angle x-ray scattering, this resonance effect provides depth sensitivity to extract buried structures in thin films of polymer and polymer/nanoparticle nanocomposite, which are not readily accessible by most surface techniques, such as scanning probe microscopy. We developed a rigorous theory of the diffuse scattering in the framework of the distorted-wave Born approximation using a discretization method analogous to Parratt's recursive formalism. In such a case, the distortion of the electric field of the unperturbed state from the nanostructures of interest is considered in a self-consistent manner. This theory allows a quantitative determination of the buried nanostructures when the x-ray waveguide enhancement is present or the size of the nanostructures of interest is comparable to or larger than the spatial frequency of electric-field intensity modulation. A unique capability afforded by this theory is that a nanometer or even subnanometer spatial resolution can be achieved in the depth information of the buried nanostructures, along with the in-plane correlation of the structures.},
	number = {7},
	urldate = {2015-03-04},
	journal = {Physical Review B},
	author = {Jiang, Zhang and Lee, Dong Ryeol and Narayanan, Suresh and Wang, Jin and Sinha, Sunil K.},
	month = aug,
	year = {2011},
	pages = {075440},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/HHJJUDFJ/PhysRevB.84.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/3IK63VXX/Jiang et al. - 2011 - Waveguide-enhanced grazing-incidence small-angle x.pdf:application/pdf}
}

@article{binnig_surface_1982-1,
	title = {Surface {Studies} by {Scanning} {Tunneling} {Microscopy}},
	volume = {49},
	doi = {10.1103/PhysRevLett.49.57},
	abstract = {Surface microscopy using vacuum tunneling is demonstrated for the first time. Topographic pictures of surfaces on an atomic scale have been obtained. Examples of resolved monoatomic steps and surface reconstructions are shown for (110) surfaces of CaIrSn4 and Au.},
	number = {1},
	urldate = {2015-01-07},
	journal = {Physical Review Letters},
	author = {Binnig, G. and Rohrer, H. and Gerber, Ch. and Weibel, E.},
	month = jul,
	year = {1982},
	pages = {57--61},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/QFB42Z7C/PhysRevLett.49.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/2KDH39VV/Binnig et al. - 1982 - Surface Studies by Scanning Tunneling Microscopy.pdf:application/pdf}
}

@article{holy_nonspecular_1994-1,
	title = {Nonspecular x-ray reflection from rough multilayers},
	volume = {49},
	doi = {10.1103/PhysRevB.49.10668},
	abstract = {X-ray reflection from periodical multilayers with randomly rough interfaces has been described within the distorted-wave Born approximation. The method is suitable for calculating both specular x-ray reflection and nonspecular (diffuse) scattering. In this paper, both in-plane and vertical correlations of the roughness profiles have been considered and it has been demonstrated that the vertical roughness correlation substantially affects the nonspecular scattering. The theory can explain resonant effects observed in the beam scattered nonspecularly from a periodical multilayer. The theoretical approach has been used for the study of interfacial roughness in a long-periodic AlAs/GaAs multilayer and good agreement has been achieved between the experimental results and the theory.},
	number = {15},
	urldate = {2015-01-06},
	journal = {Physical Review B},
	author = {Hol\'y, V. and Baumbach, T.},
	month = apr,
	year = {1994},
	pages = {10668--10676},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/6BDPXNBC/PhysRevB.49.html:text/html}
}

