Document [original]

Laboratory based GIXRF and GEXRF spectrometers

for multilayer structure investigations

Veronika Szwedowski-Rammert, *

Jonas Baumann,

Christopher Schlesiger,

Ulrich Waldschl¨

ager,

Armin Gross,

Birgit Kanngießer

and Ioanna Mantouvalou

This work reports laboratory angle resolved measurements with the goal of establishing laboratory

techniques to obtain a more complete idea of the intralayer composition of multilayer samples. While X-

ray reﬂectometry is a widely available technique for the characterization of multilayer samples, angle

resolved XRF measurements (grazing emission/incidence X-ray ﬂuorescence) are usually performed at

synchrotron radiation facilities. With the development of eﬃcient laboratory spectrometers and

evaluation algorithms for angle resolved measurements, these methods become suited for routine

measurements and screening. We present two laboratory spectrometers which make quantitative non-

destructive elemental depth proﬁling feasible. For reasons of comparison a validation sample, a nickel–

carbon multilayer sample, is measured with both setups and additional information on krypton

contamination and its distribution is retrieved. Additionally, the ﬁrst application for the characterization of

multilayer structures with sub-nanometer layer thicknesses is shown.

Introduction

In the non-destructive characterization of multilayer structures,

the X-ray reectometry (XRR) method is widely used in indus-

trial and scientic applications. In XRR measurements, X-ray

radiation is directed onto a sample at varying incidence

angles and the reected radiation is detected with a photo-

diode. The measurements can be performed at synchrotron

radiation facilities

1,2

as well as with benchtop instruments.

3,4

Due to the broad applications of XRR, several codes for the

quantication of the measurements exist, with IMD

5,6

being the

most popular. Though, as has been shown in ref. 7 and 8,

relying solely on XRR measurements for the characterization of

complex, stratied materials is insuﬃcient. The number of

degrees of freedom in the quantication rises rapidly with the

complexity of the sample, calling for complementary measure-

ments. A possible way of obtaining element specic in-depth

information from the sample non-destructively is the use of

angle resolved X-ray uorescence (XRF) methods.

As in XRR, X-

ray radiation is used, though not the reected radiation but the

element specicuorescence radiation emitted from the

sample is detected. This provides additional information about

the composition of the investigated sample since the elemental

distribution is measured. Contamination as well as intermixing

regions can be characterized. Several studies have already

combined XRR with grazing incidence XRF analysis.

10–12

Grazing angles refer to the angular range from below the

angle of total reection up to a few multiples of the value of the

angle of total reection. Depending on the energy of the inci-

dent beam and the investigated material, it is the angular range

where interference eﬀects from the samples are observable.

Angular resolution of XRF measurements can be achieved in

a twofold manner: by varying the shallow incidence angle of the

primary X-ray radiation on the sample (grazing incidence X-ray

uorescence: GIXRF) or by measuring the uorescence radia-

tion from the sample at distinct shallow emission angles

(grazing emission X-ray uorescence: GEXRF). Both methods

yield equivalent information about the sample as was shown in

ref. 13.

A benecial phenomenon for analysis occurring in both

angle resolved measurements when the interfaces of the layers

are smooth is an enhancement of excitation due to the forma-

tion of X-ray standing waves (XSW) within the sample. In the

case of GIXRF the incident X-ray beam can interfere with the

beam reected at layer boundaries

and therefore constructive

and destructive interference nodes are formed. Essential for the

standing wave eld is a monochromatic primary beam with low

divergence. Contrarily, in GEXRF measurements the quality of

the primary beam is not crucial for interference to occur. In that

case, the probability density functions of the possible paths of

the uorescence radiation released by atoms within a layer can

interfere. This eﬀect is known as the Kossel eﬀect

and can be

observed under the grazing emission conditions in all

Technische Universit¨

at Berlin, Hardenbergstr. 36, 10623 Berlin, Germany. E-mail:

