# Temperature-Dependent In-Situ LEIS Measurement of W Surface Enrichment by
250 eV D Sputtering of EUROFER

H. R. Koslowski1,¶, S. R. Bhattacharyya2, P. Hansen1, Ch. Linsmeier1, M.
Rasiński1 P. Ström3 1Forschungszentrum Jülich GmbH, Institut für Energie- und
Klimaforschung – Plasmaphysik, 52428 Jülich, Germany 2Surface Physics &
Materials Science Division, Saha Institute of Nuclear Physics, 1/AF Bidhan
Nagar, Kolkata-700064, India 3Department of Fusion Plasma Physics, School of
Electrical Engineering and Computer Science, KTH Royal Institute of
Technology, SE-10044 Stockholm, Sweden ¶ Corresponding author, email:
<EMAIL_ADDRESS>Keywords: low energy ion scattering (LEIS);
EUROFER; plasma-surface interaction; preferential sputtering; W diffusion in
Fe; diffusion activation energy ORCID IDs: S. R. Bhattacharyya
https://orcid.org/0000-0002-8210-1088 P. Hansen
https://orcid.org/0000-0003-0099-6293 H. R. Koslowski
https://orcid.org/0000-0002-1571-6269 Ch. Linsmeier
https://orcid.org/0000-0003-0404-7191 M. Rasiński
https://orcid.org/0000-0001-6277-4421 P. Ström
https://orcid.org/0000-0001-9299-3262

(3.7.2018, accepted for publication in Nuclear Materials and Energy)

###### Abstract

Tungsten surface enrichment of EUROFER steel by 250eV deuterium sputtering is
in-situ measured using low energy He+ ion scattering spectroscopy. The samples
are irradiated at various temperatures between 300 K and 800 K with a
deuterium atom flux of 2e18m^-2s^-1 and maximum fluence up to 1.1e23m^-2. The
measurements at room temperature show a clear increase of tungsten surface
density, but already at 520 K the observed enrichment is only half as large.
At a temperature of 800 K no tungsten surface enrichment is detectable. The
obtained data yield an upper limit of 1.6eV for the diffusion activation
energy of tungsten in EUROFER.

Keywords: Low energy ion scattering, Nuclear fusion, EUROFER, Plasma-wall
interaction, Preferential sputtering, Surface enrichment

##  1 Introduction

Materials for the first wall of a fusion reactor are the topic of intense
research. Although Be is chosen as first wall material for the ITER tokamak,
alternative options, involving other metals and alloys, are under
consideration for a future power plant. In this context the application of
reduced activation ferritic-martensitic (RAFM) steels like e.g. EUROFER for
application in recessed and less loaded areas is considered [1, 2, 3].
Analyses of manufactured EUROFER batches yield the following contents of the
main alloying elements: 8.9mass% Cr, 1.1mass% W, 0.44mass% Mn, 0.19mass% V,
0.14mass% Ta, 0.12mass% C, and a few other elements with a total content below
0.05mass% [4]. The envisaged operating temperature window when used as first
wall material extends up to 820K. Besides high heat loads, the wall material
has to withstand impinging particle fluxes which makes materials composed from
medium- and high-$Z$ elements more suitable due to their lower sputtering
yields. Particle fluxes onto the first wall of a future fusion power plant are
estimated to be in the range 2e19m^-2s-1 to 2e21m^-2s-1 [5]. EUROFER steel
contains 0.4at% of W [4] whose sputter yield at low energy (here: 250eV) D
irradiation is more than two orders of magnitude smaller than for the major
constituent Fe [6], which is thought to result in the surface enrichment of W
by preferential sputtering.

Roth et al. [7] have conducted dedicated experiments to study W surface
enrichment of EUROFER using the plasma device PISCES-A [8]. The erosion yield
for low energy deuterons at various temperatures is measured. An observed
decrease of sputtering yield is attributed to W surface enrichment by
preferential sputtering and increased W surface concentrations are confirmed
by Rutherford backscattering analysis of the exposed EUROFER samples, but the
limited depth resolution give lower surface concentration than anticipated due
to TRIDYN [9] modelling. However, a repeated exposure at elevated temperature
(500) reveals that the erosion yield returns to similar values as expected for
a pure Fe surface, indicating a strong influence of temperature.

Plasma exposure of EUROFER samples in the PSI-2 [10] linear plasma device at a
fluence of 1e26eV and an D ion energy of 60eV to 70eV result in a complex
change of the surface morphology and the development of a grass-like topology
[11]. Energy dispersive X-ray analysis shows W enrichment in these structures.

Recently, erosion studies of magnetron sputtered Fe-W layers, assuming them to
be a model system for RAFM steels, have been performed using either an high
current ion source [12] or the linear plasma device PSI-2 [13]. The
investigation with the high current ion source proves that the reduction in
sputtering yield is correlated to the W surface enrichment analysed by
Rutherford back scattering, and the experiment in the linear plasma device
confirms the W enrichment at low energy D erosion using glow discharge optical
emission spectroscopy to analyse the samples after exposure. The latter study
finds strong surface morphology modifications resulting in a needle-like
structure [14].

Similar results are obtained for another RAFM steel, F82H, which has been
exposed with a maximum D fluence up to 1e26m^-2 in a linear plasma generator
[15]. Again, the erosion yield decreases with increasing D atom fluence but
this effect is counteracted by an enhanced sample temperature. Post-
irradiation x-ray photoelectron spectroscopy (XPS) analysis shows W enrichment
in the near surface layer, and scanning tunnelling electron microscopy (SEM)
measurements reveals changes of the surface morphology.

Medium energy ion scattering (MEIS) analysis performed on various Fe-W coated
samples which are irradiated with 200eV deuterons at fluences up to 1e24m^-2
confirms the W surface enrichment and shows that the enriched layer depth is
up to 10nm, depending on the fluence [16, 17]. Recently, a similar series of
experiments using EUROFER samples confirms the W surface enrichment seen in
the PISCES-A experiment [7], and yield increasing enrichment even at
temperatures of 900K and 1050K where, however, recrystallisation and cracking
of the sample surface is observed [18].

The above mentioned experiments using Fe-W coatings as a proxy for RAFM steels
are modelled using the Monte-Carlo code SDTrimSP, which has been augmented by
a model for solid-state diffusion in order to account for the observed
temperature dependence [19]. Modelling results confirm the experimentally
observed trends, i.e. an increasing W surface density with deuterium atom
fluence and the weakening of the enrichment with increasing sample
temperature. Furthermore, a particle flux dependence of the W surface
enrichment is encountered. Again, the simulations show that under irradiation
conditions, which resemble those in laboratory and plasma experiments, the
depth of the enriched zone amounts a few nm and shows a strong influence of
temperature driven diffusion.

Low energy ion scattering (LEIS) is an extremely surface sensitive method
which permits quantitative elemental analysis of the surface composition [20,
21]. In many situations LEIS is predominantly sensitive to the outermost 1 to
2 monolayers and only in cases where reionisation plays a role ions scattered
at few deeper layers are detected. Even in those cases the decay length, i.e.
the depth where the ion signal has decayed to $1/{\rm e}$ is about 1nm [22].
In the following we report on the investigation of W surface enrichment by
250eV D sputtering of EUROFER steel and in-situ analysis of the W surface
density using LEIS.

##  2 Experiment

The experiments are carried out in an ultra-high vacuum chamber with a base
pressure below 5e-10mbar measured with a Pfeiffer TPG 256 A MaxiGauge
controller and a PBR 260 Bayard-Alpert hot cathode gauge. A schematic drawing
of the experimental setup is shown in figure 1. The apparatus has been
originally developed and build at IPP Garching [23] and resumed operation
after being moved to Jülich, recently. The LEIS ion source is based on a
Bayard-Alpert gauge and generates noble gas ions with a total ion current of
several 100nA. The ions are accelerated to an energy of typically 1000eV and
focused with a first einzel lens mounted within the LEIS ion source before
they pass through a sector magnet which selects the ion mass and charge state.
A second einzel lens focuses the probing ion beam onto the sample. Two sets of
deflection plates allow to steer the ion beam and correct for misalignments.
The ion current after mass/charge selection measured with a Faraday cup or on
the sample is typically in the range 1nA to 10nA. The ion beam diameter is
about 1mm. The EUROFER sample is mounted on a Prevac PTS 1000 RES/C-K sample
holder which permits resistive heating up to $\sim$1200K. The sample holder is
attached to a VG Scienta high precision 5-axis translator. The ions which are
reflected from the sample pass a hemispherical electrostatic energy analyser
and are detected with a channeltron in single ion counting mode. A multi-
channel analyser has been programmed in Labview and uses a National
Instruments PXI-8106 data acquisition system. Sample cleaning is done with a
Perkin-Elmer 04-161 sputter ion gun. The diameter of the sputter ion beam is
5mm to 6mm and total ion currents are up to 10μA.