@article{kaganer_bragg_1995-1,
	title = {Bragg diffraction peaks in x-ray diffuse scattering from multilayers with rough interfaces},
	volume = {52},
	doi = {10.1103/PhysRevB.52.16369},
	abstract = {The peaks in x-ray diffuse scattering appearing due to diffraction of incident or scattered waves on a periodically layered structure are sensitive to the perfection of multilayers. These peaks are investigated analytically and compared with numerical calculations. It is shown that, if the roughness of periodic interfaces is not correlated, the peaks follow the intensity of the x-ray standing wave on the interfaces. Interference effects due to correlated interfacial roughness can change the sense of the peak (sequence of maximum and minimum). The factors controlling the peak sense are derived and applied to explain the results of numerical calculations.},
	number = {23},
	urldate = {2015-03-03},
	journal = {Physical Review B},
	author = {Kaganer, V. M. and Stepanov, S. A. and Koehler, R.},
	month = dec,
	year = {1995},
	pages = {16369--16372},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/TE2M5Z5G/PhysRevB.52.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/JV5GXHN3/Kaganer et al. - 1995 - Bragg diffraction peaks in x-ray diffuse scatterin.pdf:application/pdf}
}

@article{soccio_assessment_2014-1,
	title = {On the assessment by grazing-incidence small-angle {X}-ray scattering of replica quality in polymer gratings fabricated by nanoimprint lithography},
	volume = {47},
	issn = {1600-5767},
	doi = {10.1107/S160057671400168X},
	number = {2},
	urldate = {2015-01-07},
	journal = {Journal of Applied Crystallography},
	author = {Soccio, M. and Alayo, N. and Mart\'in-Fabiani, I. and Rueda, D. R. and Garc\'ia-Guti\'errez, M. C. and Rebollar, E. and Martínez-Tong, D. E. and P\'erez-Murano, F. and Ezquerra, T. A.},
	month = apr,
	year = {2014},
	pages = {613--618},
	file = {On the assessment by grazing-incidence small-angle X-ray scattering of replica quality in polymer gratings fabricated by nanoimprint lithography:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/V5EGZ3TV/paper.html:text/html}
}

@article{zhang_addressing_2014-1,
	title = {Addressing {FinFET} metrology challenges in 1× node using tilt-beam critical dimension scanning electron microscope},
	volume = {13},
	issn = {1932-5150},
	doi = {10.1117/1.JMM.13.4.041407},
	language = {en},
	number = {4},
	urldate = {2014-11-26},
	journal = {Journal of Micro/Nanolithography, MEMS, and MOEMS},
	author = {Zhang, Xiaoxiao and Zhou, Hua and Ge, Zhenhua and Vaid, Alok and Konduparthi, Deepasree and Osorio, Carmen and Ventola, Stefano and Meir, Roi and Shoval, Ori and Kris, Roman and Adan, Ofer and Bar-Zvi, Maayan},
	month = oct,
	year = {2014},
	pages = {041407},
	file = {Addressing FinFET metrology challenges in 1× node using tilt-beam critical dimension scanning electron microscope | (2014) | Zhang | Publications | Spie:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/HEWW2GW2/1.JMM.13.4.html:text/html}
}

@article{rauscher_small-angle_1995-1,
	title = {Small-angle x-ray scattering under grazing incidence: {The} cross section in the distorted-wave {Born} approximation},
	volume = {52},
	shorttitle = {Small-angle x-ray scattering under grazing incidence},
	doi = {10.1103/PhysRevB.52.16855},
	abstract = {The specular and nonspecular intensity of x rays scattered from a rough surface with fluctuations in the electron density is calculated in the distorted-wave Born approximation. The contributions to the nonspecular intensity of roughness and density fluctuations can be separated. The structure factor is given by a convolution integral of the Fourier transform of the density correlation function. Special geometries of density fluctuations are discussed.},
	number = {23},
	urldate = {2015-01-07},
	journal = {Phys. Rev. B},
	author = {Rauscher, M. and Salditt, T. and Spohn, H.},
	month = dec,
	year = {1995},
	pages = {16855--16863},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/3CDCVAG3/PhysRevB.52.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/EDN4APX5/Rauscher et al. - 1995 - Small-angle x-ray scattering under grazing inciden.pdf:application/pdf}
}