jonas.baumann@physik.tu-berlin.de

Bruker Nano GmbH, Am Studio 2D, 12489 Berlin, Germany

Cite this: J. Anal. At. Spectrom.,2019,

34,922

Received 5th December 2018

Accepted 4th February 2019

DOI: 10.1039/c8ja00427g

rsc.li/jaas

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investigations with beams that excite uorescence radiation

from atoms of the sample (protons,

electrons,

and

photons

17,18

The result of both angle resolved techniques is an angular

prole where the intensity of a given uorescence line of

a specic element is shown for each measured angle. Since each

angle corresponds to a diﬀerent penetration or information

depth for a given sample, a depth-resolved elemental prole can

be calculated. Additional conclusions about the sample may be

drawn from interference structures in the GI- or GEXRF prole

in the case of multilayer samples. The position of the structures

depends on the thickness of the layers of the sample. Rough-

ness and interdiﬀusion between the layers decrease the ampli-

tude of the structures and a density variation shis the position

of the angle of total reection.

In the following, measurements of a validation sample with

a laboratory GEXRF and a commercial GIXRF setup and the

respective quantication routines are presented. The goal is to

ensure a reliable characterization of these laboratory setups,

which is crucial for the quantication of unknown samples

beyond synchrotron radiation measurements. The measure-

ments show the capabilities of these laboratory spectrometers,

their strengths, challenges and benets.

Laboratory setups for angle resolved XRF

Angle resolved XRF methods are dominantly applied at

synchrotron radiation facilities. The high ux of the X-ray beam

and a small focus size are benecial for fast and precise

measurements of X-ray uorescence. However, a rapid devel-

opment of laboratory equipment in recent years accompanied

by the improvement of eﬃcient evaluation algorithms enables

angle resolved measurements in the laboratory with compa-

rable angular resolution and statistics.

This has the potential

to expand the availability of these methods for a broader range

of users. Especially in the development of new, more eﬃcient

multilayer structures with high reectivity complementary

methods to XRR are benecial for the characterization of

interlayer diﬀusion, contaminations and roughness.

Grazing incidence X-ray uorescence

In GIXRF measurements the incidence angle of the radiation on

the sample is varied in a range depending on the beam's energy

and the investigated sample's material(s). Most commonly,

a GIXRF scan starts below the angle of total reection and

surpasses it.

To benet from the interference eﬀect enhance-

ment resulting from the formation of X-ray standing waves,

GIXRF measurements are usually performed with mono-

chromatized radiation either from an X-ray tube

or at

synchrotron radiation facilities.

The sample is tilted with

respect to the beam at dened angles and the uorescence

radiation is detected above the sample with an energy dispersive

detector, see Fig. 1. In most setups the detector is a silicon dri

detector, SDD. The achievable angular resolution is limited by

the divergence of the X-ray beam used and inuences the

intensity of the interference patterns. It is thus crucial to char-

acterize the divergence of a GIXRF setup to distinguish between

the eﬀect it has on the prole and the damping resulting from

roughness or intermixing of the interfaces of the layers. With

the NANOHUNTER II from Rigaku and the BRUKER S4 T-STAR,

benchtop GIXRF setups have become commercially available.

Grazing emission X-ray uorescence

GEXRF measurements are typically performed with the primary

X-ray radiation incident on the sample at angles much larger

than the angle of total external reection. Two possible setups

with distinct congurations are established to detect the uo-

rescence radiation from the sample at grazing emission angles:

the conventional and the so-called scan-free approach. In the

former the radiation is detected with an SDD and the angular

resolution is achieved e.g. by placing a slit in front of the

detector.

The detector or sample is moved to measure the

angular prole. The angular resolution that can be achieved is

usually limited by the slit system. Additionally, the sensitivity of

such a setup is low due to the small solid angle of detection.