The EUROFER samples have size 10mm $\times$ 10mm $\times$ 1mm and are
initially polished to a mirror finish. SEM images at magnifications up to
50000 show a smooth surface and grain sizes of a few μm.

Initial sample cleaning is performed by sputtering with 500 eV Kr+ ions. The
total ion fluence used for cleaning, expressed as accumulated charge on the
sample, is between 2mC and 5mC. After this cleaning step the residual O
contamination on the surface is very small and less than 1% of the detected
scattered He+ ions originate from collisions with O. It is well known that
sputter cleaning of alloys may alter the surface composition of the sample
already and yields surface densities of the various constituents which differ
from their bulk densities. In the simplified case of a binary alloy steady-
state conditions are obtained when surface concentrations $c_{\rm s,x}$, bulk
densities $c_{\rm b,x}$, and elemental sputtering yields $Y_{\rm x}$ obey the
relation

$\frac{c_{\rm s,1}}{\rm c_{s,2}}=\frac{Y_{\rm 2}}{Y_{\rm 1}}\frac{c_{\rm
b,1}}{c_{\rm b,2}}$ (1)

where the indices 1 and 2 label both elements of the alloy [24]. The
sputtering yield of Fe for 500eV Kr bombardment is about 30% larger than the
yield for W [25], leading already after the sputter cleaning to a moderate W
enrichment on the sample surface. This small initial W enrichment on the
surface does not cause any problems because the anticipated enrichment due to
low energy D sputtering is much larger.

A typical LEIS spectrum using singly charged He+ ions accelerated to an energy
of 1000eV measured at a scattering angle of 120∘ is shown in figure 2. The
LEIS spectrum shows a dominant peak resulting from scattering at Fe atoms, and
well separated at higher energy a much smaller W peak. A very small peak at
450eV is caused by the scattering from residual O atoms in the topmost layer
of the sample.

Several series of D sputtering steps with increasing fluences are conducted at
room temperature (RT), 520K, 660K, and 800K. The D irradiation is done by
introducing deuterium gas in the sputter ion gun, leading to an increase of
the pressure in the vacuum vessel up to 5e-6mbar of D2. The sputter ion gun
uses low energy electron impact ionisation of the working gas, thus producing
mainly D${}_{2}^{+}$ ions and up to 7% of D+ [26]. The ions are accelerated
with a voltage of 500V, thus yielding mainly 250eV deuterons impinging on the
sample surface. The sputter ion current is adjusted to get a flux density of
2e18m^-2s^-1 on the sample. The sputtering threshold energy for D atom
bombardment of W is 216eV and the sputtering yield of Fe is at least 2 orders
of magnitude larger than the sputtering yield of W for 250eV D projectiles
[6]. In-situ LEIS is conducted before and after each irradiation step. After
each D irradiation series at a certain temperature the sample surface is
removed up to a sufficient depth by applying Kr+ sputtering with a total ion
current of 1μA to 2μA for about 1 hour, thus removing the enriched surface
layer and resetting the sample. Due to the slightly different sputtering
yields for Fe and W [25] the cleaning procedure leads already to a small W
enrichment according to equation 1 which results in a ratio of surface
concentrations $c_{\rm W}/c_{\rm Fe}$ about 1.4 times larger than the
respective ratio of bulk concentrations.

The three peaks in the LEIS spectra originating from scattering at O, Fe, and
W, are fitted with Gaussian profiles. An example spectrum with fitted peaks is
shown in figure 3. Due to the composition of EUROFER, there arises one
complication which cannot be accounted for easily. EUROFER steel contains
9mass% of Cr and the mass of a Cr atom is quite close to the mass of an Fe
atom. The energy resolution of the LEIS setup (energy broadening of the
incident ion beam folded with the energy resolution of the electrostatic
energy analyser) is not good enough to separate He+ scattered at Fe and Cr.
The Cr peak is at the left wing of the Fe peak, resulting in a slight
asymmetry as can be seen in figure 3. However, the error introduced by this
superposition of scattering peaks is acceptable and, as can be seen in the
figure, the area under the fitted peak is still a good representation for the
number of scattered ions from Fe and Cr together. A similar issue is present
for the measured scattering events from W atoms, where the small Ta content
gives an additional, not discernible contribution to the measured amplitude of
the W peak.

The relative surface fraction of W is determined as the ratio between counts
in the W peak (defined by the area under the peak) divided by the sum of
counts in all measured peaks. This definition is correct in case elemental
sensitivities of all components are equal. When elemental sensitivities are
different, some systematic error is introduced. However, the main constituent
of EUROFER is Fe, the O contamination of the surface is small, and the surface
fraction (i.e. the areal coverage) of W stays always much smaller than the
surface fraction of Fe. Under these constraints the count ratio mentioned
above is a valid approximation for an uncalibrated ratio of surface fractions.
An absolute calibration is derived from a comparison of He+ scattering spectra
on pure Fe and pure W.

Surface observations are performed using a field emission scanning electron
microscope (FE-SEM) Zeiss Crossbeam 540 equipped with energy-dispersive X-ray
spectroscopy (EDX). SEM investigations are carried out using a 3kV electron
beam with current of 172pA. The low electron energy enables measurements which
are very sensitive to the surface.

##  3 Results and discussion

One fundamental question to answer with respect to a measurement of surface
enrichment of a specific alloy at various temperatures is, whether surface
segregation occurs and might superimpose or interfere with the enrichment
caused by sputtering. The LEIS spectra after cleaning (and resetting the
surface between irradiation sequences at different temperatures) are shown in
figure 4. The spectra are normalised to the Fe peak at 800eV. There is always
a small O peak, which tends to increase very little at elevated temperatures.
This behaviour may be due to the fact that the time between sample cleaning
and LEIS measurements increases when the sample has to be heated up to the
target temperature, thus allowing for a longer time O deposition from the
residual gas. The W peaks at 920eV are very small and do not show a systematic
increase with temperature. However, the measurement at 520K shows a larger W
peak which is believed to be caused by insufficient sample cleaning before the
heating. It is important to note that this larger W fraction on the sample
surface as the starting point for the irradiation sequence at 520K does not
introduce any difficulty for the subsequent irradiation measurements because
the W surface fractions obtained after each irradiation step are larger. The
absence of an increase of the W peak shows that for the temperatures used in
these experiments surface segregation does not play a role. This conclusion is
further supported by density-functional theory (DFT) calculations of the
segregation energies in transition-metal alloys, which for the segregation of
W in Fe yield a small but positive surface segregation energy, thus even
favouring a moderate anti-segregation [27]. However, this result of the DFT
calculations can only be used as a weak confirmation since EUROFER is not a
binary alloy but has multiple components and may behave differently. The
spectra show small shifts of the centre position of the Fe peaks which is
likely caused by small changes in the ion beam parameters, especially
optimisation of the extraction voltage in order to get maximum ion current
does lead to a change in beam energy.

Figure 5 shows the W peak of six LEIS spectra for the irradiation sequence at
RT. The spectrum labelled with a fluence of 0m^-2 is measured after sputter
cleaning prior to the D bombardment, four spectra are measured at various,
increasing fluence values, and the sixth spectrum is measured at the maximum D
atom fluence of 1.1e23m^-2. The spectra are normalised to the height of the Fe
peak and for better visibility only the high energy part of the spectrum with
the W peak is shown. The W peaks exhibit a clear correlation with the increase
of the D atom fluence. The relative peak height of the W peak is about 1% of
the Fe peak for the cleaned sample and reaches a value of 16% at the maximum
applied D fluence.

Similar irradiation sequences are repeated for elevated sample temperatures.
The measured W enrichments on the surface are summarised in figure 6. The
shaded area marks the range of surface densities measured for the various
sequences just after sample cleaning and heating to the desired temperature.
The upper limit is distorted due to the insufficient sample cleaning at 520K
and the measured relative densities are about $(0.01\pm 0.005)$. At RT W shows
the strongest surface enrichment up to a relative value of $0.163\pm 0.008$.
No sign for saturation of the W surface density at the maximum D fluence of
1.1e23m^-2 can be seen. This finding is in good agreement with investigations
of D sputtering of Fe/W coatings where an increase of the W surface density up
to 24% with a fluence of 1e24m^-2 has been detected [17]. With increasing
temperature the measured surface enrichment at each irradiation step
decreases. Already at a sample temperature of 520K the surface enrichment is
only half as large as at RT, and at 800K the D${}_{2}^{+}$ bombardment does
not lead to any significant increase of the W surface density. The
experimental results prove that it is possible to demonstrate in-situ the W
enrichment of EUROFER steel by preferential sputtering using D atoms with an
energy close to the sputter threshold.