@article{guinier_diffraction_1939-1,
	title = {La {Diffraction} des {Rayons} {X} aux {Très} {Faibles} {Angles}: {Applications} à l'{Etude} des {Phénomènes} {Ultra}-microscopiques},
	volume = {12},
	journal = {Ann. de. Phy. (Paris)},
	author = {Guinier, Andr\'e},
	year = {1939},
	pages = {161}
}

@article{hu_small_2004-1,
	title = {Small angle x-ray scattering metrology for sidewall angle and cross section of nanometer scale line gratings},
	volume = {96},
	issn = {0021-8979, 1089-7550},
	doi = {10.1063/1.1773376},
	abstract = {High-volume fabrication of nanostructures requires nondestructive metrologies capable of measuring not only the pattern size but also the pattern shape profile. Measurement tool requirements will become more stringent as the feature size approaches 50 nm and tolerances of pattern shape will reach a few nanometers. A small angle x-ray scattering (SAXS) based technique has been demonstrated to have the capability of characterizing the average pitch size and pattern width to subnanometer precision. In this study, we report a simple, modeling-free protocol to extract cross-section information such as the average sidewall angle and the pattern height of line gratingpatterns from the SAXS data. Diffraction peak intensities and reciprocal space positions are measured while the sample is rotated around the axis perpendicular to the grating direction. Linear extrapolations of peak positions in reciprocal space allow a precise determination of both the sidewall angle and the pattern height.},
	number = {4},
	urldate = {2015-05-29},
	journal = {Journal of Applied Physics},
	author = {Hu, Tengjiao and Jones, Ronald L. and Wu, Wen-li and Lin, Eric K. and Lin, Qinghuang and Keane, Denis and Weigand, Steve and Quintana, John},
	month = aug,
	year = {2004},
	keywords = {Diffraction gratings, Metrology, Nanopatterning, X-ray diffraction, X-ray scattering},
	pages = {1983--1987},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/PAMHW75S/Hu et al. - 2004 - Small angle x-ray scattering metrology for sidewal.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/WTDPJMXA/1.html:text/html}
}

@article{rosei_nanostructured_2004-1,
	title = {Nanostructured surfaces: challenges and frontiers in nanotechnology},
	volume = {16},
	issn = {0953-8984},
	shorttitle = {Nanostructured surfaces},
	doi = {10.1088/0953-8984/16/17/001},
	abstract = {Nanostructured surfaces can be broadly defined as substrates in which the typical features have dimensions in the range 1–100 nm (although the upper limit of 100 nm may be relaxed to greater sizes in some cases, depending on the material and the specific property being investigated). The recent surge of interest in these systems stems from the remarkable effects that may arise from the critical size reduction. Interesting novel properties (catalytic, magnetic, ferroelectric, mechanical, optical and electronic) occur as we reduce the dimensions from a practically infinite (and periodic) solid crystal to a system composed of a relatively small number of atoms. So far, nanostructured materials or nanomaterials are perhaps the only sub-field of nanoscience that has made the transition from fundamental science to real world applications, thus becoming a technology (a good example of this are nanostructured surface coatings). This paper describes some selected examples of recent progress in the study of nanostructured surfaces. Surface reconstructions, which occur either naturally or as a consequence of the interaction with adsorbates, are discussed because of their importance in model chemical reactions and for their potential use as templates for the ordered growth of nanostructures. Supramolecular assemblies and molecular nanostructures, resulting from the balance between molecule–molecule and molecule–surface interactions, are described because of their fundamental interest and their potential use in nanoelectronic devices. Recent progress in the growth of semiconductor nanostructures, in particular Ge–Si and InAs–GaAs, is briefly reviewed. A few selected examples of nanostructured functional materials, such as ferroelectric and magnetic nanostructures, are discussed in view of their potential for applications in future data storage devices. Nanostructured materials used in catalysis and gas sensor applications are briefly described. Finally, perspectives and future challenges in this emerging field of research are also discussed.},
	language = {en},
	number = {17},
	urldate = {2014-11-14},
	journal = {Journal of Physics: Condensed Matter},
	author = {Rosei, Federico},
	month = may,
	year = {2004},
	pages = {S1373},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/P8EWT9BI/Rosei - 2004 - Nanostructured surfaces challenges and frontiers .pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/NB5DNZU6/001.html:text/html}
}