These limitations prompted the development of the scan-free

GEXRF (SF-GEXRF) setup,

where the slit-detection unit is

replaced with a 2D area detector. This facilitates the recording

of several angles in one measurement without the necessity to

move parts of the setup. This version of a GEXRF setup is shown

in Fig. 2. A crucial condition to perform energy dispersive SF-

GEXRF experiments is that all photons counted by the

detector in each frame are well separated from the adjacent

photons. If this is satised, the energy and position of the

photon detected by the CCD can be reconstructed. Thus, several

frames are recorded, with the number of frames depending on

the required statistics. To full the single photon condition

either the exposure time of each frame or (if possible) the ux of

the source can be regulated.

A signicant benet of GEXRF compared to GIXRF follows

from the investigation of samples at normal incidence in the

former. This enables the scanning of laterally inhomogeneous

samples, since the footprint on the sample is smaller than that

for grazing incidence conditions as the beam is not broadened

Fig. 1 Schematic representation of the GIXRF measurement geom-

etry. The incident beam of the primary radiation on the sample is varied

by either changing the position of the X-ray source or tilting the

sample relative to the beam. The ﬂuorescence radiation from the

sample is detected in a short distance above the surface with an SDD

detector.

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by the shallow incidence angle. This was used to map impurities

in silicon wafers.

While the SF-GEXRF setup was rst

successfully introduced at a synchrotron radiation facility

could be transferred to the laboratory. Measurements were

performed in the soX-ray range

as well as with poly-

chromatic radiation in the hard X-ray range.

Materials and methods

For the validation of the laboratory angle resolved XRF tech-

niques a nickel–carbon (NiC) multilayer manufactured by AXO

DRESDEN is chosen. The carbon/nickel bi-layer structure is

repeated 15 times on a silicon substrate. From XRR measure-

ments performed by the manufacturer and evaluated with the

IMD soware package the bi-layer thickness is calculated to be

5.55 nm, with 2.42 nm for nickel and 3.13 nm for carbon. This

sample is well suited for validation purposes since a sharp

interference structure forms due to its smooth interfaces on the

X-ray wavelength length scale and neglectable interdiﬀusion.

Laboratory grazing incidence X-ray uorescence

The GIXRF scans are performed with a commercial BRUKER S4

T-STAR. This setup was developed for total reection XRF

analysis of trace elements and a new feature allows the execu-

tion of angular scans. The molybdenum Ka-line (17.4 keV) is

used as the excitation radiation, which is monochromatized

and focused on the sample with parabolic graded multilayer

optics. The beam shape is calculated by measuring the FWHM

of the beam with a CCD camera at diﬀerent distances from the

monochromator. It is determined to be Gaussian in the x-

direction with a FWHM of 100 10 mm and a rectangular

function in the y-direction with a width of 5.62 0.01 mm in the

focus. From the same measurement, beam divergence in the x-

direction is calculated to be FWHM ¼0.25 0.06 mrad. From

that the angular resolution of the GIXRF measurements can be

calculated to be FWHM ¼0.0140.003since beam diver-

gence is the limiting factor. The sample is placed on a robotic

arm and the uorescence radiation detected with an SSD

detector. The robotic arm positions the sample beneath the

SDD and tilts the sample relative to the X-ray beam about the y-

axis to perform a GIXRF scan. The SDD detector is also tilted

with the sample. Due to the shallow incidence angles the foot-

print on the sample changes during the measurement. In this

case this concerns the x-direction of the beam, thus only the

divergence in this axis is considered in calculations. The GIXRF

scan of the NiC multilayer sample is executed in an angular

range from 0up to 0.6with a detector real time of 10 seconds

and a step size of 0.001. Considering motor movements this

results in an overall measurement time of 125 minutes. In view

of the step size exceeding the limitations imposed by beam

divergence, measurements with a larger step size would be

appropriate. The divergence calculations were performed aer

the measurements, and thus this discrepancy. Including these

considerations an improvement of measurement time by

a factor of 10 is not only achievable in this case but also rational.

For each angular position a distinct spectrum is recorded and

Fig. 3 shows the sum spectrum of the whole measurement

depicted in blue. The energy resolution is 150 eV@Ni Ka.