The LEIS data presented above give relative surface densities by not
differentiating between differential scattering cross sections and
neutralisation probabilities. The count rate of particles scattered from atoms
of element i on the surface, ${\dot{N}_{i}}$ is given by

${\dot{N}_{i}}=\frac{{\rm d}\sigma_{i}}{{\rm
d}\Omega}{\dot{N}_{0}}c_{i}P^{+}_{i}T\Delta\Omega{}$ (2)

where ${{\rm d}\sigma_{i}/{\rm d}\Omega}$ is the differential cross section,
${\dot{N}_{0}}$ the rate of incident ions on the surface, $c_{i}$ the surface
density of element i, $P^{+}_{i}$ is the ion fraction, i.e. the probability
that the scattered ion is not neutralised, $T$ is the transmission and
sensitivity factor of the analyser, and $\Delta\Omega$ the detected solid
angle [20]. From equation 2 it follows that only the product of differential
cross section and ion fraction depends on the individual element i, which
permits to define the elemental sensitivity according to [21]

$\eta_{i}=P^{+}_{i}\frac{{\rm d}\sigma_{i}}{{\rm d}\Omega}.$ (3)

When resonant neutralisation or Auger neutralisation prevail and collision
induced processes are neglected, the ion yield can be expressed as the product
of the scattering cross section and an ion survival probability which is given
by $P^{+}=\exp(-v_{c}/v_{\perp})$, where $v_{c}$ is a characteristic velocity
and $v_{\perp}$ is the effective value of the velocity of the projectile
perpendicular to the surface, taking into account incoming and outgoing
trajectories. However, when more than one process contribute, the fraction of
scattered ions cannot anymore be described by a survival probability, but is
given by $P^{+}=P^{+}_{\rm in}(1-P_{\rm CIN})P^{+}_{\rm out}+(1-P^{+}_{\rm
in})P_{\rm CIR}P^{+}_{\rm out}$, where $P^{+}_{\rm in}$ and $P^{+}_{\rm out}$
are the survival probabilities on the ingoing and outgoing trajectories, and
$P_{\rm CIN}$ and $P_{\rm CIR}$ are the probabilities for collision induced
neutralisation and reionisation, respectively [21].

In order to get absolute surface fractions for W, the ion yields for
scattering from W atoms and Fe atoms need to be determined. For that purpose a
special sample is prepared. Half of a pure Fe sample is covered before
magnetron sputtering a thin layer of W onto the sample. The calibration sample
is mounted on the manipulator in a way, that by vertical translation the
probing ion beam is scattered either from a pure Fe surface or from a pure W
surface. In that way all other quantities in equation 2 are kept constant and
the number of detected scattered particles in both spectra is according to the
elemental sensitivities for both elements. Small O peaks on both calibration
surfaces are taken into account by normalisation of the Fe or W count rates to
the total count rates for the respective surface. As already discussed for the
evaluation of the W surface fraction of EUROFER, the assumption of equal
elemental sensitivities is only correct in first order and may introduce an
error. However, the W scattering spectrum shows the surface peak and an
extended wing at the low energy side which indicates that a fraction of the
scattered ions are reionised [22]. The influence of this feature on the
elemental sensitivity factor has been minimised by fitting only the high
energy half of the peak and avoiding an unreasonably large half width. This
approach is justified by neutral scattering spectroscopy measurements of 1keV
He bombardment of W which has shown that the peak of scattered and ionised He+
is displaced by 14eV to the low energy side [28]. It is important to note that
this measurement includes ionised neutrals scattered at all layers, especially
the dominant fraction with lowest energy loss which has been scattered on the
surface. Reionised particles which are scattered at the first (or second)
monolayer and feature low energy losses, i.e. superimpose the direct
scattering peak and are counted by the peak fitting procedure, are of no
concern because they detect surface atoms. The energies of particles scattered
at deeper layers (which is important in this context, because these particles
could distort the surface density determination) are shifted even more toward
the low energy side [29] and are more effectively excluded by the chosen
fitting procedure. However, an estimation of the magnitude of the error which
is introduced by these sub-surface scattering events cannot be determined from
the calibration spectrum and one has to rely on the facts that (i) the energy
of those particles moves progressively away from the surface peak the deeper
the scattering takes place [29], i.e. these ions do not contribute to the
measured surface peak, and (ii) their number decrease rapidly with depth and
limits the detected signal to a few monolayers with the dominant signal
contribution originating from the topmost monolayer [22]. The ratio of the
number of counts in the fitted W peak and the Fe spectrum is $4/3$. Due to the
unavoidable contribution of some ions scattered from deeper layers the
determined sensitivity factor constitutes an upper limit. The maximum of the
relative W surface fraction for the room temperature measurement at highest
fluence shown in figure 6 is 16.3%. Correcting for the slightly higher
sensitivity for detection of W and considering the presence of reionised
particles yields a surface coverage of up to 12%.

The relative quantification of the scattered ion signals of the various
constituents is complicated by the fact that He+ scattering from Fe and from W
at the chosen scattering energy takes place in different regimes due to their
different thresholds for reionisation. The scattering on Fe is dominated by
Auger neutralisation, whereas scattering from W is in the reionisation regime
[21]. Furthermore, due to the small O content on the surface the presence of a
matrix effect cannot be excluded. The Fe peak (see figure 2) shows almost no
contribution from reionised projectiles (which are expected to have lower
energies, i.e. are located in the left wing of the peak), but the W peaks in
figure 5 show a pronounced left wing (see e.g. the data for maximum sputter
fluence, left pointing triangles). The normalised scattering intensity at
850eV (about 60eV below the direct scattering peak) is 0.025 and does still
contain a contribution of 0.01 from the right wing of the Fe scattering peak.
The remaining amplitude of 0.015 is less than 10% of the W peak amplitude. The
same determination of the magnitude of reionisation for the pure W spectrum
measured with the calibration sample yields a value of about 1/3, i.e. a much
larger contribution. Obviously, the influence of reionisation in EUROFER,
where W is a minor constituent and the achieved surface enrichment is not very
large, is much smaller than in the pure element. This questions the conclusion
drawn in [30] where the comparison with data from a pure reference sample has
been assessed to be sufficient for quantification. From the similar shape of
the W peaks in figure 5 one can conclude that the contribution of reionised
scattered ions for all irradiation steps is similar and the relative increase
of surface concentrations is still correct.

A matrix effect due to the presence of O on the surface, as for example
documented in [31] for a NiO surface or measured in [32] for WO, has not been
detected in the present experiments. The O exposure at a base pressure of less
than 5E-10mbar amounts to 8L for the measurement at RT with maximum fluence
(which needs about 30 hours), and is 2L to 3L for the measurements with lower
fluences at elevated temperatures. During most of the time the sample is under
sputter bombardment, i.e. the adsorbed oxygen is removed immediately.
Furthermore, the heated samples do not show an increase of the O peak at all
but at 520K the W peak still increases. No decrease of the W signal with
increasing measurement time (i.e. increasing O exposure) is seen and the
variation of count rate for the Fe peak (which is within a factor of 2 for all
measurements) is compatible with variations of the probing beam intensity
between different measurements.

Two scanning electron microscopy images of the EUROFER surface after exposure
at the maximum fluence are shown in figure 7. One can notice different
sputtering behaviour depending on the grain orientation. Two types of
sputtered grain morphology can be observed. Part of the EUROFER surface is
very smooth and flat, whereas other grains exhibit formation of nanoparticles
with size below 5nm. Based on the EDX analysis one can attribute these
particles to oxide formation.

The sample at maximum W enrichment is additionally analysed with energy
dispersive X-ray spectroscopy (EDX), X-ray photoelectron spectroscopy (XPS),
and time-of-flight medium energy ion scattering (TOF-MEIS) spectroscopy. All
three methods facilitate to determine the elemental composition, but have
larger information depths than LEIS.

The EDX analysis utilises an Oxford XMax-80 detector and the Oxford AZTec
software package which applies the Pouchou and Pichoir matrix correction
method [33]. EDX gives values between $(\num{1.0}\pm\num{0.1})\,\SI{}{at\%}$
and $(\num{1.1}\pm\num{0.1})\,\SI{}{at\%}$ depending on the selected spot on
the sample. The values are almost three times larger than the W bulk
concentration of 0.4at% in EUROFER. However, the detected level of enrichment
compared to the LEIS measurements is still quite small, resulting from the
fact that the EDX measurement averages over a 50nm to 60nm thick layer.
Assuming that the actual thickness of the enriched layer is much smaller, as
indicated e.g. in the SDTrimSP modelling [19], the EDX measurement does not
conflict with the ion scattering result.

The XPS measurements of the elemental composition of the surface of the same
sample are summarised in table 1. Since the enriched layer thickness is very
small and sputter cleaning is known to strongly change the surface composition
when concentrations and sputter yields do not obey the equilibrium relation
given by equation 1, no sample cleaning has been done before the measurements.
It is therefore no surprise that the XPS data show dominant C and O
contaminations due to the storage and sample transport in air as is shown in
the first row of table 1. EUROFER steel contains about 0.5at% C and less than
0.005at% O. When O is excluded from the elemental analysis, the W
concentration rises to 5.8at%. When C and O are excluded, the W concentration
becomes 9.3at%. The actual W concentration on the surface is in the range
given by the latter two values. Compared with the LEIS measurement both values
are smaller due to the larger information depth of the XPS measurement which
is in the range 5nm to 10nm.

