# Indirect X-ray photodesorption of 15N2 and 13CO from mixed and layered ices

R. Basalgète<EMAIL_ADDRESS>Sorbonne Université,
Observatoire de Paris, Université PSL, CNRS, LERMA, F-75005, Paris, France  D.
Torres-Díaz  Sorbonne Université, Observatoire de Paris, Université PSL, CNRS,
LERMA, F-75005, Paris, France  Univ. Paris Saclay, CNRS, ISMO, 91405 Orsay,
France  A. Lafosse  Univ. Paris Saclay, CNRS, ISMO, 91405 Orsay, France  L.
Amiaud  Univ. Paris Saclay, CNRS, ISMO, 91405 Orsay, France  G. Féraud
Sorbonne Université, Observatoire de Paris, Université PSL, CNRS, LERMA,
F-75005, Paris, France  P. Jeseck  Sorbonne Université, Observatoire de Paris,
Université PSL, CNRS, LERMA, F-75005, Paris, France  L. Philippe  Sorbonne
Université, Observatoire de Paris, Université PSL, CNRS, LERMA, F-75005,
Paris, France  X. Michaut  Sorbonne Université, Observatoire de Paris,
Université PSL, CNRS, LERMA, F-75005, Paris, France  J-H. Fillion  Sorbonne
Université, Observatoire de Paris, Université PSL, CNRS, LERMA, F-75005,
Paris, France  M. Bertin  Sorbonne Université, Observatoire de Paris,
Université PSL, CNRS, LERMA, F-75005, Paris, France

###### Abstract

X-ray photodesorption yields of 15N2 and 13CO are derived as a function of the
incident photon energy near the N ($\sim$ 400 eV) and O K-edge ($\sim$ 500 eV)
for pure 15N2 ice and mixed 13CO:15N2 ices. The photodesorption spectra from
the mixed ices reveal an indirect desorption mechanism for which the
desorption of 15N2 and 13CO is triggered by the photo-absorption of
respectively 13CO and 15N2. This mechanism is confirmed by the X-ray
photodesorption of 13CO from a layered 13CO/15N2 ice irradiated at 401 eV, on
the N 1s $\rightarrow\pi^{*}$ transition of 15N2. This latter experiment
enables to quantify the relevant depth involved in the indirect desorption
process, which is found to be 30 - 40 ML in that case. This value is further
related to the energy transport of Auger electrons emitted from the photo-
absorbing 15N2 molecules that scatter towards the ice surface, inducing the
desorption of 13CO. The photodesorption yields corrected from the energy that
can participate to the desorption process (expressed in molecules desorbed by
eV deposited) do not depend on the photon energy hence neither on the photo-
absorbing molecule nor on its state after Auger decay. This demonstrates that
X-ray induced electron stimulated desorption (XESD), mediated by Auger
scattering, is the dominant process explaining the desorption of 15N2 and 13CO
from the ices studied in this work.

††preprint: AIP/123-QED

##  I Introduction

Diatomic molecules such as CO and N2 have been extensively studied in
laboratory at very low temperature (T < 20 K), in their solid phase. Indeed,
these molecules are expected to play an important role in astrophysical
environments. For instance, they are observed directly (especially for CO) or
indirectly (especially for N2) in the interstellar medium (ISM) and the solar
system in a diversity of icy solids such as interstellar ices (Boogert,
Gerakines, and Whittet, 2015), comets (Mumma and Charnley, 2011; Rubin  _et
al._ , 2015) and icy moons and planets (Owen  _et al._ , 1993; Cruikshank  _et
al._ , 1993; Bennett, Pirim, and Orlando, 2013). Interaction of these icy
solids with photons coming from nearby or distant stars can be at the origin
of exchanges between solid and gas phases via the so-called photodesorption
phenomenon. Photodesorption is a non-thermal process through which the energy
of incident photons is absorbed by the ice and partly converted to the
desorption of molecules from its surface. In the last decades, it has been
extensively studied in the vacuum ultraviolet (VUV) range (7 - 13.6 eV) for N2
and CO ices (Öberg  _et al._ , 2007; Öberg, van Dishoeck, and Linnartz, 2009;
Muñoz Caro, G. M.  _et al._ , 2010; Fayolle  _et al._ , 2011, 2013; Bertin
_et al._ , 2013).

More recently, the desorption induced by the irradiation of X-rays, referred
to as X-ray photodesorption, was also highlighted as a significant process for
ices composed of simple (Dupuy  _et al._ , 2018, 2021b) and complex molecules
(Jiménez-Escobar  _et al._ , 2018; Ciaravella  _et al._ , 2020; Basalgète  _et
al._ , 2021a). More importantly, it was suggested that X-ray photodesorption
of neutral molecules was strongly dependent on the ice composition via
indirect desorption mechanisms (Basalgète  _et al._ , 2021b). A detailed
comprehension of these indirect processes on a microscopic scale is of primary
importance to understand their implication in astrophysical environments. For
a proper modeling of such processes, it is also required to access
quantitative data concerning desorption yields.

The X-ray photodesorption from condensed N2 and CO has been previously studied
for thin layers deposited on top of transition and noble metals (Frigo  _et
al._ , 1998; Feulner  _et al._ , 2000; Romberg  _et al._ , 2000; Feulner  _et
al._ , 2002). In that case, desorption of neutral and ionic molecules (N2, CO,
CO+) as well as fragments (N, N+, N2+, C, O, O+, C+) was found to strongly
depend on singly or multiply valence-excited states, after decay of the core
hole state. These states were associated with specific desorption mechanisms.
In some cases, ultra-fast processes occurring during the core hole state
lifetime were also suggested to play a role for the desorption of ionic
fragments (Frigo  _et al._ , 1998).

For thick molecular ices, characterized by a higher number of layers deposited
onto a substrate (generally more than 50 layers), the processes leading to
desorption may be different. For instance, after X-ray absorption by molecules
in the ice, the relaxation of the core hole state results in the emission of
an Auger electron with a probability close to 1 for low Z elements (Walters
and Bhalla, 1971; Krause, 1979). This Auger electron carries most of the
initial photon energy and scatters inelastically in the ice, creating
secondary events (e.g. ionization and excitation of the surrounding molecules)
and especially, a cascade of secondary low energy (< 20 eV) electrons, that
may lead in fine to the desorption of molecules from the ice surface. This
process is known as X-ray induced electron stimulated desorption (XESD). XESD
was not suggested to be the dominant process for the X-ray photodesorption of
ions from pure N2 and CO ice (Feulner  _et al._ , 1992; Dupuy  _et al._ ,
2021b). Whereas for the desorption of neutrals, it was assumed to be the case
for pure CO ice (Dupuy  _et al._ , 2021b), pure H2O ice (Dupuy  _et al._ ,
2020) and pure and mixed methanol-containing ices (Basalgète  _et al._ ,
2021a, b).

Based on quantitative data, X-ray photodesorption of ions from molecular ices
is expected to be negligible compared to the desorption of neutrals (Dupuy
_et al._ , 2018, 2021b). In the present work, we experimentally study the
X-ray photodesorption process for neutral desorption from pure 15N2 ice and
from mixed and layered 13CO:15N2 ices (isotopes are chosen to differentiate
the molecules by mass spectrometry). Resonant 1s core excitation (or
ionization) near the N ($\sim$ 400 eV) or O ($\sim$ 500 eV) K-edge, can be
achieved thanks to tunable and high spectral resolution X-rays from
synchrotron facilities, allowing thereby to selectively photo-excite 15N2 or
13CO to trigger desorption from ices containing these molecules. We first
provide a quantitative study of the X-ray photodesorption of neutral molecules
from pure 15N2 ice. Then, we quantify this process for mixed 13CO:15N2 and
layered 13CO/15N2 (13CO on top of 15N2) ices. This latter set of experiments
brings important information to discuss the desorption mechanisms.