Laboratory grazing emission X-ray uorescence

The laboratory scan-free GEXRF spectrometer for hard X-rays is

set up at the Berlin Laboratory for innovative X-ray technologies

(BLiX). An X-ray tube with a rhodium target operated at 50 kV

and 600 mA is equipped with a polycapillary lens to focus the

Fig. 2 Schematic representation of the SF-GEXRF measurement

geometry. The primary radiation is incident on the sample at a ﬁxed

angle, usually 90. The ﬂuorescence radiation from the sample is

detected with a position and energy sensitive detector. The geometry

of the setup remains ﬁxed throughout the measurement in which

several CCD frames are recorded. For each ﬂuorescence line a CCD

frame solely containing the events with the respective energy is

created in the evaluation. Here, the CCD frame for a Ni Kaﬂuores-

cence line is shown. The GEXRF proﬁle is calculated from the CCD

frame by summing the events along isoangular lines as indicated by the

Ni Kaproﬁle on the right.

Fig. 3 Sum spectra of the GI- and GEXRF measurements. The GIXRF

sum spectrum (blue) is generated from 600 individual spectra recor-

ded during a scan in the range 0–0.6with a step size of 0.001. For

the GEXRF sum spectrum (red) 2200 CCD frames were evaluated. The

elemental labels are indicated in red if the element can only be found

in the GEXRF sum spectrum, blue if solely the GIXRF spectrum shows

it, and black when the element is present in both sum spectra.

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radiation to the pivotal point of a vacuum chamber.

A back

illuminated deep-depletion CCD (BI Princeton PI-SX:1300) with

1340 1300 pixels, each with the dimensions of 20 mm20

mm, is used to detect the uorescence radiation from the

sample. The deep-depleted sensor of the CCD is a crucial

improvement of the setup compared to the rst proof-of-

principle measurements published in ref. 24, since hard X-

rays of up to 20 keV are detected. Throughout the measure-

ment the CCD’s temperature was set to 45 C and was moni-

tored to ensure an unchanged dark current. To achieve an

angular resolution of below 0.005the CCD is mounted 57 cm

away from the sample. This resolution is required to resolve ne

interference structures in the GEXRF prole of the multilayer

(corresponding to Kiessig fringes in XRR) and can be calculated

from trigonometric considerations when the pixel size of the

CCD is known. For this specic measurement the covered

angular range is 2.2(0–1.4shown in Fig. 4 top) and the

angular resolution is 0.005. For the SF-GEXRF measurement

a total number of 2200 CCD frames and additionally 18 dark

frames are recorded. The exposure time is 3 seconds and a read-

out speed of 1 MHz is used. This results in an overall

measurement time of 160 minutes. The GEXRF frames are dark

frame corrected, which means that from each pixel a median

value calculated from the dark frames for the respective pixel is

subtracted. Furthermore, from the dark frames the standard

deviation of each pixel is calculated and used as a threshold to

evaluate the CCD frames. Thus, there is a necessity to ensure

a constant temperature throughout the measurement. The

clustering PEE algorithm

is applied and on average 600 events

are registered in one GEXRF frame. The sum spectrum of the

NiC multilayer is calculated and shown in Fig. 3 depicted in red.

The energy resolution is 306 eV@Ni Ka.

Comparison of the sum spectra of GI- and GEXRF

measurements

Both sum spectra show nickel, silicon and scattering peaks

from the primary radiation as expected. In the sum spectrum of

the laboratory SF-GEXRF measurement there are multiple lines

which do not originate from the sample (aluminum, chromium,

etc.) and which are missing in the GIXRF spectrum. The pres-

ence of these lines results from the primary radiation scattered

from the sample exciting uorescence radiation from the walls

of the experimental chamber. The small detector–sample

distance in the GIXRF setup prevents such artefacts in the

respective sum spectrum. On the other hand, the GIXRF sum

spectrum contains a prominent krypton peak that cannot be

assigned to artifacts originating from the setup. Krypton is used

as the sputtering gas in the magnetron sputtering process of

manufacturing the sample, and hence it is present in the

sample. In the SF-GEXRF measurement a CCD is used as

a detector and the quantum eﬃciency of such detectors dras-

tically decreases for energies above 10 keV.