The result of the TOF-MEIS measurement is shown in figure 8. The applied MEIS
setup is described in detail in [34]. A He+ beam with 60keV is used for the
measurement and scattered ions are detected under an angle of 155. Three
individual measurements are taken and averaged to obtain a spectrum with
better statistics. The resulting spectrum is compared to simulations using the
TRBS code [35]. A reasonable estimate for the depth resolution of the MEIS
measurement is 2nm based on the energy resolution of 1keV of the time-of-
flight system. The quantitative analysis of the TOF-MEIS spectra follows the
procedure outlined in [18]. The thicknesses of the various layers and the
concentrations of O, Fe, and W are adapted until satisfactory agreement with
the measured spectrum is obtained. Similar to the LEIS measurements, the
measured continuum for scattering events resulting from Fe and Cr (and V, Mn)
are summed up and attributed to Fe, scattering events resulting from W and Ta
are both attributed to the W signal.

There are two free parameters required when setting up the TRBS simulation.
These are the atomic fractions of W and O, the atomic fraction of Fe follows
from the condition that all fractions should add up to one. The measured
quantities are the Fe and W signal amplitudes in the spectrum, therefore both
free parameters can be clearly determined. This is true for every depth, i.e.
every corresponding energy interval. The relationship between energy spectrum
and depth profile can be non-ambiguously obtained. The signal normalisation is
done in the energy range 20keV to 30keV at sample depths beneath 20nm assuming
an unmodified composition. The above reasoning is weakened if other elements
than Fe (+ Cr, V, Mn), W (+Ta), and O are present. However, even in this case
the $A(\rm Fe)/(A(\rm Fe)+A(\rm W))$ ratio is accurate when the O fraction is
interpreted to represent ”everything else”, e.g. C. A small error is
introduced by this assumption because the stopping power of other elements is
different.

The result shows a $A_{\rm W}/(A_{\rm Fe}+A_{\rm W})$ ratio of roughly 8% and
a thickness of the enriched layer of about 4nm. As with the XPS analysis, no
sputter cleaning of the sample is done.

The W surface concentration measured with LEIS is larger than the values
determined by any of the other methods, proving the extreme surface
sensitivity of LEIS.

The results from LEIS and the other methods show that the measured value of W
surface enrichment depends on the information depth of the applied analysis
method. The larger the information depth, the smaller is the obtained surface
density, showing that the W enrichment happens in a thin layer. However, the
extreme surface sensitivity of LEIS raises the question what the outermost
atomic layer in reality is, especially in view of the fact that crystal
orientation can influence the scattering signal [36] and the surface exhibits
some strong features of morphology changes after the irradiation sequences (as
can be seen in the SEM images). For simplicity we adopt the point of view that
incident ions are scattered on the same surface layers as would be particles
from the plasma under real exposure conditions. In that respect the ion beam
experiment is relevant and mimics the intended application.

In the following the diffusion kinetics of W is determined from the LEIS
measurements of the temperature-dependent W surface concentration. The
analysis presented here follows general ideas outlined in [37, 38, 39, 40].
For that purpose a simplified model taking into account only the most relevant
contributions and restricting the components of the sample to be only Fe and
W, is constructed. The model is sketched in figure 9. The exponentially
decaying curve is the W concentration $c_{\rm W}(x,t_{0})$ as function of
depth $x$ at time $t_{0}$, where $c_{\rm s}$ and $c_{\rm b}$ denote surface
and bulk values of W concentration, respectively. The vertical dotted line
indicates the position of the surface of the sample at time $t_{0}$.
$\Gamma_{\rm D}$ is the sputtering D flux, $\Gamma_{\rm s,Fe}$ denotes the
flux of sputtered Fe atoms which leave the sample. Due to continuous
sputtering and removal of Fe atoms the surface recesses at a speed $v_{\rm r}$
and W atoms from the bulk enter the surface. This particular feature is
accounted for by introducing the recession flux $\Gamma_{\rm r,W}$. The last
contribution is the temperature driven diffusion of W atoms away from the
surface back into the bulk, $\Gamma_{\rm d,W}$.

The above mentioned fluxes can be expressed as follows:

$\Gamma_{\rm s,Fe}=\Gamma_{\rm D}Y_{\rm Fe}(1-c_{\rm W})$ (4)

where $Y_{\rm Fe}$ is the sputtering yield, i.e. the number of sputtered Fe
atoms per incident D atom. The recession flux of W atoms is given by

$\Gamma_{\rm r,W}=nc_{\rm W}v_{\rm r}=\Gamma_{\rm D}Y_{\rm Fe}c_{\rm
W}(1-c_{\rm W})$ (5)

where $v_{\rm r}$ is the recession velocity given by $\Gamma_{\rm s,Fe}/n$
with $n$ being the number density of atoms on the surface of the alloy [38,
39]. The diffusion flux of W from the enriched surface layer into the bulk is

$\Gamma_{\rm d,W}=-nD\frac{\partial c_{\rm W}}{\partial x}$ (6)

where $D$ denotes the diffusion coefficient. The difference of W fluxes given
by equations 5 and 6 provides the effective flux of W atoms to the surface.
Note that the diffusion flux is always smaller than the recession flux.

$\Gamma_{\rm W}=\Gamma_{\rm r,W}-\Gamma_{\rm d,W}=\frac{{\rm d}\varrho_{\rm
W}}{{\rm d}t}$ (7)

where $\varrho_{\rm W}=n^{2/3}c_{W}$ is the surface density of W atoms. The
temporal change of the W surface density is given by

$\frac{{\rm d}\varrho}{{\rm d}t}=n^{2/3}\frac{{\rm d}c_{W}}{{\rm
d}t}=n^{2/3}\frac{{\rm d}c_{W}}{{\rm d}\mathit{\Phi}}\frac{{\rm
d}\mathit{\Phi}}{{\rm d}t}$ (8)

where $\mathit{\Phi}$ is the fluence of D atoms bombarding the surface. The
quantity ${\rm d}c_{W}/{\rm d}\mathit{\Phi}$ is obtained from the measurements
shown in figure 6 by fitting the data for a specific temperature using the
analytical expression $c_{W}=A(1-B\exp(-C\mathit{\Phi}))$, from which the
required derivative is obtained in a straightforward way. There is another
obstacle which cannot be easily worked out. The spatial gradient of the W
concentration is not accessible from the LEIS measurement. Because equation 7
gives the diffusion flux of W atoms as difference between the recession flux
and the measured effective W flux, setting the diffusion flux at room
temperature to zero yields the recession flux and permits to determine the
diffusion flux at higher temperatures. Figure 10 shows the Arrhenius plot of
the logarithm of the diffusion flux versus reciprocal temperature using the
data for fluences of 1e22m^-2 and 2e22m^-2. The diffusion activation energy is
derived from the slope and equals $E_{\rm a}=\SI{1.6}{eV}$. Since the
diffusion at room temperature is arbitrarily set to zero and may be larger,
this value represents an upper limit.

No other data on the W diffusion activation energy in EUROFER could be found
in the literature, but there is some data for the activation energy for W
diffusion in Fe available. All of the reported experiments are done at
considerably higher temperatures (¿1000K) and analysed either by electron
probe micro analysis (EPMA) or by measuring radioactive tracer isotope
diffusion. In these studies activation energies of 2.47eV [41], 2.97eV [42],
and 2.61eV [43] are obtained. Compared to the present results, these are
significantly larger values. There are various factors which might contribute
to the different behaviour. On the one hand, EUROFER is a more complex alloy
with multiple constituents. On the other hand, the microstructure may play a
decisive role. The EUROFER samples have small grains in the μm range as is
shown in figure 7. The Fe samples investigated in the referred diffusion
studies are carefully annealed and have a different structure with larger
grains. An enhanced grain boundary diffusion in EUROFER could be responsible
for the observed much lower diffusion activation energy

##  4 Summary and Conclusion

The W surface enrichment by preferential sputtering of EUROFER samples has
been measured in-situ by LEIS in an ion beam experiment. Sputtering with 250eV
D atoms clearly leads to W enrichment on the surface which is at room
temperature not yet saturated at fluences up to 1e23m^-2. Already at a
moderately increased temperature of 520K the measured enrichment is only half
as large, and at a temperature of 800K no increase in the W surface
concentration at the applied sputtering atom flux of 2e18m^-2s^-1 is
detectable. The W surface concentration data measured at various temperatures
yield an upper limit for the diffusion activation energy of $E_{\rm
a}=\SI{1.6}{eV}$. This value for EUROFER is considerably smaller than
activation energies for W diffusion in Fe (in the range 2.5eV to 3eV) which
are reported in the literature. One important reason for the different finding
in the EUROFER system may be the difference in grain structure and size, which
shows rather small grains in the μm range. An absolute calibration of the LEIS
data is done by comparing scattering spectra for pure Fe and pure W. The
surface enrichment has been additionally determined by TOF-MEIS, XPS, and EDX.
All of these methods show smaller values which confirms that the thickness of
the enriched surface layer is rather small with a half width in the range of a
few nm.