##  II Experiment and methodology

###  II.1 Setup and X-ray beamline

To run the experiments, the Surface Processes and ICES (SPICES) setup was
connected to the SEXTANTS beamline of the SOLEIL synchrotron facility at
Saint-Aubin, France (Sacchi  _et al._ , 2013). SPICES consists of an Ultra-
High Vacuum (UHV) chamber (base pressure of $\sim$ 10-10 mbar) at the center
of which a copper substrate (polycrystalline oxygen-free high-conductivity
copper, surface of 1.5 $\times$ 1.5 cm2) can be cooled down to $\sim$ 15 K by
a closed-cycle Helium cryostat. The substrate is electrically insulated from
its sample holder by a Kapton foil. This enables the measurement of the drain
current generated by electrons escaping the ice after X-ray absorption, which
we referred to as the Total Electron Yield (TEY) in the following. The TEY can
be measured while scanning the energy of the incident photons and it is
representative of the X-ray absorption profile of the ices studied in this
work. It is expressed in electrons per incident photon (displayed as e-
photon-1 for more simplicity) by correcting the drain current from the photon
flux.

The photon flux is measured by a calibrated silicon photodiode mounted on the
beamline. The SEXTANTS beamline provides X-ray photons, energy of which can be
finely tuned by means of a monochromator. The energy resolution can also be
controlled by adjusting slits apertures at the exit of the monochromator. In
the present studies, we have used photons in the 390 - 460 eV range (Nitrogen
K-edge) and in the 530 - 560 eV range (Oxygen K-edge). Spectral resolutions of
$\sim$ 100 meV and $\sim$ 350 meV were used to run the experiments. The photon
flux varies with the energy and the spectral resolution between 1011 and 1012
photon s-1. The beam was sent at a 47∘ incidence relative to the normal of the
substrate surface and the spot area at the surface was approximately 0.1 cm2.

The calibration of the energy scale of the beamline was performed near the N
K-edge and the O K-edge as followed:

  * •

near the N K-edge, the TEY was measured on a pure 15N2 ice as a function of
the energy of the incident photons and it was compared to gas phase X-ray
absorption spectroscopy experiments (e.g. Chen, Ma, and Sette (1989); Feifel
_et al._ (2004)). The TEY peak corresponding to the N 1s $\rightarrow$
$\pi^{*}$ ($v^{\prime}$ = 0) transition of 15N2 was set to 400.868 eV
according to Chen, Ma, and Sette (1989) (see Figure 1 and Section III.1). We
therefore assumed that this energy position was not significantly shifted when
going from gas phase to solid phase, as observed for a similar molecule: CO
(Jugnet  _et al._ , 1984). Note that the energy of the transition is slightly
varying ($\pm$ 20 meV) from one gas phase experiment to another (King, Read,
and Tronc, 1977; Hitchcock and Brion, 1980; Sodhi and Brion, 1984; Kempgens
_et al._ , 1996; Feifel  _et al._ , 2004; Kato  _et al._ , 2007).

  * •

near the O K-edge, the O 1s $\rightarrow$ $\pi^{*}$ transition of 13CO
observed on the TEY of a mixed 13CO:15N2 ice was centered at 534.4 eV (see
Figure 2 and Section III.1) according to pure CO ice spectroscopy experiments
(Jugnet  _et al._ , 1984), assuming that the inter-molecular interactions
between 13CO and 15N2 are not significantly shifting the energy position of
the electronic transition, which is reasonable considering such weakly
interacting solids

###  II.2 Ice deposition

Within the SPICES setup, a tube connected to a gas introduction system, that
can be translated a few millimeters in front of the substrate surface, enables
to inject a partial pressure of gas-phase molecules that stick on the cold
surface to form the molecular ices without significantly modifying the base
pressure of the UHV chamber. The gaseous molecules used during this work were
molecular nitrogen 15N2 (98.6% 15N purity, Eurisotop) and carbon monoxide 13CO
(99% 13C purity, Eurisotop). The ices thickness is expressed in monolayer
(ML), equivalent to a molecule surface density of approximately 1015 molecule
cm-2. Prior to the synchrotron experiments, the temperature-programmed
desorption (TPD) technique was used to calibrate the rate and deposition time
needed to grow a targeted ice thickness. The relative uncertainty on the
number of ML deposited during a deposition procedure is about 10% (see e.g.
Doronin  _et al._ (2015)).

The ices studied in this work were deposited at 15 K. The mixed 13CO:15N2 ices
were grown by controlling in situ the partial pressure of each species
injected in the UHV chamber independently (two different valves connected to
the deposition tube were used). In this way, the mixing ratio is set by
adjusting the partial pressures corresponding to each species. The experiment
regarding the layered 13CO/15N2 ice (see Section III.2.3) was achieved by
first depositing 50 ML of 15N2 at 15 K. Then, on top of it, a given number of
ML of 13CO was deposited and the ice was irradiated to measure the
photodesorption yields. This operation (deposition of 13CO on top and
irradiation) was sequentially repeated on the same ice until reaching $\sim$
90 ML of 13CO on top of the 15N2 ice. The number of ML of 13CO deposited at
each step is displayed in Figure 5 (see Section III.2.3).

###  II.3 Derivation of the photodesorption yields

The photodesorbed molecules are probed in the gas phase during the X-ray
irradiation of the ice by means of a quadrupole mass spectrometer (QMS)
equipped with an electron impact ionization chamber at 70 eV. The
photodesorption of 13CO and 15N2 was monitored by recording the QMS signal on
the mass channel 29 u. and 30 u. respectively. The signal intensities are
divided by the photon flux and multiplied by a factor $k$ to obtain the X-ray
photodesorption yields $\Gamma_{raw}$ expressed in molecule desorbed per
incident photon (displayed as molecules photon-1 in the following for more
simplicity). The factor $k$ was derived prior to the synchrotron runs to
relate the QMS current to a calibrated number of 15N2 molecules desorbed
during a TPD experiment. For more details on the calibration procedure, see
Basalgète  _et al._ (2021b). The apparatus function of our QMS can be
considered constant between the mass channels 29 u. and 30 u. and the non-
dissociative electron impact ionization cross sections at 70 eV of 13CO (Tian
and Vidal, 1998) and 15N2 (Straub  _et al._ , 1996) are nearly equals such
that we considered that the detection efficiency of our QMS is similar for
13CO and 15N2. This results in using a similar factor $k$ for quantifying the
photodesorption yields of 13CO and 15N2. The systematic uncertainty on the
photodesorption yields provided by this calibration method is estimated to be
$\sim$ 50%.