Thus, the statistics

of the SF-GEXRF measurement are insuﬃcient for the detection

of the krypton peak at 12.6 keV. Moreover, the polycapillary lens

in the GEXRF setup has a neglectable transmission above 20

keV, additionally limiting the excitation of krypton. The GIXRF

measurements are performed in air (which explains the pres-

ence of argon) and a beryllium window is in front of the

detector. This all together prevents the detection of low Z

elements and the L-line of nickel in the GIXRF experiment. The

fact that carbon could not be measured in the in-vacuum SF-

GEXRF experiment is a result of using hard X-rays as the exci-

tation radiation and additionally the prominent noise peak for

low X-ray energies. The lines not assigned to any element in

both sum spectra are either escape or pile-up peaks. Even

though the measurement time of the SF-GEXRF measurement

is longer, the GIXRF measurement has better statistics. This

results from the small solid angle of detection of the measure-

ment in the SF-GEXRF case. Improving this factor or more

eﬃcient excitation of uorescence radiation would signicantly

improve the statistics of the SF-GEXRF measurement.

Angular GI- and GEXRF proles

From the measured spectra angular XRF proles for each

measurement and each relevant element are generated. In the

Fig. 4 Angle resolved elemental proﬁles of the NiC multilayer. For the

SF-GEXRF measurements (top) only the Ni Kaﬂuorescence line proﬁle

is shown. An angular resolution of 0.005enables the discrimination of

ﬁne interference structures not visible in the respective GIXRF proﬁle

(bottom). The GIXRF proﬁles of the Ni Ka(green) and Si K (red) ﬂuo-

rescence lines are shown. The proﬁle of silicon is multiplied by a factor

5 to display it in one plot with nickel.

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case of the GIXRF measurement each spectrum recorded at

each respective angle is deconvolved with a code provided by the

manufacturer. The calculated intensity of the individual

elemental lines is plotted over the angular position of the cor-

responding measurement.

Contrarily, in the SF-GEXRF measurements only the Ni Ka

uorescence line prole is shown. This results from the absorp-

tion of the silicon uorescence line due to the extended paths

through the sample at low emission angles. The intensity of the

detected silicon signal starts rising at around 1.7.Noadditional

information can be extracted from the measured silicon prole

range in the SF-GEXRF case, consequently it is not shown or

discussed further. To generate the SF-GEXRF prole a region-of-

interest (ROI) around the Ni Kauorescence line peak is chosen

(7.07–7.69 keV) and the 2200 CCD frames aer dark frame

correction are searched for events within this ROI. A new CCD

frame is generated and at the x,y-position of each Ni Kauo-

rescence photon detection position in the recorded CCD frames

the value of the corresponding pixel in the new frame is increased

by one. As a result, a CCD image with the interaction positions of

all Ni Kauorescence photons is generated. This image is shown

in Fig. 2 on the CCD. To calculate a GEXRF prole from the CCD

image the pixels are summed along isoangular lines and each

pixel intensity is normalized to its solid angle of detection

resulting in a GEXRF prole as depicted next to the ROI image in

Fig. 2. The geometrical information necessary to perform these

calculations is gathered beforehand in a calibration routine.

These geometrical parameters are the distance between the

sample and the detector and the tilt of the CCD since the CCD’s

position cannot be adjusted once mounted on the chamber.

Additionally, with these parameters the angular range covered in

one scan and the theoretical angular resolution of the measure-

ment can be calculated.

The resulting GIXRF proles of silicon and nickel are shown

in the bottom of Fig. 4, where the intensity of silicon is multi-

plied by a factor 5 to display the proles clearly in one plot. The

rapid increase of intensity above 0.1occurs when the angle of

total reection is surpassed and the signal from the depth of the

sample is detected. The prominent interference structure with

a minimum at 0.38and a maximum at 0.42in the nickel

prole corresponds to angles where the intensity of the

standing wave eld in the nickel layers is the largest and

smallest, respectively. The top of that gure shows the SF-

GEXRF prole of the Ni Kauorescence line with the equiva-

lent interference structure and additionally a substructure of

ne oscillations. These correspond to the Kiessig fringes visible

in XRR measurements between two reectivity maxima.