@article{kato_effect_2010-1,
	title = {Effect of line roughness on the diffraction intensities in angular resolved scatterometry},
	volume = {49},
	doi = {10.1364/AO.49.006102},
	abstract = {Scatterometry is a common technique for the characterization of nanostructured surfaces. With shrinking dimensions, fewer and fewer propagating diffraction orders exist, and structure roughness becomes more important. Recent investigations suggest that roughness has to be taken into account for structure reconstruction. The short wavelength of the extreme UV (EUV) is advantageous, since it provides more propagating diffraction orders as compared to UV and visible radiation and increases the sensitivity to small structural features, particularly roughness. We present a method to numerically estimate changes in measured diffraction intensities in angular resolved EUV scatterometry induced by line roughness. The model can be used to include the estimation of the roughness into the structure reconstruction algorithm.},
	number = {31},
	urldate = {2014-11-17},
	journal = {Applied Optics},
	author = {Kato, Akiko and Scholze, Frank},
	month = nov,
	year = {2010},
	keywords = {roughness, Scattering measurements, Scattering theory, Surface measurements},
	pages = {6102--6110},
	file = {Appl. Opt. Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/S9ZUP8GA/abstract.html:text/html}
}

@article{kendrew_three-dimensional_1958-1,
	title = {A {Three}-{Dimensional} {Model} of the {Myoglobin} {Molecule} {Obtained} by {X}-{Ray} {Analysis}},
	volume = {181},
	copyright = {© 1958 Nature Publishing Group},
	doi = {10.1038/181662a0},
	language = {en},
	number = {4610},
	urldate = {2015-05-27},
	journal = {Nature},
	author = {Kendrew, J. C. and Bodo, G. and Dintzis, H. M. and Parrish, R. G. and Wyckoff, H. and Phillips, D. C.},
	month = mar,
	year = {1958},
	pages = {662--666},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/R3EAZ3HK/Kendrew et al. - 1958 - A Three-Dimensional Model of the Myoglobin Molecul.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/FE8ZMIKW/181662a0.html:text/html}
}

@article{wang_resonance-enhanced_1992-1,
	title = {Resonance-enhanced x-rays in thin films: a structure probe for membranes and surface layers},
	volume = {258},
	issn = {0036-8075, 1095-9203},
	shorttitle = {Resonance-enhanced x-rays in thin films},
	doi = {10.1126/science.1439784},
	abstract = {An x-ray resonance effect in an organic thin film on an x-ray reflecting mirror is reported. The resonance effect is the result of interference between reflected and refracted x-rays at the air-organic thin film interface and occurs at incident angles slightly above the critical angle of the film. In excellent agreement with theory, the primary resonant x-ray electric field that is confined in the organic thin film is approximately 20 times as intense as the electric field of the incident beam when measured at a position close to the center of the film. Resonance-enhanced x-rays can be used to characterize the internal structure of Langmuir-Blodgett thin film membranes. This effect may also find use in x-ray-based thin film devices and in the structural analysis of adlayers and surfaces that have thus far proved difficult, if not impossible, to study because of sensitivity limitations.},
	language = {en},
	number = {5083},
	urldate = {2015-04-08},
	journal = {Science},
	author = {Wang, J. and Bedzyk, M. J. and Caffrey, M.},
	month = oct,
	year = {1992},
	pmid = {1439784},
	pages = {775--778},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/X8CJSEK4/Wang et al. - 1992 - Resonance-enhanced x-rays in thin films a structu.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/SVKM8MVA/775.html:text/html}
}

