EXPERIMENTAL DETERMINATION OF TANTALUM L-SHELL FLUORESCENCE YIELDS AND COSTER -KRONIG TRANSITION PROBABILITIES

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EXPERIMENTAL DETERMINATION OF TANTALUM L-SHELL

FLUORESCENCE YIELDS AND COSTER-KRONIG TRANSITION

PROBABILITIES

Nils Wauschkuhn, Katja Frenzel, Burkhard Beckhoff, Philipp Hönicke

Physikalisch-Technische Bundesanstalt

Abbestr. 2-12

10587 Berlin

Germany

nils.wauschkuhn@ptb.de

ABSTRACT

Using radiometrically calibrated instrumentation of Physikalisch-Technische Bundesanstalt, the

L-shell ﬂuorescence yields and Coster-Kronig factors of tantalum (including the uncertainty budget)

were experimentally determined based on transmission and X-ray ﬂuorescence experiments. The

determined ﬂuorescence yields (

ωL3= 0.247(12)

ωL2= 0.278(15)

ωL1= 0.157(12)

) were

independently validated trough XRR-GIXRF experiments. Both, the Coster-Kronig factors (

f23 =

0.123(84)

f13 = 0.328(152)

f12 = 0.14(11)

) as well as the ﬂuorescence yields are in good

agreement with the most established databases in the ﬁeld of X-ray ﬂuorescence.

Keywords

tantalum

ﬂuorescence yield

Coster-Kronig

fundamental parameter

Photon-in/photon-out experiment

XRF ·GIXRF ·XRR

1 Introduction

The knowledge of atomic fundamental parameters (FP) such as the ﬂuorescence yield, the photoionization cross section

and the Coster-Kronig transition probabilities is of great importance for any quantitative analysis involving X-ray

ﬂuorescence (XRF). The majority of the available experimental and theoretical FP values for different elements were

obtained more than forty years ago. For some chemical elements and some FPs, the tabulated data is based solely on

interpolations as no experimental or theoretical data exists. Unfortunately, the uncertainties of most tabulated FP data

often are not available or only estimated. As this is certainly an improvable situation, the International initiative on

X-ray fundamental parameters [

] and others are working on revisiting and updating FP databases with new experiments

and calculations employing state-of-the-art techniques.

In this work, the tantalum L-shell fundamental parameters, namely the ﬂuorescence yields and the Coster-Kronig

factors, are being experimentally redetermined. Tantalum is a key element in microelectronics[

], solar industry[

medicine and more. On the other hand, the availability of experimentally determined Ta-L shell FPs is rather scarce.

The majority of the available experimental data is older than 30 years and the uncertainties as estimated for the most

common tabulations[

] are only estimated. In this work, we apply the reference-free XRF equipment of PTB[

] and

dedicated transmission and ﬂuorescence measurements[8] using to revisit these parameters for tantalum.

2 Experimental

2.1 Photon-in/photon-out experiment

The experiments were performed at the wavelength-shifter beamline BAMline[

] at the BESSY II electron storage ring.

This beamline provides hard monochromatic X-ray synchrotron radiation in the photon energy range from 5 keV up to

60 keV. Usually, the double crystal monochromator (DCM, with Si(111) crystals, d

E/E = 0.2

% between 8 and 50

arXiv:2210.02752v1 [physics.atom-ph] 6 Oct 2022

keV) is used for applications comparable to the one in this study. The experiments were carried out using an in-house

developed vacuum chamber[

] equipped with calibrated photodiodes and an energy-dispersive silicon drift detector

(SDD) with experimentally determined response functions and radiometrically calibrated detection efﬁciency[

]. The

sample was placed into the center of the chamber by means of an x-y scanning stage and the incident angle

θin

between

the surface of the sample and the incoming beam was set to 45

◦

. As a sample, we have obtained a nominally 250 nm

thick Ta deposition on a Si

-membrane. The membrane has a thickness of nominally 1000 nm. Furthermore, a blank

Si3N4-membrane deposition was used to subtract the membrane contribution.

For both samples, transmission experiments were performed in the vicinity of the Ta-L absorption edges between 7 keV

and 13 keV. In addition, the X-ray ﬂuorescence emission from the coated sample was measured for photon energies

ranging from about 10 keV to 13 keV. From these experiments, the Ta L-shell ﬂuorescence yields and the Coster-Kronig

factors can be determined as follows.