Only

those maxima in the angular prole correspond to minima in

the XRR prole and vice versa. What additionally can be seen in

this prole is that for higher angles angle resolved proles

become approximately constant. Compared to the SF-GEXRF, in

the GIXRF prole no ne interference structure can be detected.

This is mainly caused by the lower angular resolution due to the

beam divergence of this setup. This decreases the amplitude of

the structure and is a crucial factor in GIXRF setups.

To measure the interference fringes a combination of suﬃ-

cient temporal and spatial coherence needs to be considered.

The temporal coherence is mainly inuenced by the natural line

width which is a comparable factor for both angle resolved

setups. In the GIXRF setup, this concerns the characteristic

emission lines from the X-ray tube. The applied multilayer

optics is adapted for the respective energy, and the brems-

strahlung background within the bandwidth of the multilayer is

negligible. In GEXRF the temporal coherence is given by the

natural line width of the uorescence radiation if the detector’s

energy resolution is suﬃcient to isolate the line. Contrarily,

spatial coherence is inuenced by angular resolution. This

means divergence of the incidence beam in GIXRF and the

geometry of the setup (pixel size and detector–sample distance)

for GEXRF. Thus, these factors are entirely setup dependent and

there always is a compromise between setup eﬃciency and

angular resolution.

Comparison with simulations

The quantication of angle resolved measurements can be

performed by varying the parameters of a simulated sample to

achieve an agreement with the measured proles. This requires

well-known and well-characterized instrumental parameters of

the setup.

In the demonstrated case a well-characterized

sample, the NiC multilayer, is used to validate the established

experimental parameters of the introduced setups. The data

from the XRR measurements of the NiC multilayer are applied

to perform simulations of the angular proles with an in-house

code based on the solution of the Sherman equation:

the

xrfLibrary. However, the simple Sherman approach is insuﬃ-

cient if an X-ray standing wave eld is formed in the sample. In

that case reection and refraction need to be additionally

considered. In the xrfLibrary the algorithm introduced by de

Boer

9,14

is used in the case of GIXRF and of Urbach and de

Bokx

for GEXRF. The code facilitates the application of any X-

ray excitation radiation, the use of optics and both scanning

geometries. The angular scans are implemented by varying the

excitation angle (GIXRF) or the detection angle (GEXRF). In the

latter the angular calibration is used in the calculation of the

isoangular lines and the solid angle of detection.

For GIXRF the geometry of the setup is additionally included

in the calculations of the solid angle of detection. Furthermore,

beam divergence must be considered in the simulations since it

causes damping of the amplitude of the interference structures.

The solid angle is calculated by means of a Monte-Carlo

approach. The geometry of the setup is implemented in the

code as obstructions for the X-ray trajectories. 10

X-rays are

generated within the point of origin, which is the footprint of

the beam on the sample considering its shape: Gaussian in one

and rectangular in the perpendicular direction. From there the

X-rays proceed in arbitrary directions within a half sphere solid

angle. Whenever the X-ray paths collide with the collimator the

trajectory is disregarded from further calculations. The solid

angle of detection is hence the ratio of photons hitting the

detector without collision to the number of emitted photons

times the emission solid angle (2p). A respective solid angle is

calculated for each angular position of the sample by smearing

the area of origin with respect to the X-ray beam. Smearing of

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the footprint at shallow incidence angles is thus included in the

calculation.