@article{binnig_atomic_1986-1,
	title = {Atomic {Force} {Microscope}},
	volume = {56},
	doi = {10.1103/PhysRevLett.56.930},
	abstract = {The scanning tunneling microscope is proposed as a method to measure forces as small as 10−18 N. As one application for this concept, we introduce a new type of microscope capable of investigating surfaces of insulators on an atomic scale. The atomic force microscope is a combination of the principles of the scanning tunneling microscope and the stylus profilometer. It incorporates a probe that does not damage the surface. Our preliminary results in air demonstrate a lateral resolution of 30 ÅA and a vertical resolution less than 1 Å.},
	number = {9},
	urldate = {2015-01-07},
	journal = {Physical Review Letters},
	author = {Binnig, G. and Quate, C. F. and Gerber, Ch.},
	month = mar,
	year = {1986},
	pages = {930--933},
	file = {APS Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/XN3PJVNP/PhysRevLett.56.html:text/html;Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/E34IKFXA/Binnig et al. - 1986 - Atomic Force Microscope.pdf:application/pdf}
}

@article{wernecke_direct_2012-1,
	title = {Direct structural characterisation of line gratings with grazing incidence small-angle x-ray scattering},
	volume = {83},
	issn = {0034-6748, 1089-7623},
	doi = {10.1063/1.4758283},
	abstract = {Grazing incidence small-angle x-ray scattering (GISAXS) and x-ray reflectometry (XRR) have been used to investigate structural parameters, especially period length, line width, groove width, and line height, of grating test structures in the sub-micron range. The gratings are e-beam written structures on a quartz substrate with a fixed period length, but different line and groove widths, covered by a layer of ruthenium. A Ru layer thickness of 9.4 nm has been determined with XRR. GISAXS was performed in two orientations, with an incident beam alignment perpendicular and parallel to the grating lines. The scattering patterns in parallel orientation have been analysed without numerical simulation by Fourier transformation. The obtained results for line and groove width are in good agreement with nominal values. The analysis method has been validated by analysing simulated scattering data. A superposition of scattering intensities measured for different azimuthal rotation angles close to parallel alignment was used to determine the line height of a grating of 27.3 nm, which is also close to the nominal value. The Fourier analysis procedure opens up the possibility of traceable structure determination with GISAXS in the nanometre range.},
	number = {10},
	urldate = {2015-01-07},
	journal = {Rev. Sci. Instrum.},
	author = {Wernecke, Jan and Scholze, Frank and Krumrey, Michael},
	month = oct,
	year = {2012},
	keywords = {Diffraction gratings, Multiple scattering, Position sensitive detectors, Surface scattering, X-ray scattering},
	pages = {103906},
	file = {Full Text PDF:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/DEFNDBQW/Wernecke et al. - 2012 - Direct structural characterisation of line grating.pdf:application/pdf;Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/MN83HDKG/1.html:text/html}
}

@article{schadle_domain_2007,
	title = {Domain decomposition method for {Maxwell}'s equations: {Scattering} off periodic structures},
	volume = {226},
	issn = {0021-9991},
	shorttitle = {Domain decomposition method for {Maxwell}'s equations},
	doi = {10.1016/j.jcp.2007.04.017},
	abstract = {We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). An adaptive strategy to determine optimal PML parameters is developed. Thus we can treat Wood anomalies appearing in periodic structures. We focus on the application to typical EUV lithography line masks. Light propagation within the multilayer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer.},
	number = {1},
	urldate = {2014-10-28},
	journal = {Journal of Computational Physics},
	author = {Sch{\"a}dle, Achim and Zschiedrich, Lin and Burger, Sven and Klose, Roland and Schmidt, Frank},
	month = sep,
	year = {2007},
	keywords = {Conical diffraction, Domain decomposition, Electro-magnetic scattering, EUV, Finite elements, Lithography, Maxwell's equations, Perfectly matched layer method},
	pages = {477--493},
	file = {ScienceDirect Snapshot:/Users/victorsoltwisch/Library/Application Support/Zotero/Profiles/opjo1xqf.default/zotero/storage/XBB778RP/S0021999107001684.html:text/html}
}