The results of the present study raises a question for the intended
application of EUROFER as a first wall material in a fusion power plant.
Because of the envisaged high operational temperature the strong W diffusion
may counteract the beneficial W enrichment which reduces the erosion rate and
prolongs the lifetime of the respective wall components. The present data has
been obtained in an ion beam experiment using rather low values of incident
particle fluxes compared to the conditions in a fusion reactor. According to
the estimates in [5] in a fusion reactor the lower bound for eroding particle
fluxes will be about one to two orders of magnitude larger than used in the
present laboratory study. Therefore, the experimental results do not rule out
that there still might be W enrichment at higher incident particle fluxes
which have to produce W recession fluxes due to preferential sputtering of Fe
which exceed the reduction of W surface concentration by diffusion. Recently,
similar experiments showed W surface enrichment after D sputtering of EUROFER
samples up to a temperature of 1050K when a four times higher D+ ion flux was
used [18]. However, the W enrichment will come at the price of larger net wall
erosion. In recessed areas with very low impinging particle fluxes the
achievable W surface enrichment may still be influenced by diffusion, but will
strongly depend on the operating temperature.

## Acknowledgements

We thank Mr. Albert Hiller for the technical support in re-building the
apparatus and during the experiments, Mr. Robert Habrichs for setting up the
S7 control system of the apparatus, Mr. Stefan Kirtz for installing the
personal computers used for data acquisition, Mrs. Beatrix Göths for polishing
the samples, and Dr. Anne Houben for her assistance with the magnetron sputter
coating of the calibration sample.

The operation of the ToF-MEIS setup at Uppsala University has been supported
by infrastructure grants from the Swedish Foundation for Strategic Research
(SSF) and the Swedish Research Council (VR-RFI). We are thankful to Dr. Daniel
Primetzhofer for providing help with the ToF-MEIS measurement and its
interpretation.

This work has been carried out within the framework of the EUROfusion
Consortium and has received funding from the Euratom research and training
programme 2014-2018 under grant agreement No 633053. The views and opinions
expressed herein do not necessarily reflect those of the European Commission.

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| at% Fe | at% Cr | at% W | at% C | at% O
---|---|---|---|---|---
all | 22.6 | 2.0 | 2.5 | 16.4 | 56.5
neglect O | 52.0 | 4.6 | 5.8 | 37.6 |
neglect O & C | 83.4 | 7.3 | 9.3 |  |
Table 1:  Surface concentrations of the EUROFER sample after D atom
irradiation with a fluence of $\mathit{\Phi}=\SI{1.1e23}{m^{-2}}$ at room
temperature determined with XPS.

Figure 1:  Schematic drawing of the LEIS apparatus.

Figure 2:  LEIS spectrum of 1 keV He+ ions scattered on EUROFER.

Figure 3:  LEIS spectrum measured after preferential sputtering using D with
$E=\SI{250}{eV}$ and a fluence of $\mathit{\Phi}=\SI{1.1e22}{m^{-2}}$.
Gaussian profiles are fitted to the O, Fe, and W peaks.

Figure 4:  Normalised He+ scattering spectra at 300K, 520K, 660K, and 800K
showing that no surface segregation of W occurs at elevated temperatures.

Figure 5:  High energy range of several LEIS spectra showing the W peak in a
series of consecutive measurements taken with increasing D fluence. The sample
is at room temperature. All spectra are normalised to the height of the Fe
peak.

Figure 6:  Relative surface density of W vs fluence of 250 eV D atoms at
various temperatures.

Figure 7:  SEM images of EUROFER sample after 250eV D bombardment with a
fluence of $\mathit{\Phi}=\SI{1.1e23}{m^{-2}}$ with two magnifications.

Figure 8:  MEIS analysis of EUROFER sample after 250eV D bombardment with a
fluence of $\mathit{\Phi}=\SI{1.1e23}{m^{-2}}$

Figure 9:  Simple model outlining the various particle fluxes leading to W
surface enrichment which have to be accounted for.

Figure 10:  Arrhenius plot of W diffusion coefficient vs inverse temperature.


# Phonon-dominated energy transport in purely metallic heterostructures

M. Herzog  Institut für Physik & Astronomie, Universität Potsdam, Karl-
Liebknecht-Str. 24-25, 14476 Potsdam, Germany  A. von Reppert  Institut für
Physik & Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24-25, 14476
Potsdam, Germany  J.-E. Pudell  Institut für Physik & Astronomie, Universität
Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany  Helmholtz Zentrum
Berlin, Albert-Einstein-Str. 15, 12489 Berlin, Germany  C. Henkel  Institut
für Physik & Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24-25,
14476 Potsdam, Germany  M. Kronseder  Institut für Experimentelle und
Angewandte Physik, Universität Regensburg, Germany  C. H. Back  Institut für
Experimentelle und Angewandte Physik, Universität Regensburg, Germany  Physics
Department, Technical University Munich, 85748 Garching, Germany  A. Maznev
Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA
02139, USA  M. Bargheer<EMAIL_ADDRESS>Institut für Physik &
Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam,
Germany  Helmholtz Zentrum Berlin, Albert-Einstein-Str. 15, 12489 Berlin,
Germany

(August 30, 2024)

###### Abstract

We use ultrafast x-ray diffraction to quantify the transport of energy in
laser-excited nanoscale Au/Ni bilayers. Electron transport and efficient
electron-phonon coupling in Ni convert the laser-deposited energy in the
conduction electrons within a few picoseconds into a strong non-equilibrium
between hot Ni and cold Au phonons at the bilayer interface. Modeling of the
subsequent equilibration dynamics within various two-temperature models
confirms that for ultrathin Au films the thermal transport is dominated by
phonons instead of conduction electrons because of the weak electron-phonon
coupling in Au.

††preprint: AIP/123-QED

##  I Introduction

Thermal transport in metallic heterostructures at the nanoscale is highly
relevant for diverse fields ranging from thermal management in
nanoelectronics[1, 2], spin-caloritronics[3] and ultrafast spin dynamics[4] to
photothermal processes [5] and plasmonic chemistry[6]. The thermal transport
in elemental metals is usually dominated by conduction electrons as the
thermal conductivity by phonons (lattice vibrations) is typically one or two
orders of magnitude smaller than its electronic counterpart[7, 8]. In thermal
equilibrium the mean-free path and thus the thermal conductivity of electrons
is typically limited by the electron-phonon interaction which simultaneously
excites phonons. Under non-equilibrium conditions, for example, in metals
right after absorption of an ultrashort laser pulse, the enhanced specific
heat and thermal conductivity of the hot electron gas in conjunction with
ballistic or superdiffusive electron transport tend to even enhance the role
of electron thermal transport[9, 10, 11, 12].

Modern device architectures as well as samples used in material science are
typically nano-scale heterostructures containing materials with different
properties to enable specific functionalities. The importance of phonon
thermal transport is obvious in metal-insulator heterostructures. Thermal
resistance network models assume a dominant role of the phonons for heat
transport through sub 10 nm metal layers of Mo/Si superlattices [13]. Phonon
thermal transport in metal-metal heterostructures has been rarely studied as
it is often disregarded for being a marginal effect[14, 15, 2].

A standard experimental method in order to address dynamical processes on
picosecond time scales is the pump-probe technique. Here, the sample of
interest is driven out of equilibrium by an intense laser pump pulse and the
resulting changes in the multipartite and mutually coupled degrees of freedom
are detected with a delayed probe pulse. The characteristics of the probe
pulse depend on the desired information. Using a visible or near-infrared
probe pulse provides access to the coupled dynamics of electrons, phonons and
spins in condensed matter, e.g., by means of thermoreflectance, transient
absorption and the magneto-optical Kerr effect (MOKE) [15, 16, 17, 18].
Although tremendous insight in the involved physical processes has been gained
in the last decades exploiting these techniques, the experimental results are
often difficult to interpret, in particular, far from non-equilibrium
conditions or in heterostructures with dimensions approaching the skin depth
of the probe light[18]. Experimental techniques that are able to precisely
determine the layer- and subsystem-specific energy content during the non-
equilibrium dynamics in nanoscopic metal heterostructures are sparse. This has
limited the dimensions of the investigated metal films in previous experiments
to several tens of nanometers. Under such circumstances the phonon
contribution to the energy exchange among the constituents was indeed
negligible or very small[14, 15].