Fig. 5 top shows the comparison of the simulated and

measured GIXRF proles of nickel and silicon. The data are

normalized since the eﬃciency of the focusing multilayer and the

detecting system is unknown. This is justiable since the sample

is dened by the shapes of the proles and not the absolute

intensities. In the bottom of the same gure the GEXRF prole of

the Ni Kauorescence line is shown and the region around the

prominent ne interference structures is enlarged. In contrast to

GIXRF, the geometrical parameters of the setup are not included

in the simulation, rather they are used to generate proles from

CCD frames. Since no investigations on the detector's eﬃciency

were performed and a consistent investigation into the poly-

capillary lenses’absolute transmission is currently executed, the

GEXRF proles are also normalized.

The presented simulated and measured data overlap for

both setups and in the GIXRF case for both uorescence lines.

The validation sample is well dened and thus these results

allow the characterization of these laboratory setups. This

enables the application of recursive algorithms for quantitative

results when unknown samples are investigated.

As already mentioned, krypton was found in the GIXRF sum

spectra. Interestingly, the analysis of the krypton Kauores-

cence line prole shows that this sputtering gas is preferably

deposited in the carbon layers of the multilayer. This can be

seen in Fig. 6 where the measured GIXRF krypton uorescence

line prole (dark blue) and the simulated proles of carbon

(light blue), krypton (orange) and nickel (green) are shown. The

shapes of the carbon and measured krypton proles follow

a similar trend, indicating that krypton uorescence is excited

when the standing wave eld is formed within the carbon

layers. In the simulation of the krypton prole it was assumed

that 1 at% of the carbon layer is krypton. Except for the region

around 0.1this assumption generates an overlap of the simu-

lated and measured krypton proles. The mismatch in the low

angle region indicates that krypton is preferably concentrated

deeper inside the rst carbon layer. This qualitative analysis of

the results indicates how the system can be used to determine

in-depth contaminations in samples with nanometer layer

thickness. A dedicated sample could be used to characterize the

angle dependent lower limits of detection of the nal setup.

Discussion and outlook

For both presented angle resolved laboratory XRF measure-

ments the measured and simulated proles agree. Since the

investigated sample is well-known and well-characterized by

XRR measurements, this proves the applicability of these

laboratory spectrometers. The benet of the SF-GEXRF method

is the independence of the interference structure from the

quality of the primary radiation. This facilitates the resolution

Fig. 5 Comparison of normalized simulated and measured angle

resolved XRF proﬁles of the NiC multilayer. For GIXRF (top) the proﬁles

of the ﬂuorescence lines of Ni Ka(green) and Si K (red) are evaluated,

and for SF-GEXRF (bottom) only those of Ni Ka. A magniﬁed image of

the angular region from 0.3up to 0.6of the SF-GEXRF proﬁle is

shown to emphasize the overlap of the ﬁne interference structures of

the proﬁle.

Fig. 6 The measured GIXRF proﬁle of the krypton Kaﬂuorescence line

(dark blue) and the simulated GIXRF proﬁles of carbon (light blue),

nickel (green) and krypton (orange). In the simulation the krypton is

assumed to accumulate in the carbon layers and make up 1 at% of the

respective layers.

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of ne interference structures in the NiC multilayers’Ni Ka

uorescence line prole which are not present in the GIXRF

measurement due to beam divergence. On the other hand, the

angular resolution of the SF-GEXRF strongly depends on the

pixel size of the CCD and its distance from the sample. Due to

the better excitation and detection eﬃciency of krypton in the

GIXRF measurement additional information such as the pref-

erable deposition of krypton in carbon layers can be extracted.

In the discussed case the sample has sharp interfaces and

a period thickness in the nm range. For samples with sub-nm

layer thickness and worse quality of the layer boundaries the

measurement time for the SF-GEXRF case increases drastically

to achieve good statistics. This is demonstrated in Fig. 7 with

the comparison of a GIXRF (top) and SF-GEXRF (bottom) prole

of the Cr Kauorescence line of a chromium–scandium

multilayer with a bi-layer thickness of 1.7 nm (repeated 100

times) and strong intermixing between the respective layers.