In Section IV.4, we compute the photodesorption yields $\Gamma_{eV}$ expressed
in molecule desorbed per eV deposited by correcting the experimental
photodesorption yields $\Gamma_{raw}$ (expressed in molecules photon-1)
considering the absorption cross section. This results in the following
formula:

$\Gamma_{eV}(E)=\frac{\Gamma_{raw}(E)}{E\,a_{dil}\,(1-e^{-\sigma(E)N})}$ (1)

where $E$ is the energy of the incident photon, $a_{dil}$ is a factor taking
into account the dilution of the photodesorbing molecules in the case of mixed
ices (namely $a_{dil}$ = 1/3 and 2/3 for the photodesorption yield of,
respectively, 15N2 and 13CO from a mixed 13CO:15N2 \- 2:1 ice), $\sigma(E)$ is
the photo-absorption cross section at $E$ and $N$ is the column density
involved in the desorption process. $N$ is equal to $N=\Lambda_{des}\times
b_{dil}\times 10^{15}$ cm-2 where $\Lambda_{des}$ is the desorption-relevant
depth expressed in ML (this notion is explained in more details in Section IV)
and $b_{dil}$ is a factor taking into account the dilution of the photo-
absorbing molecule in the case of mixed ices (namely $b_{dil}$ = 1/3 and 2/3
for the yields derived, respectively, near the N and O K edge).

Figure 1:  Upper right panel: TEY of 15N2 ice at 15 K (50ML) from our
experiments in the N K-edge region between 398 and 430 eV. The upper left
panel shows the N 1s $\rightarrow\pi^{*}$ excitation region and the lower
panel shows the region near the ionization threshold between 405 and 430 eV.
In solid red lines are the X-ray photoabsorption spectra of gas phase 14N2
from Chen, Ma, and Sette (1989) with a spectral resolution of 40 meV. In solid
green lines are the partial electron yields (PEYs) of 50 ML of 14N2 ice at 15
K from Feulner  _et al._ (1992) with a spectral resolution of 100 meV. In blue
lines are the TEYs of 50 ML of 15N2 ice at 15 K from our experiments with a
spectral resolution of 100 meV for the upper left panel and 350 meV for the
lower and upper right panels. The baselines of the different curves have been
shifted for more clarity. The red dashed vertical lines in the upper left
panel are centered on the gas phase vibrational bands.

##  III Results

###  III.1 X-ray absorption spectra

####  III.1.1 15N2 ice photoabsorption near N K-edge

The X-ray absorption spectrum of pure 15N2 ice at 15 K near the N K-edge,
assimilated to our TEY measurements, is displayed in Figure 1 (blue lines) for
different energy ranges and spectral resolutions. The absorption is dominated
by the N 1s $\rightarrow\pi^{*}$ transition of 15N2 near 401 eV, whose
vibrational structure has been resolved with a spectral resolution of 100 meV.
Our TEY in the N 1s $\rightarrow\pi^{*}$ region (see upper panel of Figure 1)
compares well with other absorption spectra of gas phase 14N2 (Chen, Ma, and
Sette, 1989) and 14N2 ice at 15 K (Feulner  _et al._ , 1992). The N
1s${}^{-1}\pi^{*}$ core electronic state of the free molecule is not
significantly modified in the solid phase, as expected for weak Van der Waals
interactions between N2 molecules in the solid. There are however some slight
discrepancies in the position of the vibrational levels between the three
curves in the upper panel of Figure 1. When going from gas phase (red line) to
solid phase (green line), the small differences in the position of the
vibrational levels of the N 1s${}^{-1}\pi^{*}$ state of 14N2 could be
attributed to either experimental uncertainties on the relative position of
the peaks or to inter-molecular interactions in the solid phase. The
comparison of our TEY of 15N2 ice (blue line) with the PEY of 14N2 ice (green
line) shows a smaller vibrational level spacing for 15N2. This is expected to
come from an isotopic effect. A similar behaviour is observed in the
vibrational level spacing of the A${}^{1}\Pi$ state of 13CO versus 12CO ice
and of the b${}^{1}\Pi_{u}$ state of 15N2 versus 14N2 ice probed by Vacuum
UltraViolet (VUV) photodesorption experiments (Bertin  _et al._ , 2012;
Fayolle  _et al._ , 2013).

Figure 2:  TEY of a mixed 13CO:15N2 \- 2:1 ice at 15 K (total of 100 ML) in
the O K-edge region between 530 and 560 eV from our experiments, with a
spectral resolution of 350 meV.

In the lower panel of Figure 1, the Rydberg states of gas phase 14N2 seen
below the ionization potential (IP) are significantly modified in the solid
phase, as expected from the overlapping of the Rydberg orbitals with that of
the neighboring molecules in the solid. Instead, series of broad peaks
(labelled (*) and (**) in Figure 1), whose positions go above the gas phase
IP, populate this region. There is no significant difference in this region
between 14N2 and 15N2 in solid phase. The first series of the four peaks
labelled (*) has been attributed to the equivalent of the gas phase Rydberg
states 3s$\sigma$, 3p$\pi$, 4s$\sigma$ and 5s$\sigma$ in solid phase by
Feulner  _et al._ (1992), based on polarization dependent X-ray
photodesorption of N+ and based on the data from Chen, Ma, and Sette (1989).
The attribution of the peaks labelled (**) above the gas phase IP in Figure 1
has not been studied in the literature to our knowledge. The gas phase broad
feature observed near 415 eV has been attributed by Chen, Ma, and Sette (1989)
to shake-up states, temptatively associated with the state configurations
(1s)-1(5$\sigma$)-1(1$\pi_{g}^{*}$)1(3s$\sigma$)1 and
(1s)-1(1$\pi$)-1(1$\pi_{g}^{*}$)1(3p$\pi$)1. As one can see in Figure 1, a
similar feature is observed in this region for 15N2 and 14N2 ice. The feature
observed near 419 eV in the gas phase has been attributed to a $\sigma$ shape
resonance (Chen, Ma, and Sette, 1989). A similar feature is observed for 15N2
ice.

####  III.1.2 13CO:15N2 ice photoabsorption near O K-edge

The TEY of a mixed 13CO:15N2 ice (2:1) ice at 15 K near the O K-edge is
displayed in Figure 2. The absorption is dominated by the O 1s
$\rightarrow\pi^{*}$ transition of 13CO centered at 534.4 eV. The spectrum is
similar to that of a pure CO ice studied in similar experiments and for which
more details are available regarding the attribution of the spectral features
(Dupuy  _et al._ , 2021b). The inter-molecular interactions between 13CO and
15N2 in the mixed ice are not modifying the transitions observed in this
energy range compared to a pure CO ice. The N 1s core electron photo-
ionization of 15N2 is expected to contribute to the absorption spectrum in
this energy range but it is reasonably assumed to be negligible compared to
13CO photo-absorption, and it should in any case account for a monotonically
decreasing signal over the whole energy range.

Figure 3:  X-ray photodesorption yields of 15N2 (green lines) from pure 15N2
ice at 15 K (50 ML) in the N 1s $\rightarrow\pi^{*}$ excitation region (upper
panel, spectral resolution of 100 meV) and in the near-IP region (lower panel,
spectral resolution of 350 meV). The TEYs measured during the irradiations are
also displayed for comparison (in blue lines). Figure 4:  X-ray
photodesorption yields of 13CO and 15N2 (solid lines) in the N K-edge (left
panels) and O K-edge (right panels) regions from mixed 13CO:15N2 ices at 15 K
(total of 100 ML) with mixing ratio of 2:1 (red lines) and 20:1 (blue lines).
The TEYs measured simultaneously during the corresponding irradiation
procedure are also displayed in dashed lines in arbitrary units.