Here we showcase that the exchange of energy between nanoscale metal films can
be dominated by the phonons instead of the conduction electrons. We
exemplarily consider Au-Ni bilayers supported by an insulating MgO substrate.
After excitation with an ultrashort laser pulse, we exploit the material-
specific sensitivity of ultrashort x-ray diffraction (UXRD) to infer the
evolution of the energy content from the strain response in each of the metal
layers. The time-dependent shifts of the layer-specific Bragg peaks precisely
quantify the energy exchange between the ultrathin films. We model the
underlying dynamics using two-temperature models with various levels of
complexity for the coupled electron-phonon systems in the heterostructure. As
pictorially summarized in Fig. 1(a), the analysis of our experimental data
reveals the intriguing scenario that in few-nm thin films energy transport
across the metal-metal interface by phonons (red arrows) dominates over the
transport via electrons and electron-phonon coupling (blue arrows). The
crucial ingredient for this unconventional thermal transport between the two
metals is their strongly differing electron-phonon coupling (EPC) strength.
The very efficient EPC in Ni rapidly concentrates almost the entire laser-
deposited energy in the Ni phonons thus generating a large gradient in the
phonon temperature. Although the conduction electrons have a superior thermal
conductivity, the weak EPC represents a particularly tight bottleneck in very
thin Au films for transferring energy into the large heat reservoir of the Au
phonons. This leaves the major contribution to the thermal interlayer
equilibration to phonon transport.

##  II Experiment

A series of Au-Ni bilayers of various thickness combinations was grown on
commercial MgO substrates by molecular beam epitaxy (MBE). The thickness of
the Au and Ni layers (see Table 1) were precisely characterized by x-ray
reflectivity (XRR) measurements at the KMC3-XPP beamline at BESSY II[19].
Figure 2(a) schematically shows the layered structure of the samples S1-S4.

We use ultrashort x-ray pulses generated by a table-top laser-driven plasma
x-ray source (PXS) to record transient angular shifts of Au (111) and Ni (002)
Bragg reflections after excitation of the sample with an ultrashort 800 nm
laser pulse[20, 21]. The shifts of the material-specific Bragg reflections in
reciprocal space are converted to a time-dependent average lattice strain for
each layer[22]. The experimental results for the samples S1-S4 at a common
incident pump fluence of approx. 10 mJ/cm2 are gathered in Fig. 1.

Figure 1: (a) Schematic of the Au-Ni heterostructure with variable Au
thickness on a MgO substrate. The figure visualizes the energy flow inside the
heterostructure after the Au and Ni electrons have equilibrated with the Ni
phonon system. The arrows depict the energy flow via electron diffusion and
EPC (blue) and via direct phonon diffusion (red). The transport via electrons
is very efficient and long-ranging, however, the weak EPC in Au forms a
bottleneck for this channel. (b)-(c) Results of UXRD experiments on samples
with systematic thickness variation for a common incident pump fluence of
approx. 10 mJ/cm2. Panel (b) and (c) depict the transient Ni and Au strain,
respectively, after excitation with an ultrashort laser pulse. The symbols
represent the experimentally measured transient layer strains which are
derived from the shifts of the respective Bragg reflections in reciprocal
space. Dashed lines are empirical fits according to eq. (6) representing the
rise and decay of the incoherent Au stress/strain. The solid lines are results
of the numerical modelling of the coherent and incoherent layer strains using
the d2TM. Note that the Au strain transients in panel (c) are offset and
normalized between 50 and 100 ps for a better comparability. The legends
provide the sample number and the Au thickness.

The transient strain evolution in Ni and Au (Fig. 1(b) and (c)) consists of a
superposition of coherent longitudinal acoustic phonon wavepackets and
incoherent contributions (thermal expansion)[23, 12]. Right after excitation
at zero time delay the Ni layer rapidly expands111Note that not all samples
exhibited a sufficiently intense Ni Bragg peak for measuring the transient Ni
strain with satisfactory statistics., evidencing the expected sub-picosecond
energy transfer from the laser-heated conduction electrons into Ni [23, 12].
This quick stress rise in the Ni lattice launches a coherent strain wavepacket
which causes the oscillatory signatures in the first tens of picoseconds in
Fig. 1(b) and (c) as it is reflected and transmitted through the layer
interfaces. All transients reveal that the Au layer is compressed immediately
after excitation, which shows that the Au contains substantially less energy
than the Ni layer on that time scale. Irrespective of the layer thickness, the
incoherent strain within Au grows extraordinarily slowly compared to the
intrinsic few-picosecond EPC time scale[25, 16] and reaches its maximum around
80 ps after excitation[23] which is much longer than previously expected[2].
At later time scales both layers obviously relax by heat diffusion into the
MgO substrate.

##  III Modified Two-Temperature Model (m2TM)

The pump pulse energy is absorbed exclusively by the conduction electrons
inside the Au-Ni bilayer whereby the electron-phonon (e-ph) system of the
metals is strongly driven out of equilibrium. Immediately after laser
excitation neither the electron nor the phonon system are perfectly described
by Fermi and Bose distribution functions, respectively[26]. However, our
experimental observable, the strain, is sensitive to the local energy
densities $\Delta\rho^{Q}(z,t)$ rather than to details of the distribution
functions[27, 28, 29]. Therefore, we define local (quasi-equilibrium)
temperatures $T_{\text{e/ph}}(z,t)$ for each subsystem via
$\Delta\rho^{Q}_{\text{e/ph}}=\int_{\Delta
T_{\text{e/ph}}}C_{\text{e/ph}}(T_{\text{e/ph}})\,\text{d}T_{\text{e/ph}}$.

The main idea of this paper is that the non-equilibrium between electrons and
phonons in the metal heterostructure is converted into a spatial temperature
step, where the Ni phonons are hot and the Au phonons are cold. This
temperature gradient in the phonon system efficiently drives thermal transport
by phonons across the interface. The alternative channel for heat transport
via the conduction electrons and EPC is proportional to the Au layer
thickness. That is, for very thin Au films the EPC is inefficient and the
equilibration of the phonon systems across the interface is thus predominantly
mediated by phonons.

| S1 | S1.1 | S2 | S3 | S4
---|---|---|---|---|---
Au thickness (nm) | 5.6 | 5.7 | 8.1 | 14.4 | 34.4
Ni thickness (nm) | 12.4 | 21.2 | 11.4 | 7.0 | 6.0
Table 1: Au and Ni layer thickness in nm in the investigated samples as
determined by x-ray reflectivity.

Before we discuss a diffusive two-temperature model (d2TM) with proper spatial
and temporal resolution[12], we emphasize this main outcome by approximating
the situation in a modified two-temperature model (m2TM), which describes the
stress that drives the lattice strain in ultrathin films on the ps-time scale
[23]. It disregards spatial gradients, thus being suited for rather thin
films, and separates the phonon temperature in the material with weak EPC (Au)
from the common temperature of conduction electrons (Au+Ni) and strongly
coupled phonons (Ni).

This is equivalent to assuming the entire electron system of the
heterostructure to be in thermal equilibrium with the Ni phonons. Hence, in
the m2TM the transient temperature of the Au phonons
$T_{\text{Au}}^{\text{ph}}$ and the combined system of Au and Ni electrons and
Ni phonons $T_{\text{Ni}}$ evolve according to:

$\displaystyle d_{\text{Au}}C_{\text{Au}}^{\text{ph}}\frac{\partial
T_{\text{Au}}^{\text{ph}}}{\partial t}$ $\displaystyle=G_{\text{Au-
Ni}}\left(T_{\text{Ni}}-T_{\text{Au}}^{\text{ph}}\right)$ (1) $\displaystyle
d_{\text{Ni}}C_{\text{Ni}}\frac{\partial T_{\text{Ni}}}{\partial t}$
$\displaystyle=G_{\text{Au-
Ni}}\left(T_{\text{Au}}^{\text{ph}}-T_{\text{Ni}}\right)+G_{\text{sub}}\left(T_{\text{sub}}-T_{\text{Ni}}\right)$
(2)

where $T_{\text{sub}}$ is the substrate temperature. Due to the one-
dimensional nature of the dynamics in homogeneously excited multilayers we
formulate the above equations using conductances $G_{i}$ representing an
energy flow per time and cross-sectional area. Moreover, $d_{\text{Au/Ni}}$
and $C_{\text{Au/Ni}}$ are the layer thickness and volumetric heat capacity of
the Au and Ni layer, respectively.