The procedure to determine L-shell ﬂuorescence yields, as well as Coster-Kronig factors using physically calibrated

instrumentation for reference-free X-ray spectrometry of PTB is already quite well established[

]. Here,

Sherman’s equation[

] provides the basis for the calculation of ﬂuorescence intensities of thin foils. It is a product

of the incident monochromatic photon ﬂux, a ﬂuorescence production factor for a given shell

σS

, an instrumentation

factor containing the solid angle of detection and the detection efﬁciency and the self-attenuation correction factor. This

factor considers the attenuation of the photons on their way through the sample: For the incoming photons

Φ0(E0)

the

attenuation on their way to the point of interaction is considered, for the ﬂuorescence photons Φd

i(E0)the attenuation

on their way from the point of interaction to the detector is considered. Employing tunable photon sources or as

recently shown also employing energy dispersive detectors[

], this factor can be easily determined by transmission

measurements for the relevant photon energies.

The ﬂuorescence production factor σLi is deﬁned as follows:

σL3(E0) = ωL3(τL3(E0) + f23τL2(E0)+[f13 +f12f23]τL1(E0)) (1)

σL2(E0) = ωL2(τL2(E0) + f12τL1(E0)) (2)

σL1(E0) = ωL1τL1(E0)(3)

It is depending on the photon energy

and is calculated employing the respective subshell ﬂuorescence yield

ωLi

, the

subshell photoionization cross sections

τLi(E0)

as well as the Coster-Kronig factors

fji

. The latter are irrelevant for

photon energies below the edge energy of the respective subshell as the photoelectric cross section is zero for energies

below the corresponding subshell threshold energy. Thus, for photon energies between

EL3

and

EL2

σL3(E0)

simply the product of ﬂuorescence yield and photoionization cross section so that the ﬂuorescence yield

ωL3

can be

derived. By further employing this selective excitation to the other edges, also the

and

subshell ﬂuorescence

yields as well as the Coster-Kronig factors can be determined.

In other words, if EL3≤E0≤EL2, the ﬂuorescence production factor for L3reduces to

σL3(E0)ρd =ωL3τL3(E0)ρd =Φd

i(E0)Mi,E0

Φ0(E0)Ω

4π

(4)

with

Mi,E0=(µS(E0)ρd

sin θin +µS(Ei)ρd

sin θout )

(1 −exp[−(µS(E0)ρd

sin θin +µS(Ei)ρd

sin θout )]),(5)

where

θin

and

θout

are incident and exit angles respectively. Due to the use of PTB’s physically calibrated instrumen-

tation for reference-free X-ray spectrometry, all of the relevant measures can be accessed. The ﬂuorescence photon

ﬂux

Φd

i(E0)

is derived from the recorded ﬂuorescence spectra by means of a spectral deconvolution procedure. Here,

the detector response functions for all relevant ﬂuorescence lines as well as relevant background contributions, e.g.

bremsstrahlung, originating from photo-electrons are included. In addition, we determine and apply ﬁxed line sets for

each of the three L-shells in order to stabilize the deconvolution[

]. An exemplary spectrum including the deconvolution

is shown in ﬁg. 1. The incident photon ﬂux

Φ0(E0)

and the solid angle of detection

Ω

4π

are known due to the use of

calibrated instrumentation [

]. The sample speciﬁc attenuation correction factor

Mi,E0

for the incident (

) – as well

as the ﬂuorescence radiation (

) is calculated according to Eq. 5 using the experimentally determined sample speciﬁc

attenuation coefﬁcients µS(E0)ρd and µS(Ei)ρd.

Employing the experimental

µS(E0)ρd

and

µS(Ei)ρd

values, one can calculate the total sample speciﬁc photoionization

cross sections

τS(E0)ρd

and

µS(Ei)ρd

by removing the scattering contributions. For this purpose, we derive the

relative scattering contribution at each photon energy from a database (e.g. X-raylib) and use this data to determine

τS(E0)ρd

. The thereby obtained photoionization cross sections are shown in ﬁgure 2 as blue dots. For the determination

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EXPERIMENTALDETERMINATIONOFTANTALUML-SHELLFLUORESCENCEYIELDSANDCOSTER-KRONIGTRANSITIONPROBABILITIESNilsWauschkuhn,KatjaFrenzel,BurkhardBeckhoff,PhilippHönickePhysikalisch-TechnischeBundesanstaltAbbestr.2-1210587BerlinGermanynils.wauschkuhn@ptb.deABSTRACTUsingradiometricallycalibratedinstrumentationo...

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EXPERIMENTAL DETERMINATION OF TANTALUM L-SHELL FLUORESCENCE YIELDS AND COSTER -KRONIG TRANSITION PROBABILITIES

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