The measurements are performed under the same conditions as

the measurements of the NiC multilayer. Though, to resolve the

interference structure of the chromium Kauorescence line

from this sample for the SF-GEXRF prole 10 000 frames with

an exposure time of 3 seconds are recorded. This yields an

overall measurement time of 950 minutes compared to the 15

minutes needed to record the GIXRF scan. This diﬀerence

results mainly from the small solid angle of detection of the SF-

GEXRF setup. Additionally, the excitation at normal incidence is

less eﬃcient than at grazing incidence angles.

One approach to tackle the challenge of long measurement

times of the SF-GEXRF setup is the use of a diﬀerent position

sensitive detector, a single photon detector as in the studies of

Kayser

and Baumann.

These specialized detectors facilitate

fast read-out speeds while maintaining very low noise.

29,30

For

laboratory angle resolved setups, the high price and the

complexity of operation of these detectors are serious draw-

backs. Especially considering that with the specic GEXRF

geometry introduced in this work within an exposure time of 3

seconds around 2000 photons are detected by the CCD for the

samples presented. Thus, a faster read-out would reduce the

measurement time by around 20% and a further reduction of

measurement time could only be achieved by a higher ux on

the sample. This is possible by using rotating anode X-ray tubes

or metal-jet anodes,

which have the same drawbacks as the

photon counting detectors and additionally the former

produces a large footprint on the sample. An increase of ux in

the SF-GEXRF measurements could also be achieved if the

sample was investigated at shallower incidence angles. From

geometrical considerations it follows that for an incidence

angle of 6an increase of detected uorescence intensity by

a factor 10 is expected. Though, the inuence on the solid angle

of detection of this modication needs to be included in the

calculations as it can have an impact on the measured prole.

Another option is to decrease the distance between the sample

and the detector, which also decreases the angular resolution if

the pixel size remains unchanged. Another perspective is the

use of cmos detectors, since they enable fast read-out and small

pixel size. So far, the depletion zone thickness has been insuf-

cient for this kind of investigation but there is a rapid devel-

opment in this area.

The main drawback of GIXRF is the lower angular resolution

which can only be improved by lowering the divergence of the X-

ray beam. This is possible by adding collimators to the setup or

crystal optics. The former would result in a lowered ux on the

sample, but due to the small sample–detector distance this

parameter is not critical in the GIXRF spectrometer used.

Furthermore, the necessity to scan the sample for GIXRF

measurements increases the complexity of the setup. A

substantial benet of GIXRF is the possibility to combine the

GIXRF setup with XRR measurements. This has been shown in

the literature

and provides two complementary measurements

at once. Additionally, a combined analysis lowers the uncer-

tainties of the results as thoroughly discussed e.g. by D. Ingerle

et al.

Conclusions

The demonstrated experiments prove that angle resolved tech-

niques are reliable enough to serve as complementary

Fig. 7 GI- (top) and SF-GEXRF (bottom) of a chromium–scandium

multilayer with a period thickness of 1.7 nm. The GIXRF scan is per-

formed with an angular resolution of 0.001and each point is

measured for 5 seconds. In the SF-GEXRF measurement 10 000 CCD

frames are recorded with an exposure time of 3 seconds.

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measurements to XRR in the laboratory. Especially for samples

with strong intermixing the angle resolved methods benet

from the element specic in-depth information. Opposed to

XRR, not only contaminations can be identied but also their

distribution in the sample can be calculated. Since both

methods yield theoretically equivalent information about the

sample the choice of which method, GI- or SF-GEXRF, to use

depends on the sample and available hardware.

Conﬂicts of interest

There are no conicts to declare.

Acknowledgements

The authors would like to thank Helga for her reliability, Bruker

Nano GmbH for the permission to perform the GIXRF

measurements and the constant support, AXO DRESDEN

GmbH for manufacturing the validation sample, Philippe Jon-

nard and Meiyi Wu from Universit´

e Pierre et Marie Curie in

Paris for providing the Cr/Sc sample, Daniel Gr¨

otzsch for con-

structing substantial components of both setups, and Michael

Haschke for inspiring this comparative work. J. B. would like to

thank the Helmut Fischer Foundation for nancial support.

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