@article{wang_saxs_2007,
	title = {Characterization
of correlated line edge roughness of nanoscale line gratings
using small angle x-ray scattering},
	volume = {102},
	journal = {J. Appl. Phys.},
	author = {Wang, C. and Jones, R. L. and Lin, E. K. and Wu, W. and  Rice, B. J. and Choi, K. and Thompson, G. and Weigand, S. J. and Keane, D. T.},
	year = {2007},
	pages = {024901},
}
@article{Babonneau:hx5104,
author = "Babonneau, David",
title = "{{\it FitGISAXS}: software package for modelling and analysis of GISAXS data using IGOR Pro}",
journal = "J. Appl. Cryst.",
year = "2010",
volume = "43",
number = "4",
pages = "929--936",
month = "Aug",
abstract = {A software package for performing modelling and analysis of GISAXS (grazing-incidence small-angle X-ray scattering) data within the distorted-wave Born approximation has been developed using the IGOR Pro scripting language (http://www.wavemetrics.com). The tool suite uses a slab-model approach with the Ab{\'{e}}l{\`{e}}s matrix method to calculate X-ray reflectivity curves, electric field intensity distributions and GISAXS intensities from supported or buried scatterers arranged in two or three dimensions in a stratified medium. Models are included to calculate the scattered intensity for monodisperse, polydisperse and interacting particles with various size distributions, form factors and structure factors. The source code for the entire package is freely available, allowing anyone to develop additional tools.},
keywords = {X-ray scattering, distorted-wave Born approximation},
}

@article{Babonneau_PhysRevB,
  title = {Waveguiding and correlated roughness effects in layered nanocomposite thin films studied by grazing-incidence small-angle x-ray scattering},
  author = {Babonneau, D. and Camelio, S. and Lantiat, D. and Simonot, L. and Michel, A.},
  journal = {Phys. Rev. B},
  volume = {80},
  issue = {15},
  pages = {155446},
  numpages = {12},
  year = {2009},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.80.155446},
  url = {http://link.aps.org/doi/10.1103/PhysRevB.80.155446}
}
@Article{V.Soltwisch2018,
  author    = {V. Soltwisch and P. H\"{o}nicke and Y. Kayser and J. Eilbracht and J. Probst and F. Scholze and B. Beckhoff},
  title     = {Element sensitive reconstruction of nanostructured surfaces with finite-elements and grazing incidence soft X-ray fluorescence},
  journal   = {Nanoscale},
  year      = {2018},
  volume    = {10},
  pages     = {6177-6185},
  doi       = {10.1039/C8NR00328A},
  file      = {:c8nr00328a.pdf:PDF},
  groups    = {meine Paper, 7.24 Paper, GIXRF},
  owner     = {phoenick},
  timestamp = {2018-01-03},
}
@article{Lazzari:vi0158,
author = "Lazzari, R{\'{e}}mi",
title = "{{\it IsGISAXS}: a program for grazing-incidence small-angle X-ray scattering analysis of supported islands}",
journal = "J. Appl. Cryst.",
year = "2002",
volume = "35",
number = "4",
pages = "406--421",
month = "Aug",
abstract = {This paper describes a Fortran program, {\it IsGISAXS}, for the simulation and analysis of grazing-incidence small-angle X-ray scattering (GISAXS) of islands supported on a substrate. As is usual in small-angle scattering of particles, the scattering cross section is expressed in terms of an island form factor and interference function. However, the emphasis is placed on the specificity of the grazing-incidence geometry, in particular in the evaluation of the island form factor in the distorted-wave Born approximation. A library of simple geometrical shapes is available. A full account of size and possible shape distributions is given in the decoupling approximation, where sizes and positions are not correlated, and in the local monodisperse approximation. Two types of island repartitions on the substrate are considered: disordered systems characterized by their particle{--}particle pair correlation functions, and bidimensional crystalline or paracrystalline systems of particles.},
keywords = {grazing-incidence small-angle X-ray scattering, surface, island growth, nanostructures},
}
@article{Jones_2006,
author = {Jones, R. and Hu, T. and Soles, C. and Lin, K. and Reano, M. and Pang,S. and and Casa,D.},
title = {Real-Time Shape Evolution of Nanoimprinted Polymer Structures during Thermal Annealing},
journal = {Nano Let.},
volume = {6},
number = {8},
pages = {1723-1728},
year = {2006},