##  IV Electronic transport alone does not explain the data

In a first approach, we disregard direct phonon thermal transport across the
Au-Ni interface as is usually done in literature[14, 15]. We only account for
electron transport and subsequent EPC in Au. In this simplified case the
corresponding conductance is given by $G_{\text{Au-
Ni}}=d_{\text{Au}}g_{\text{Au}}$[16], as long as $d_{\text{Au}}$ is well below
the mean electron diffusion length given by
$L_{\text{diff}}^{\text{e}}=\sqrt{\kappa_{\text{Au}}^{\text{e}}/g_{\text{Au}}}\approx
125$ nm[25, 15]. Here, $g_{\text{Au}}$ is the EPC parameter in Au. The
coupling $G_{\text{sub}}$ across the Ni-MgO interface is about an order of
magnitude weaker, since e-ph equilibration and heat transfer into the MgO
substrate appear on well-separated time scales (Fig. 1(c)). Disregarding the
last term in eq. (2) and assuming temperature-independent material properties,
we may first solve the m2TM by an exponential rise and fall of the Au and Ni
temperatures, respectively,

$\Delta T_{\text{Ni}}\propto e^{-\frac{t}{\tau_{\text{rise}}}},\qquad\Delta
T_{\text{Au}}^{\text{ph}}\propto\left(1-e^{-\frac{t}{\tau_{\text{rise}}}}\right)$
(3)

where the rise time of the Au phonon temperature is given by

$\displaystyle\tau_{\text{rise}}^{-1}$ $\displaystyle=G_{\text{Au-
Ni}}\left(\frac{1}{d_{\text{Au}}C_{\text{Au}}^{\text{ph}}}+\frac{1}{d_{\text{Ni}}C_{\text{Ni}}}\right)$
(4)
$\displaystyle=g_{\text{Au}}\left(\frac{1}{C_{\text{Au}}^{\text{ph}}}+\frac{d_{\text{Au}}}{d_{\text{Ni}}}\frac{1}{C_{\text{Ni}}}\right).\quad\text{(no
phonons)}$ (5)

Eq. (5) is an approximation for the simplified case of exclusive energy
exchange via conduction electrons.

Figure 2: (a) Schematics of the investigated metal heterostructures S1-S4. The
empty symbols in the following panels represent a sample S1.1 similar to S1
with identical Au thickness but half the Ni thickness. (b) Au strain/stress
rise times $\tau_{\text{rise}}$ derived from the experimental data (blue
bullets) and the corresponding prediction from the m2TM in absence of phonon
transport (red diamonds) using an EPC constant $g_{\text{Au}}=2\cdot
10^{16}\,$W/(m3 K). (c) Total conductance $G_{\text{Au-Ni}}$ (blue bullets)
determined from the measured $\tau_{\text{rise}}$ in (b) via eq. (4). Red
diamonds show the conductance via electrons ($d_{\text{Au}}g_{\text{Au}}$)
assuming $g_{\text{Au}}=2\cdot 10^{16}\,$W/(m3 K). Black squares present the
difference of the former two which is attributed to the phonon conductance
$G_{\text{ph}}$. (d) Relative contribution of phonon transport to the total
energy arriving in the Au phonon system as derived from the m2TM (black
squares) and the d2TM (green triangles). Both models predict that for Au films
below approx. 10 nm thermal transport via phonons dominates.

On time scales beyond 100 ps the layers and subsystems have equilibrated and
the slowly relaxing strain of both layers indicate that heat diffuses from the
bilayer into the substrate via phononic thermal transport. Assuming a constant
temperature of the substrate222This is a reasonable approximation on the sub-
nanosecond time scale given the large thermal conductivity of MgO of approx.
50 W/(m K)[45]., eqs. (1) and (2) imply an exponential decay of the bilayer
temperature. In total, our m2TM suggests a time-dependent temperature of the
Au phonons of the form

$\Delta
T_{\text{Au}}^{\text{ph}}\propto\left(1-e^{-\frac{t}{\tau_{\text{rise}}}}\right)e^{-\frac{t}{\tau_{\text{fall}}}}.$
(6)

In order to check the validity of the assumption that vibrational thermal
transport between the metal layers is negligible in our m2TM, we fit the
experimental UXRD transients for the Au layer with eq. (6) ignoring the
oscillatory contributions to the signal. Here we assume that the thermal
expansion coefficient of Au is approximately temperature-independent, which is
reasonable above its Debye temperature $\Theta_{\text{D}}\approx 185\;$K[31].
The best fits to the normalized UXRD data are shown in Fig. 1(c) as dashed
lines. The incoherent rise and decay dynamics of the Au layer strain are well
reproduced. The obtained rise times $\tau_{\text{rise}}$, are shown in Fig.
2(b) as blue bullets with only weak variations from sample to sample. In
contrast, the rise times predicted by eq. (5) of our m2TM shown as red
diamonds vary by a factor of five and only agree for the sample with the
thickest Au layer.

This observation calls for adding a mechanism to the model which accelerates
energy transfer into Au phonons especially in ultrathin Au layers. One option
would be a strongly enhanced EPC constant $g_{\text{Au}}$. Indeed, scattering
of the hot conduction electrons at the interface or grain boundaries may
couple to surface and interface vibrational modes of the lattice. Also non-
thermal electron distributions may alter $g_{\text{Au}}$. However, for the
moderate Au electron temperature increase after equilibration with Ni of only
a few hundred Kelvin in the present cases, previous experiments and theory
suggest only tiny variations of $g_{\text{Au}}$[32, 33, 34, 35] and a required
increase by almost one order of magnitude is thus unreasonable. Alternatively,
the direct thermal transport between the hot Ni and cold Au via phonons is an
inevitable process that must contribute to an accelerated energy transfer from
Ni to Au, especially on the sub-10 nm length scale of the phonon mean-free
path.[13, 16]

It is straightforward to introduce an interface conductance $G_{\text{ph}}$
into our m2TM representing direct phonon thermal transport across the Au-Ni
interface. According to Fig. 1(a) it acts in parallel to the conductance via
EPC in Au. The coupling constant in eqs. (1) and (2) then reads

$G_{\text{Au-Ni}}=d_{\text{Au}}g_{\text{Au}}+G_{\text{ph}}.$ (7)

From the experimental rise times $\tau_{\text{rise}}$ (Fig. 2(b)) we obtain
the total conductance $G_{\text{Au-Ni}}$ via eq. (4) and then solve eq. (7)
for the phonon interface conductance $G_{\text{ph}}$, assuming a constant EPC
constant $g_{\text{Au}}=2\cdot 10^{16}\,$W/(m3 K)[10]. Figure 2(c) compares
the individual conductances obtained by this procedure. We find an average
phonon interface conductance $G_{\text{ph}}$ on the order of a few 100 MW/(m2
K). As a first consistency check, the quantity $G_{\text{ph}}$ can be
estimated for a Au-Ni interface using the respective acoustic phonon
dispersions within the radiation limit[36, 37]. The calculations yield
consistent values on the order of 50-300 MW/(m2 K) depending on the
assumptions being made with respect to mode conversion at the interface. Fig.
2(c) directly compares the EPC channel (red diamonds) and the phonon transport
across the interface (black squares). For very thin Au films below approx. 10
nm (S1 & S2) the phonon interface conductance is larger than the EPC
conductance. The main reason for this is that the energy transport into the Au
phonons via EPC scales the Au film thickness $d_{\text{Au}}$ and thus becomes
very inefficient in ultrathin films. The analysis of our UXRD data presented
so far strongly suggests that the direct phonon-mediated energy transport in
nanoscopic metal heterostructures cannot generally be ignored and at structure
dimensions of a few nanometers the energy transport can even be dominated by
phonon transport.

##  V Diffusive Two-Temperature Model (d2TM)

The m2TM relies on the very different EPC in Au and Ni, which is the main
ingredient for different phonon temperatures in Au and Ni. In order to cross-
check the validity of the m2TM and to resolve the energy flow within Au and Ni
layers, we numerically solve a spatially resolved diffusive 2TM (d2TM)
including electron and phonon heat diffusion. We utilize our simulation
toolbox udkm1Dsim[38, 39] which proved to yield precise modelling of
experimental UXRD data in the context of non-equilibrium e-ph dynamics and
transport in one-dimensional systems[12, 29]. Although ballistic electron
transport is relevant on a sub 100 fs timescale, the diffusive treatment
yields useful results in the discussed context, because the equilibration
within the electron system is much faster than both the time-resolution of the
experiment and any other dynamics in the samples. The coupled differential
equations of the d2TM read