###  III.2 X-ray photodesorption yields

####  III.2.1 15N2 pure ice

The photodesorption spectra of 15N2 from a pure 15N2 ice at 15 K are shown in
Figure 3 (green lines) with the upper panel corresponding to the N 1s
$\rightarrow\pi^{*}$ transition and the lower panel corresponding to the near-
IP region. The TEYs measured simultaneously during the irradiation procedure
are also displayed in blue lines for comparison. The photodesorption yields
are higher by more than one order of magnitude in the N 1s
$\rightarrow\pi^{*}$ region than in the near-IP region, with a maximum of
$\sim$ 5 molecules photon-1 at the N 1s $\rightarrow\pi^{*}$ ($v^{\prime}$ =
0, 1) transitions. The photodesorption spectra are following the same
variations as the TEYs except for small discrepancies on the relative
intensities of the features, that are likely due to background correction
issues and for which we do not attribute any physical meaning. The
photodesorption yields of 15N2 and the TEYs are obtained from an ice having
received a fluence $<3.10^{16}$ ph cm-2. They both decrease with increasing
fluence due to the ice photo-ageing, that is the structural and chemical
modifications of the ice due to photo-absorption, but the shape of the spectra
remains the same and no significant new absorption features are observed in
the energy range probed (400 - 450 eV). The possible photodesorption of 15N3
and 15N4 were monitored during the irradiation but no desorption signals were
found (with a detection limit of 10-2 molecules photon-1 considering the mass
channels and photon flux). Photodesorption of atomic 15N was only detectable
(with a detection limit of 10-3 molecules photon-1) at the N 1s
$\rightarrow\pi^{*}$ transition, with a yield of $\sim$ 0.01 molecules
photon-1, which is two orders of magnitude less than the desorption yield of
15N2.

####  III.2.2 Mixed 13CO:15N2 ice

The photodesorption yields of 13CO and 15N2 from mixed 13CO:15N2 (2:1 and
20:1) ices are displayed in Figure 4 in the N K-edge and O K-edge energy
range. The TEYs measured simultaneously during the irradiation procedures are
also displayed in dashed lines and vertically shifted for more clarity. The
shape of the photodesorption spectra are well-correlated to the TEYs both at
the N and O K-edge, similarly to what is observed for a pure 15N2 ice. There
is however a small discrepancy: in the lower panels of Figure 4, the
photodesorption yield of 15N2 from a mixed 13CO:15N2 (2:1) ice is decreasing
after 403 eV for the N K-edge and after 555 eV for the O K-edge whereas the
corresponding TEY is constant. This is due to background correction issues.

The photodesorption of 15N2 from mixed 13CO:15N2 ices is significantly
decreasing between the 2:1 and 20:1 ratio both at the N and O K-edge (lower
panels of Figure 4) due to the high dilution of 15N2 whereas 13CO desorption
yield is in any case found in the same order of magnitude (upper panels). In
the case of a mixed 13CO:15N2 (2:1) ice, the photodesorption yields of 13CO
and 15N2 are found in the same order of magnitude at the N 1s
$\rightarrow\pi^{*}$ ($\sim 1.4-1.5$ molecules photon-1) and the O 1s
$\rightarrow\pi^{*}$ ($\sim 0.5-0.7$ molecules photon-1) transitions of 15N2
and 13CO respectively. This is consistent with the fact that CO and N2 have
similar binding energies in mixed CO:N2 ices (Öberg  _et al._ , 2005; Bisschop
_et al._ , 2006). The fact that the photodesorption yields are lower at the O
1s $\rightarrow\pi^{*}$ transition compared to the N 1s $\rightarrow\pi^{*}$
transition in the case of the 2:1 ratio is probably due to a higher absorption
cross section (based on gas phase experiments) of 15N2 at 401 eV ($\sim$ 26
Mbarn from Kato  _et al._ (2007) and when considering the spectral resolution
of our photon source) compared to that of 13CO at 534.4 eV ($\sim$ 2.8 - 3.2
Mbarn from Barrus  _et al._ (1979)).

Despite a higher photoabsorption of 13CO expected for a dilution ratio of 20:1
compared to 2:1, the TEY value at the O 1s $\rightarrow\pi^{*}$ transition of
13CO is lower for the 20:1 ratio (see right panels of Figure 4). We would have
expected the photodesorption yield of 13CO to also follow this trend. However,
the photodesorption yield of 13CO at this energy is not significantly changing
from a 2:1 to a 20:1 ratio (the yield is at $\sim$ 0.7 molecules photon-1). A
higher fluence received by the 13CO:15N2 (20:1) ice before this specific
measurement seems to be responsible for this behaviour. The fluences
corresponding to the other measurements displayed in Figure 4 are similar (< 2
$\times$ 1016 ph cm-2).

Photodesorption signals were observed on the mass channels 28 u. and 44 u..
They could correspond to the desorption of 13C15N and 13C15NO respectively.
However, the signals were too weak (S/N $\gtrsim$ 1, with a photodesorption
yield of $\sim$ 0.02 molecules photon-1 at the N 1s $\rightarrow\pi^{*}$ and
the O 1s $\rightarrow\pi^{*}$ for both mass channels) and more easily detected
in the case of a 20:1 ratio such that we cannot totally exclude the
contribution of 12CO, 14N2 (mass 28 u.) and 12CO2 (mass 44 u.) photodesorption
to these mass channels due to natural isotopes in our gas samples ($\sim$ 1%).
Finally, a desorption signal was found on the mass channel 31 u., which is
associated with the X-ray photodesorption of 15NO. The photodesorption spectra
of 15NO are also following the same variations as the TEYs and the
corresponding yields are $5.3\times 10^{-2}$ molecules photon-1 at the N 1s
$\rightarrow\pi^{*}$ transition of 15N2 and $2.7\times 10^{-2}$ molecules
photon-1 at the O 1s $\rightarrow\pi^{*}$ transition of 13CO for a 13CO:15N2
(2:1) ice. The formation of 15NO is expected to originate from chemistry
induced by the dissociation of 15N2 and 13CO. Its presence in the ice has also
been evidenced, in very small quantities, by TPD of the photo-irradiated ice
at the end of the experiment. The photodesorption yields of the previous
photo-products (possibly 13C15N and 13C15NO for the mass 28 u. and 44 u.
respectively, and unambiguously 15NO for the mass 31 u.) are at least an order
of magnitude lower than the yields of 13CO and 15N2. This shows that, if some
photo-chemistry occurs, its impact on the photodesorption process from mixed
ices is limited. Photodesorption of atomic 15N, 13C and O was not detected
(with a detection limit of 10-3 molecules photon-1).

####  III.2.3 Layered 13CO/15N2 ice

Figure 5:  X-ray photodesorption yields at 401 eV of 13CO (upper panel) and
15N2 (lower panel) from a layered 13CO / 15N2 ice at 15 K, as a function of
the number of ML of 13CO deposited on top of a 50 ML 15N2 ice.