}

@article {Meier_2012,
author = {Meier, R. and Chiang, H. and Ruderer, M. and Guo, S. and K{\"o}rstgens, V. and Perlich, J. and M{\"u}ller-Buschbaum, P.},
title = {In situ film characterization of thermally treated microstructured conducting polymer films},
journal = {J. Polym. Sci. Part B Polym. Phys.},
volume = {50},
number = {9},
publisher = {Wiley Subscription Services, Inc., A Wiley Company},
pages = {631--641},
keywords = {conducting polymers, crystallization, GISAXS, microstructure, thermal annealing, thin film},
year = {2012},
}

@Article{Nikulaev2019,
  author    = {K. V. Nikolaev and V. Soltwisch and P. Hönicke and F. Scholze and J. de la Rie and S. N. Yakunin and I. A. Makhotkin and R. W. E. van de Kruijs and F. Bijkerk},
  title     = {A semi-analytical approach for the characterization of ordered 3D nano structures using grazing-incidence X-ray fluorescence},
  journal   = {Journal of Synchrotron Radiation},
  year      = {2020},
  volume    = {27},
  number    = {2},
  pages     = {386--395},
  month     = {feb},
  doi       = {10.1107/S1600577519016345},
  file      = {:hf5393.pdf:PDF},
  groups    = {meine Paper, 7.24 Paper},
  publisher = {International Union of Crystallography ({IUCr})},
  timestamp = {2020-03-08},
}
@article{honicke_grazing_2020,
  author      = {P. Hönicke and A. Andrle and Y. Kayser and K.V. Nikolaev and J. Probst and F. Scholze and V. Soltwisch and T. Weimann and B. Beckhoff},
  journal     = {Nanotechnology},
  title       = {Grazing incidence-X-ray fluorescence for a dimensional and compositional characterization of well-ordered 2D and 3D nanostructures},
  year        = {2020},
  month       = {sep},
  number      = {50},
  pages       = {505709},
  volume      = {31},
  doi         = {10.1088/1361-6528/abb557},
  file        = {:PHoenicke_Nanotechn_2020.pdf:PDF},
  genehmigung = {1},
  groups      = {meine Paper, GIXRF, XRR},
  pdf         = {PHoenicke_Nanotechn_2020.pdf},
  publica     = {noch nicht},
  publisher   = {{IOP} Publishing},
  timestamp   = {2020-10-06},
}
@article{kennedy_oxidation_1999,
	title = {Oxidation of silicon nitride films in an oxygen plasma},
	volume = {85},
	issn = {0021-8979, 1089-7550},
	url = {http://aip.scitation.org/doi/10.1063/1.369678},
	doi = {10.1063/1.369678},
	language = {en},
	number = {6},
	urldate = {2020-10-09},
	journal = {Journal of Applied Physics},
	author = {Kennedy, G. P. and Buiu, O. and Taylor, S.},
	month = mar,
	year = {1999},
	pages = {3319--3326},
	file = {Kennedy et al. - 1999 - Oxidation of silicon nitride films in an oxygen pl.pdf:/home/andrle01/Zotero/storage/FX3JL92W/Kennedy et al. - 1999 - Oxidation of silicon nitride films in an oxygen pl.pdf:application/pdf}
}
@Comment{jabref-meta: databaseType:bibtex;}