$\displaystyle C_{\text{e}}(T_{\text{e}})\frac{\partial T_{\text{e}}}{\partial
t}$ $\displaystyle=\frac{\partial}{\partial
z}\left(\kappa_{\text{e}}(T_{\text{e}},T_{\text{ph}})\frac{\partial
T_{\text{e}}}{\partial z}\right)-g(T_{\text{e}}-T_{\text{ph}})+S(z,t)$ (8)
$\displaystyle\underbrace{C_{\text{ph}}\frac{\partial T_{\text{ph}}}{\partial
t}}_{\dot{\rho}^{Q}_{\text{tot,ph}}}$
$\displaystyle=\underbrace{\frac{\partial}{\partial
z}\left(\kappa_{\text{ph}}\frac{\partial T_{\text{ph}}}{\partial
z}\right)}_{\dot{\rho}^{Q}_{\text{ph}}}+\underbrace{g(T_{\text{e}}-T_{\text{ph}})}_{\dot{\rho}^{Q}_{\text{ep}}}$
(9)

where the upper/lower equation represents the evolution of the electron/phonon
temperature after excitation of the electrons via absorption of the laser
pulse energy represented by the source term $S(z,t)$. Here, $z$ is the spatial
coordinate perpendicular to the sample surface. The quantities
$C_{\text{e/ph}}$, $\kappa_{\text{e/ph}}$ and $g$ are the specific heat and
thermal conductivity of the electrons and the phonons as well as the EPC
constant, respectively. As we investigate heterostructures consisting of
different materials including their interfaces these quantities have an
explicit spatial dependence. We also take into account the explicit
temperature dependencies $C_{\text{e}}=\gamma T_{\text{e}}$ and
$\kappa_{\text{e}}=\kappa_{\text{e}}^{0}T_{\text{e}}/T_{\text{ph}}$ implied by
the Sommerfeld model of free electrons[12], whereas we omit the weak
temperature dependence of the phonon counterparts. We assume negligible
interface resistance for the electrons [15], but in order to parametrize the
energy exchange across the metal-metal interface by phonons we include a
finite interface conductance $G_{\text{ph}}$ in terms of a tiny interface
layer with suppressed phonon conductivity. Note that the m2TM fitting analysis
presented above correctly recovers the $G_{\text{ph}}$ applied in a
corresponding d2TM calculation given the latter uses the same simplifying
assumptions such as infinite conductivities in Au and Ni and vanishing heat
conduction into the substrate.

In analogy to recent investigations[12, 29], we numerically solve the system
of coupled differential eqs. (8) and (9) using bulk parameters for the
involved materials. In particular, we fix the EPC constant in Au to
$g_{\text{Au}}=2\cdot 10^{16}\,$W/(m3 K)[10]. The thermal stress related to
the heated subsystems drives coherent and incoherent spatiotemporal lattice
strain which is calculated using a linear-chain model[40, 38, 39]. The average
strain in the Au and Ni layers obtained by these calculations is compared to
the UXRD data in Fig. 1. We find a very satisfactory agreement of the
numerical results with the experimental data for the various samples with
different Ni and Au layer combinations. In particular, the initial compression
of the cold Au lattice by the adjacent Ni layer due to its fast heating is
well reproduced, evidencing the fast and efficient funneling of the excitation
energy into the Ni phonons[12, 29]. The slow rise of the incoherent Au strain
is matched in all samples simultaneously assuming a finite phonon interface
conductance of $G_{\text{ph}}=270$ MW/(m2 K). In accord with the predictions
by our m2TM summarized in Fig. 2(b), the build-up of the incoherent
stress/strain in Au would be much slower when omitting the direct energy
exchange between Ni and Au via phonon diffusion (not shown), in particular,
for the samples with single-digit nanometer Au thickness.

We emphasize that the local internal mechanical stress inside a material is
proportional to the local energy density of its subsystems[41, 42, 43, 44].
That is, the incoherent lattice strain measured in our UXRD experiments
directly quantifies the transient layer-averaged energy density. We thus
discuss the energy transport processes from the perspective of our direct
observable, i.e., the transient Au strain shown in Fig. 1(c).

In the following we dissect the d2TM given by eqs. (8) and (9) thereby showing
how to individually quantify the energy transport within the heterostructure
by electrons and phonons. In essence, the left side of eq. (8) and (9)
represents the total time-dependent rate of local energy density
$\dot{\rho}^{Q}_{\text{tot}}$ in the electron and phonon subsystems,
respectively. To illustrate the two channels that funnel energy into the Au
phonon subsystem we depict the total energy density rate
$\dot{\rho}^{Q}_{\text{tot,ph}}=\dot{\rho}^{Q}_{\text{ph}}+\dot{\rho}^{Q}_{\text{ep}}$
corresponding to the calculation for sample S4 (34.4 nm Au layer) in the
false-color plot in Fig. 3(a).

Figure 3: (a) Spatiotemporal energy density rates inside the Au phonon
subsystem corresponding to the strain simulations shown in Fig. 1(c) for the
sample S1 with thinnest Au layer (contour lines) and S4 with the thickest Au
layer (false-color plot). The interface to the Ni layer is located at the
right-hand side of the plot. (b)-(c) Time evolution of the layer-integrated
energy density rates $\dot{\rho}^{Q}$ (dotted lines) and accumulated energy
$\rho^{Q}$ per unit area (solid lines) for sample S4 and S1, respectively. The
line colors encode the total energy (black) and its separation into EPC (red)
and phonon transport channels (blue). While EPC dictates the energy flow into
thick Au, phonon transport dominates after a few picoseconds in thin Au.

Note the broken abscissa scaling in order to highlight the region near the Au-
Ni interface. Two main sources of Au phonon energy increase can be identified:
(i) a spatially homogeneous energy input within the first picosecond due to
EPC via the homogeneously distributed hot electrons in Au and (ii) energy
entering inhomogeneously from the Ni layer (right-hand border of plot) by
phonon diffusion. The contour lines superimposed on the false-color plot
correspond to the rate of energy density transported into the 5.6 nm thick Au
layer of S1. Clearly, the local energy input into the Au phonons is nearly
independent of the Au thickness. As already mentioned above, the main
difference is that the thick film offers much more volume for energy transfer
via EPC, which is proportional $d_{\text{Au}}$ (cf. eq. (7)). Of course, this
only holds up to roughly the electron-phonon diffusion length
$L^{\text{e}}_{\text{diff}}$ mentioned above.

While Fig. 3(a) illustrates the energy flowing into the Au phonon system with
full spatial resolution, we plot the spatially integrated quantities as dashed
lines in Fig. 3b) for the thickest and in Fig. 3(c) for the thinnest Au film.
Here we differentiate the two channels from eq. (9) by color: Initially the
EPC channel ($\dot{\rho}^{Q}_{\text{ep}}$, dashed red) dominates in both
samples. In case of the thinner Au film (panel (c)), the phonon transport rate
($\dot{\rho}^{Q}_{\text{ph}}$, dashed blue) across the Au/Ni interface becomes
dominant after about 2 ps. Beyond 5 ps more than half of the energy
accumulated in the Au phonons was received via this channel (solid blue line).
For the thicker Au film, however, the EPC is always the dominant channel
(solid red line). For the thinnest film S1 (Fig. 3(c)) we find that at the
moment of maximum total energy arrived in the Au phonons, 2/3 of the energy
density via phonon diffusion and only 1/3 via EPC. This phonon-dominated
thermal transport is a remarkable observation given that two elemental metals
are considered where thermal transport via phonons is usually at least an
order of magnitude weaker than via conduction electrons[7, 8].

The results of the above analysis on all investigated samples is summarized in
Fig. 2(d) as green triangles. Clearly, the quantitatively much more reliable
d2TM verifies the conclusions drawn from the conceptually simpler m2TM,
namely, that the energy exchange in our Au-Ni bilayers is dominated by phonon
diffusion if the Au thickness falls below approx. 10 nm.

##  VI Conclusion

We have investigated Au-Ni heterostructures with Au layer thicknesses ranging
from 5.6 to 34 nm excited by ultrashort laser puses. The modeling of UXRD
experiments via a simplified (m2TM) and a more complex and quantitative two-
temperature model (d2TM) (Fig. 2(d)) consistently reveals that energy
transport from the hot Ni into the cold Au phonon system is dominated by
phonon diffusion across the Au/Ni interface, provided the Au layer’s thickness
is on the order of the phonon diffusion length of approx. 10 nm. The main
ingredient to realize dominant phonon heat transport in the discussed
nanoscale heterostructures is the combination of the weak EPC in Au and the
strong EPC in Ni. As a consequence, the energetic conduction electrons rapidly
transfer the excess energy to the Ni phonons. Shortly after laser excitation,
this gives rise to a large phonon temperature gradient causing a large energy
flow across the Au-Ni interface via phonons. These processes at the interface
occur independent of the Au layer thickness (see comparison in Fig. 3a)). When
the Au thickness drops below the electron diffusion length of approx. 125 nm,
the energy transfer to Au phonons via EPC decreases linearly. For thicknesses
on the order of the phonon diffusion length, the direct phonon transport
prevails over the electronic channel. The strong EPC in Ni remains crucial
during the energy transfer to the Au lattice, because any excess energy in the
electron system migrates preferentially to Ni phonons, thus stabilizing the
phonon temperature gradient across the Au/Ni interface.

We conclude that at the nanoscale, phonon thermal transport cannot be
neglected even for noble metals if they are in contact with another metal with
large EPC. We believe that this surprising fact will be useful in
understanding and tailoring energy transport in various systems ranging from
plasmonic heterostructures with applications in chemistry to (magnetic) data-
processing and storage in nanoscale device structures.

###### Acknowledgements.

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) via BA 2281/11-1. We acknowledge the characterization of
the heterostructures via XRR at the XPP-KMC3 synchrotron radiation beamline
D13.2 at the BESSY II electron storage ring operated by the Helmholtz-Zentrum
Berlin.

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