The photodesorption yields at 401 eV of 13CO and 15N2 from a layered 13CO/15N2
ice are displayed in Figure 5 as a function of the number of ML of 13CO on top
of a 15N2 ice. For this experiment, the photon flux was low ($\sim 10^{11}$
photon s-1) and the irradiation time was short (a few seconds) to ensure that
the number of 13CO molecules photodesorbed during one irradiation step are
negligible compared to the number of ML of 13CO deposited on top of the 15N2
ice. Considering a X-ray photodesorption yield of 13CO between 1.0 and 2.4
molecules photon-1, an equivalent of 0.01 - 0.03 ML of 13CO is desorbed during
one irradiation step. In comparison, the first point measured in Figure 5 is
at 1.4 ML of 13CO on top of the 15N2 ice. We do not expect significant
structural changes of the ice during each irradiation step at such low
fluence. Chemical changes are also not expected based on the fact that no
signs of significant chemistry are observed on both the TEYs and in desorption
for the previous pure and mixed irradiated ices.

At 401 eV, photo-absorption of 15N2 is due to the N 1s $\rightarrow\pi^{*}$
transition and photo-absorption of 13CO is due to the ionization of its C 1s
electron (IP $\sim$ 296 eV). Quantitatively speaking, and based on gas phase
data, the absorption cross section of 15N2 and 13CO at 401 eV are $\sim$ 20 -
40 Mbarn and $\sim$ 0.3 Mbarn respectively (Barrus  _et al._ , 1979; Kato  _et
al._ , 2007). Hence, photo-absorption at 401 eV in our layered 13CO/15N2 ice
is dominated by 15N2 photo-absorption. The idea of this experiment is
therefore to trigger the desorption of the above lying 13CO molecules by
photo-excitation of the supporting 15N2 molecules and to estimate the depth of
this indirect desorption mechanism (see Section IV) by sequentially depositing
monolayers of 13CO on top of the ice and irradiate it. The contribution of
13CO photo-absorption to the desorption of 13CO at 401 eV can be estimated by
considering that it is quantitatively similar to the photodesorption of CO
from a pure CO ice at 530 eV, which exhibits a photodesorption yield of $\sim$
0.1 molecules photon-1 (Dupuy  _et al._ , 2021b). This stems from the fact
that the photo-absorption of 13CO at 530 eV is also due to the ionization of
its C 1s electron and that we do not expect the ionization cross section to
significantly differs between 401 to 530 eV. Consequently, the photodesorption
yield of 0.1 molecules photon-1 is used as a reference to estimate the
contribution of 13CO photo-absorption to the desorption of 13CO at 401 eV in
our layered ice experiment (it is displayed as a horizontal dashed green line
in the upper panel of Figure 5). From the upper panel of Figure 5, we observe
two different regimes for the photodesorption yield of 13CO:

  * •

a low to medium coverage regime, for a number of ML of 13CO from 1 to roughly
30 - 40 ML. In this regime, the photodesorption yield of 13CO is $>$ 0.1 - 0.2
molecules photon-1 such that the desorption of 13CO is dominantly triggered by
photo-excitation of 15N2. In that case, the photodesorption yield of 13CO is
increasing until $\sim$ 10 ML and then starts to decrease

  * •

a high coverage regime, for a number of ML of 13CO $>$ 40 ML. In this regime,
the photodesorption yield of 13CO is close to 0.1 molecules photon-1 such that
the desorption of 13CO is dominantly triggered by photo-ionization of 13CO. In
that case, the possible photodesorption of 13CO triggered by photo-excitation
of 15N2 can be neglected

The photodesorption yield of 15N2 from our layered ice is displayed in the
lower panel of Figure 5. It is decreasing as the number of ML of 13CO
increases until it goes below our detection limit of $\sim$ 0.05 molecules
photon-1 (considering the low photon flux for this experiment) for a number of
ML of 13CO $>$ 15 ML. The fact that we still observe 15N2 desorption even when
the 15N2 ice is covered by a few ML of 13CO may be due to diffusion of 15N2
from below the ML of 13CO or to a few 15N2 molecules still present at the
surface due to inhomogeneous deposition of 13CO. This is further discussed in
Section IV.3.

##  IV Discussion

###  IV.1  Indirect desorption and estimation of $\Lambda_{des}$

Our experiments on mixed 13CO:15N2 ices highlight an indirect desorption
mechanism, in the sense that the photo-absorption of one molecule is inducing
the desorption of another one. This is clearly seen in the mixed 13CO:15N2
(2:1) ice for which the photodesorption of 13CO at the 15N2 N 1s
$\rightarrow\pi^{*}$ transition (upper left panel of Figure 4) and that of
15N2 at the 13CO O 1s $\rightarrow\pi^{*}$ transition (lower right panel of
Figure 4) dominate the photodesorption spectrum of respectively 13CO and 15N2.
More globally, the fact that the photodesorption spectrum of 15N2 and 13CO
follows the X-ray absorption spectrum of, respectively, 13CO near the O K-edge
and 15N2 near the N K-edge confirms this indirect mechanism. Our experiment on
the layered 13CO/15N2 ice also sheds light on this process: the ice is
irradiated at 401 eV (N 1s $\rightarrow\pi^{*}$ transition of 15N2) and 13CO
desorption is observed.

This indirect desorption mechanism necessarily involves energy transport from
the molecule that absorbs the incident photon to the molecule that desorbs
from the ice surface. The length scale of such energy transport can be defined
as the maximum distance from the ice surface (or the depth) at which an
absorbed photon can induce desorption. This depth will be defined as
$\Lambda_{des}$ in the following and it will be expressed in ML.
$\Lambda_{des}$ depends on the indirect desorption mechanism and may vary with
the photon energy and the ice composition.

Our experiment on the layered 13CO/15N2 ice nicely enables to estimate
$\Lambda_{des}$ for the indirect desorption process of 13CO induced by the
photo-absorption of 15N2 at 401 eV. In Figure 5, we can see that 15N2 photo-
absorption can induce 13CO desorption when the 15N2 ice is covered by a number
of ML of 13CO from 1 to roughly 30 - 40 ML, with a maximum efficiency around
10 ML. Above 40 ML, the photodesorption yield of 13CO from the layered ice is
similar to the one induced by the photo-ionization of the core C 1s electron
of 13CO at 530 eV in pure CO ice (Dupuy  _et al._ , 2021b) and the indirect
desorption mechanism of 13CO induced by photo-absorption of 15N2 is
negligible. After fitting, the exponential decay of the 13CO photodesorption
yield starting at $\sim$ 10 ML is associated with a characteristic length of
$\Lambda_{c}\sim$ 11 ML. The exponential reaches 95% extinction at
3$\times\Lambda_{c}=$ 33 ML, which corresponds to a good estimate of
$\Lambda_{des}$ and for which the indirect desorption of 13CO becomes
negligible. In order to take into account the uncertainty associated with the
number of ML of 13CO, which is approximately 10%, we finally estimate that
$\Lambda_{des}$ is between 30 - 40 ML in the case of our layered 13CO/15N2 ice
and at 401 eV. This shows that desorption can be triggered from the bulk of
the ice, beyond the first few ML.

This conclusion can also be drawn for the case of mixed 13CO:15N2 ices. In
that case, the photodesorption yield of 13CO at the N 1s $\rightarrow\pi^{*}$
transition of 15N2 is exactly following the variations of the TEY from a 2:1
to a 20:1 ratio (see upper left panel of Figure 4). This is not the case for
the desorption of 15N2 which is barely visible in the case of a 20:1 ratio
(see lower left panel of Figure 4). This could be explained as followed. In
the case of the 2:1 ratio, 15N2 molecules are sufficiently present near the
ice surface and within its bulk to observe desorption of both 15N2 and 13CO at
the N 1s $\rightarrow\pi^{*}$ transition of 15N2. Whereas, in the case of the
20:1 ratio, 15N2 molecules are not sufficiently present near the ice surface
to significantly desorb but they are sufficiently photo-absorbing from the
surface to the bulk of the ice to produce a non-negligible TEY value and to
induce the desorption of 13CO. In the case of mixed 13CO:15N2 ices, X-ray
photodesorption can therefore also be triggered from the bulk of the ice.

###  IV.2  Indirect desorption mechanisms

In this section, we discuss the possible mechanisms responsible for the
indirect desorption of 13CO by excitation of 15N2 observed in our layered ice
experiment. Extrapolation to the case of the pure and mixed ices will be
discussed afterwards. One possible mechanism which has been suggested for the
X-ray photodesorption of neutrals from ices of simple (CO, H2O) and more
complex (CH3OH) molecules (Dupuy  _et al._ , 2018, 2020, 2021b; Basalgète  _et
al._ , 2021a, b) is X-ray induced electron stimulated desorption (XESD). XESD
is a consequence of the relaxation of the core hole photo-excited or photo-
ionized state which decays by emission of an Auger electron with a probability
close to 1 for low Z elements (Walters and Bhalla, 1971; Krause, 1979). This
Auger electron scatters inelastically in the ice, creating secondary events
(e.g, ionizations and excitations) and a cascade of low energy (< 20 eV)
secondary electrons that may lead in fine to desorption.

On the other hand, mechanisms decorrelated from Auger scattering may also play
a role. This include all the mechanisms related to the energy left to the
photo-absorbing molecule after Auger decay. Quantitatively, most of the photon
energy is given to the Auger electron in the form of kinetic energy ($\sim$
380 eV for the N 1s $\rightarrow\pi^{*}$ transition of 15N2; Moddeman  _et
al._ (1971)) and a few tens of eV is left to the photo-absorbing molecule.
This latter found itself in a singly or multiply valence-excited state, singly
or doubly ionized depending on the energy of the incident photon. For
instance, in the specific case of our layered ice experiment at 401 eV, 15N2
is expected to be left, after Auger decay, in an excited ionized state
(15N${}_{2}^{+}$)∗. The energy left to the molecule in the form of electronic
excitation may be transported towards the ice surface via different mechanims
to cause indirect desorption (i.e. desorption of other molecules). These
mechanisms possibly include:

  1. (1)

    1. (a)

indirect desorption due to migration of the electronic excitation through the
ice (exciton migration). This mechanism concerns the transport of exciton in
ices, a process that stems from the work of Kimmel and co-workers on electron-
stimulated desorption (ESD) from D2O ice (Orlando and Kimmel, 1997; Petrik and
Kimmel, 2003). It has also been suggested to play a role in the ESD of C6H6 on
top of water ice by migration of long-lived excitons through the ice
(Marchione, Thrower, and McCoustra, 2016; Marchione and McCoustra, 2017)

    2. (b)

relaxation of the excited state to modes coupled with desorption similar to
what is observed in VUV photodesorption experiments (Bertin  _et al._ , 2013)
for which it has been shown that excitation of 13CO (to the A${}^{1}\Pi$
state) and 15N2 (to the b${}^{1}\Pi_{u}$ state) can induce the desorption of
respectively 15N2 and 13CO from layered ices. In that case, it was suggested
an energy transfer between the excited and the desorbing molecule via
excitation of collective vibrational modes (phonons). To simplify the
following discussion, we will consider that this process occurs without
exciton migration but one should note that it could take place after exciton
migration (in that case, it is included in process (1)(a))

  2. (2)

indirect desorption due to diffusion of energetic fragments if the ionized
excited state is dissociative, similar to the kick-out mechanism suggested in
the case of indirect desorption of simple molecules on top of water ice,
induced by energetic H atoms that are produced from photodissociation of H2O
in the VUV range (Dupuy  _et al._ , 2021a). In some extreme cases, the
dissociation may occur before Auger decay

The aim of our discussion is then to identify the main mechanism responsible
for the indirect desorption observed in our layered 13CO/15N2 ice experiment.
We will especially discriminate between the XESD process and the other
processes cited previously that are decorrelated from the Auger scattering and
discuss the processes with respect to the value derived for $\Lambda_{des}$
(30 - 40 ML).

For a XESD process, the energy absorbed in the bulk of the ice by 15N2 can be
transported towards the ice surface by the scattering of the Auger electron.
Considering the energy deposition profile of keV electrons in light materials
(1 $\leq$ Z $\leq$ 18) from the work of Valkealahti, Schou, and Nieminen
(1989), we can reasonably expect that the Auger electron and the secondary
electrons can deposit their energy through a few tens of ML. In that sense,
the value of $\Lambda_{des}$ previously estimated (30 - 40 ML) is consistent
with a XESD process. The migration distance of excitons in water ice is
potentially tens of ML (Petrik and Kimmel, 2003). Migration of excitons in the
case of weakly interacting Van der Waals solids such as in 15N2 ice and
migration between 15N2 and 13CO layers has not been studied yet such that the
process (1)(a) cannot be discussed regarding the value derived for
$\Lambda_{des}$. However, as discussed in Section IV.4, we expect this process
to depend on the exciton state hence on the incident photon energy.

Figure 6:  Left side: scheme of our simple model to estimate the energy
deposited to the top 13CO layer of a layered 13CO/15N2 ice by scattering of
Auger electrons emitted after photo-absorption by 15N2 molecules. Right side:
in green is displayed the estimation of this energy (in arbitrary units and
where the zero of the right side distribution has been scaled with a
photodesorption yield of 0.1 molecules photon-1), compared with the X-ray
photodesorption yields of 13CO (orange squares) from our layered 13CO/15N2 ice
(from Figure 5). The blue squares show the sum of the photodesorption yields
of 13CO plus 15N2 from our layered 13CO/15N2 ice. The upper and lower green
curve were computed by taking a photoabsorption cross section at 401 eV of 40
and 20 Mbarn respectively.

Process (1)(b) has been characterized by Bertin  _et al._ (2013) for the
indirect desorption of 13CO and 15N2 by excitation of respectively 15N2 and
13CO in layered ice experiments. In that case, it has been shown that the
energy can be efficiently transferred over $\sim$ 5 ML to the desorbing
molecules at the surface (this value was similar for excitation of 13CO to the
A${}^{1}\Pi$ state and for excitation of 15N2 to the b${}^{1}\Pi_{u}$ state).
Therefore, we expect process (1)(b) to be a near-surface process. Process (2)
involves the diffusion of ionic or neutral fragments (in that case N or N+)
towards the ice surface and collision with 13CO molecules followed by
desorption. After possible dissociation of (15N${}_{2}^{+}$)∗, we expect the
fragments to have less than 10 eV of kinetic energy. Although no studies are
available on the typical diffusion length of such fragments in the bulk of
molecular ices, we do not expect it to be comparable with the value of
$\Lambda_{des}$ derived. Instead, we expect process (2) to be a near-surface
process involving just the first few ML of the ice. This is also supported by
the very low level of desorbing 15N fragments from pure 15N2 ice (see section
III.2.1).

Processes (1)(b) and (2) are then expected to possibly occur in the low
coverage regime of our layered ice experiment, for a few ML of 13CO on top of
the 15N2 ice. Regarding the photodesorption yields of 13CO in Figure 5, these
near-surface processes seem to be negligible compared to the processes
involving deeper layers of the 15N2 ice, such as XESD. In fact, the yields of
13CO at low coverage (between 1 and 10 ML) and higher coverage are similar. In
the low coverage regime, both near-surface processes and bulk processes can
participate to indirect desorption whereas for higher coverage, only bulk
processes participate. The fact that the yields are similar in both regimes
excludes a significant contribution of the near-surface processes compared to
the bulk ones. Therefore, processes (1)(b) and (2) can be neglected.

In the following sections, we focus on characterizing the XESD process for our
layered ice experiment and we conclude on the dominant mechanism expected for
indirect desorption of neutral 15N2 and 13CO from the ices studied in this
work.

###  IV.3 Modeling of the energy deposited in the ice by Auger electrons

XESD is mediated by the scattering of Auger electrons. These electrons deposit
their energy through the ice via ionization and excitation of the molecules in
their path. For a XESD process, the photodesorption yields are expected to be
correlated to the amount of energy deposited near the ice surface by the
scattering of Auger electrons. This amount of energy can be estimated based on
the work of Valkealahti, Schou, and Nieminen (1989). They showed, by Monte
Carlo simulations, that the energy deposition profile of a keV electron in a
light material (1 $\leq$ Z $\leq$ 18) as a function of depth can be
approximated by a Gaussian distribution (in 1D). The parameters of the
distribution depend on the energy of the electron and on the stopping power of
the material at this energy. These parameters have been fitted for a N2 ice.
We can therefore estimate the amount of energy deposited near the ice surface
by the scattering of Auger electrons in the case of our layered 13CO/15N2 ice
experiment using the following methodology and assumptions (this is also
sketched in the left side of Figure 6):

  * •

we consider a layered 13CO/15N2 ice: 50 ML of 15N2 on top of which an
increasing number of ML of 13CO is deposited. We neglect the photo-absorption
of the 13CO layers at 401 eV

  * •

we assume that the initial kinetic energy of the Auger electron emitted by
relaxation of the N (1s)${}^{-1}\pi^{*}$ state of 15N2 is $\sim$ 380 eV, based
on Auger spectra of gas phase N2 (Moddeman  _et al._ , 1971)

  * •

we only consider the emitted Auger electrons that statistically contribute the
most to the energy deposited near the ice surface, i.e. the Auger electrons
that are emitted from the bulk towards the surface of the ice

  * •

the energy deposition profile of the Auger electrons is approximated by a
Gaussian distribution with parameters from Valkealahti, Schou, and Nieminen
(1989), in 1D. This also takes into account the energy loss of secondary
electrons and it is computed as the sum of the average kinetic energy of all
electrons in a depth element. According to the Born-Bethe approximation and
Bragg’s rule, the stopping power of 13CO and 15N2 at 380 eV are similar such
that we reasonably assume that the energy deposition profile does not
significantly differs in 15N2 or 13CO layers. The shape of the energy
deposition profiles are plotted in arbitrary units in the left panel of Figure
6

  * •

we consider that each ML of 15N2 is emitting a number of Auger electrons that
are equal to the number of photons absorbed in that ML. It results that the
relative intensity of the energy deposition distributions from two different
ML is driven by a Beer-Lambert law, with an absorption cross section at 401 eV
taken between 20 and 40 Mbarn (Kato  _et al._ , 2007)

The energy deposited in the top layer of the 13CO ice is then computed by
summing the contributions from each ML of 15N2. This operation is repeated for
an increasing number of ML of 13CO deposited on top of the 15N2 ice. The
results are presented in the right panel of Figure 6: the energy deposited on
the top layer of the 13CO ice is compared to the experimental photodesorption
yields of 13CO from our layered 13CO/15N2 ice (taken from Figure 5). A
comparison with the sum of the photodesorption yields of 13CO plus 15N2, which
have similar photodesorption yields at 401 eV when mixed in similar
stoichiometries (according to our results from mixed ices), is also done for
the following discussion. At low coverage (number of ML of 13CO $\lesssim$ 10
ML), the ice surface is not homogeneously covered by 13CO molecules and the
photodesorption yield of 13CO increases linearly with the number of 13CO
molecules available for desorption. Therefore, in this regime, the
photodesorption yield of 13CO is not correlated to the energy deposition of
Auger electrons since it actually depends on the ice surface homogeneity. This
lack of homogeneity is supported by the fact that 15N2 still desorbs in this
regime. Furthermore, in this low coverage regime, we observe a good agreement
between the energy deposition profile and the sum of the photodesorption
yields of 13CO plus 15N2 (see blue squares in Figure 6). This is consistent
with the ice surface being composed of a mix of 13CO and 15N2 molecules in the
low coverage regime and for which photodesorption of neutral molecules is
correlated to the energy deposited at the top layer and dominated by 13CO plus
15N2 desorption (no significant desorption is found for other possible neutral
molecules). For medium coverage (number of ML of 13CO between 10 and 40 ML),
the exponential decay of the 13CO desorption yield is in good agreement with
the modeled deposited energy. For high coverage (number of ML of 13CO $>$ 40
ML), the photodesorption is triggered by the photo-ionization of 13CO (see
Section III.2.3).

These results strongly suggest that XESD is the dominant mechanism responsible
for the indirect desorption of 13CO at 401 eV from our layered 13CO/15N2 ice.
It also confirms our estimated value for $\Lambda_{des}$. In that case,
excitation of 13CO to non-dissociative states by low energy secondary
electrons (produced by the Auger scattering) may be the exact mechanism
explaining 13CO desorption. For comparison, ESD of CO from pure CO ice has an
energy threshold around 6 eV (Rakhovskaia, Wiethoff, and Feulner, 1995), which
is accessible to the secondary electrons, as suggested in Dupuy  _et al._
(2021b). This energy threshold is around 7 eV for the ESD of N2 from pure N2
ice.

Auger emission occurs with a probability close to one for each core hole state
of 15N2 or 13CO above and below their respective IP. The energy deposition
profile due to the Auger scattering is also reasonably expected to be similar
in the different ices tested in this work (pure 15N2 ice, mixed 13CO:15N2 ices
and layered 13CO/15N2 ice), based on the fact that 13CO and 15N2 have similar
stopping power in the energy range considered. It is therefore straightforward
to consider that XESD should also play a role for the desorption of 15N2 from
pure 15N2 ice and for the desorption of 13CO and 15N2 from mixed 13CO:15N2
ices, at each photon energy. The simple model previously implemented nicely
enables to estimate $\Lambda_{des}$ for a XESD process at different photon
energy as long as the photo-absorption cross section and the initial kinetic
energy of the Auger electron emitted after core hole decay are known. This is
used in the next section.

Table 1: Photodesorption yields expressed in molecule desorbed by eV
deposited, of 13CO and 15N2 from different ices and at different energies,
computed via equation (1) and by using the experimental yields derived in this
work. The lower and higher values of the yields are derived by taking the
higher and lower value of $\Lambda_{des}$ respectively.

|  |  | Photodesorption yield ($\times 10^{-2}$ molecules (eV deposited)-1)
---|---|---|---
|  |  |  15N2 from |  13CO from
Photon Energy |  $\sigma$ (Mbarn)(a) |  $\Lambda_{des}$ (ML) | Pure 15N2 |  13CO:15N2 (2:1) | Pure 13CO |  13CO:15N2 (2:1)
401 eV (15N2; N 1s $\rightarrow\pi^{*}$) | 26 | 30 - 40 | 1.9 - 2.3 | 3.2 - 4.1 |  | 1.9 - 2.5
425 eV (15N2; N 1s ionization) | 1.8 | 30 - 40 | 0.6 - 0.8 | (*) |  | 2.1 - 2.8
534.2 eV (13CO; O 1s $\rightarrow\pi^{*}$) | 3.0 | 40 - 50 |  | 2.8 - 3.5 |  | 2.1 - 2.6
570 eV (13CO; O 1s ionization) | 0.8 | 40 - 50 |  | (*) | 1.5(b) | 2.4 - 3.0
8.3 eV (13CO; A${}^{1}\Pi$ \- X${}^{1}\Sigma^{+}\ (2,0)$)(c) | 15 | 5 |  | 18 | 8.3 | 21

  * (*)

Background issues on the mass channel 30 around 425 eV and 570 eV during the
X-ray irradiation of the 13CO:15N2 -2:1 ice prevent us from using the
experimental yields of 15N2 at these energies

  * (a)

The photo-absorption cross section are taken from gas phase measurements
(Barrus  _et al._ , 1979; Kato  _et al._ , 2007) and we took into account the
spectral resolution of our photon source.

  * (b)

Taken from Dupuy  _et al._ (2021b) where it was assumed $\Lambda_{des}=$ 30 ML

  * (c)

From Bertin  _et al._ (2013)

###  IV.4 Conversion of the absorbed energy to desorption

In this section, we correct our X-ray photodesorption yields by taking into
account only the part of the absorbed energy that can participate to the
desorption process. This results in expressing the yields in molecules (eV
deposited)-1 using equation (1). We consider that the number of the top
monolayers involved in the desorption process ($\Lambda_{des}$) should be at
least equal to the one corresponding to a XESD process. The energy absorbed in
the layers beyond $\Lambda_{des}$ is "lost" in the sense that it cannot be
converted to desorption. This results in taking $\Lambda_{des}=$ 30 - 40 ML
near the N K-edge, where the photo-absorption is dominated by 15N2 absorption.
Near the O K-edge, the photo-absorption is dominated by 13CO absorption and
the Auger electron is expected to have an initial kinetic energy between 500
and 520 eV (Moddeman  _et al._ , 1971). Based on our simple modeling in
Section IV.3, this results in a slightly higher $\Lambda_{des}$ (40 - 50 ML).
The results are presented in Table 1 (first four rows) for the desorption of
13CO and 15N2 from their respective pure ice and from mixed 13CO:15N2 (2:1)
ices at different photon energy.

The yields displayed in Table 1 represent a quantitative estimate of how
efficiently the absorbed energy (only the part that can participate to the
desorption process) is converted to the desorption channel. This takes into
account all the desorption processes that may occur due to photo-absorption in
the first $\Lambda_{des}$ ML of the ice. The estimated yields are very similar
for the desorption of 13CO and 15N2 from pure or mixed ices and at each energy
considered. They range between $\sim$ 0.02 and $\sim$ 0.04 molecules (eV
deposited)-1. There is however a small discrepancy with the photodesorption
yield of 15N2 from pure 15N2 ice at 425 eV, which is lower than the previous
values. This is assumed to be due to a higher fluence received by the ice
before this specific measurement compared to the other ones.

These results indicate that there is presumably a unique dominant process
explaining the desorption of 13CO and 15N2 from the ices tested and whose
efficiency does not strongly depend on the photon energy hence neither on the
photo-absorbing molecule nor on its state after Auger decay (singly or doubly
ionized excited state). This is fully consistent with a XESD process for which
desorption depends only on the Auger scattering, the latter being expected to
not significantly differ between pure and mixed ices of 13CO and 15N2. The
similarity of the yields between 13CO and 15N2 is also consistent with their
similar binding energies in pure or mixed ice (Öberg  _et al._ , 2005;
Bisschop  _et al._ , 2006). A possible significant desorption due to exciton
migration from the photo-absorbing molecule (process (1)(a) defined in Section
IV.2) can also be excluded by the fact that the efficiency of this process is
expected to depend on the exciton state after Auger decay and therefore on the
photon energy, which is not what we observe in Table 1.

Finally, in Table 1, we also computed the VUV photodesorption yields in
molecules (eV deposited)-1 at 8.3 eV, which corresponds to the A${}^{1}\Pi$ \-
X${}^{1}\Sigma^{+}\ (2,0)$ electronic transition of 13CO, from the data
published in Bertin  _et al._ (2013). In this study, $\Lambda_{des}$ was
estimated to be $\sim$ 5 ML for the indirect desorption mechanism from layered
15N2/13CO experiments. The yields in molecules (eV deposited)-1 are found
higher in the VUV range (at 8.3 eV) than in the X-ray range. This means that
the energy absorbed by a valence excitation of 13CO (to the A${}^{1}\Pi$
state), is more efficiently converted to desorption, by a process similar to
the one described in Section IV.2 (process (1)(b)), than the energy absorbed
by a core hole excitation or ionization (of 13CO or 15N2) and for which a XESD
process is expected to be dominant according to our results. This is true for
both the VUV photodesorption of 13CO (direct and/or indirect process) and 15N2
(indirect process) from pure 13CO ice and mixed 13CO:15N2 ice.

##  V Conclusion

X-ray photodesorption of 15N2 from pure 15N2 ice and of 15N2 and 13CO from
mixed 13CO:15N2 ices is found to follow the X-ray absorption profile of the
ices in the N and O K-edge energy range (near 400 and 500 eV respectively).
Photodesorption experiments on mixed 13CO:15N2 ices revealed an indirect
desorption mechanism triggered by the absorption of 15N2 near the N K-edge and
13CO near the O K-edge leading both to 13CO and 15N2 desorption. This indirect
mechanism is also highlighted by the desorption of 13CO from a X-ray
irradiated layered 13CO/15N2 ice at 401 eV. This latter experiment enables to
derive the relevant depth of desorption $\Lambda_{des}$ which is a
quantitative measure of depth involved in the indirect desorption process. It
was estimated to be 30 - 40 ML near the N K-edge. The photodesorption yields
of 13CO from the layered 13CO/15N2 ice as a function of 13CO coverage are
found to be well-correlated to the amount of energy deposited at the top layer
by the scattering of Auger electrons after X-ray absorption, the latter being
estimated by a simple model based on the work of Valkealahti, Schou, and
Nieminen (1989). The desorption yields of 13CO and 15N2 corrected from the
absorbed energy that can participate to desorption do not significantly depend
on the photon energy (hence on the photo-absorbing molecule, 13CO or 15N2) and
on the nature of the ice (pure or mixed). These results indicate that XESD,
mediated by the scattering of Auger electrons, is the dominant mechanism
explaining the X-ray photodesorption of 15N2 and 13CO from the ices tested in
this work.

## Acknowledgements

This work was done with financial support from (i) the Region Ile-de-France
DIM-ACAV+ program, (ii) the Sorbonne Université “Emergence” program, (iii) the
ANR PIXyES project, grant ANR-20-CE30-0018 of the French “Agence Nationale de
la Recherche,” and (iv) the Programme National “Physique et Chimie du Milieu
Interstellaire” (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES. We
would like to acknowledge SOLEIL for provision of synchrotron radiation
facilities under Project Nos. 20210142, and we thank N. Jaouen, H. Popescu and
R. Gaudemer for their help on the SEXTANTS beam line.

## Notes and References

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