# Optical properties of MoSe2 monolayer implanted with ultra-low energy Cr
ions

Minh N. Bui<EMAIL_ADDRESS>Peter Grünberg Institute 9 (PGI-9),
Forschungszentrum Jülich, 52425 Jülich, Germany  Stefan Rost  Peter Grünberg
Institute 1 (PGI-1) and Institute for Advanced Simulation 1 (IAS-1),
Forschungszentrum Jülich and JARA, 52425 Jülich, Germany  Manuel Auge  II.
Institute of Physics, University of Göttingen, 37077 Göttingen, Germany
Lanqing Zhou  Peter Grünberg Institute 9 (PGI-9), Forschungszentrum Jülich,
52425 Jülich, Germany  Christoph Friedrich  Peter Grünberg Institute 1 (PGI-1)
and Institute for Advanced Simulation 1 (IAS-1), Forschungszentrum Jülich and
JARA, 52425 Jülich, Germany  Stefan Blügel  Peter Grünberg Institute 1 (PGI-1)
and Institute for Advanced Simulation 1 (IAS-1), Forschungszentrum Jülich and
JARA, 52425 Jülich, Germany  Silvan Kretschmer  Institute of Ion Beam Physics
and Materials Research, Helmholtz‐Zentrum Dresden‐Rossendorf, 01328 Dresden,
Germany  Arkady V. Krasheninnikov  Institute of Ion Beam Physics and Materials
Research, Helmholtz‐Zentrum Dresden‐Rossendorf, 01328 Dresden, Germany  Kenji
Watanabe  Research Center for Functional Materials, National Institute for
Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan  Takashi Taniguchi
International Center for Materials Nanoarchitectonics, National Institute for
Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan  Hans C. Hofsäss  II.
Institute of Physics, University of Göttingen, 37077 Göttingen, Germany
Detlev Grützmacher  Beata E. Kardynał<EMAIL_ADDRESS>Peter Grünberg
Institute 9 (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany

###### Abstract

The paper explores the optical properties of an exfoliated MoSe2 monolayer
implanted with Cr+ ions, accelerated to 25 eV. Photoluminescence of the
implanted MoSe2 reveals an emission line from Cr-related defects that is
present only under weak electron doping. Unlike band-to-band transition, the
Cr-introduced emission is characterised by non-zero activation energy, long
lifetimes, and weak response to the magnetic field. To rationalise the
experimental results and get insights into the atomic structure of the
defects, we modelled the Cr-ion irradiation process using ab-initio molecular
dynamics simulations followed by the electronic structure calculations of the
system with defects. The experimental and theoretical results suggest that the
recombination of electrons on the acceptors, which could be introduced by the
Cr implantation-induced defects, with the valence band holes is the most
likely origin of the low energy emission. Our results demonstrate the
potential of low-energy ion implantation as a tool to tailor the properties of
2D materials by doping.

###### keywords:

transition metal dichalcogenide monolayer, ultra-low energy ion implantation,
MoSe2, van der Waals heterostructure, photoluminescence, molecular dynamics,
density functional theory

Department of Physics, RWTH Aachen University, 52074 Aachen, Germany
Department of Physics, RWTH Aachen University, 52074 Aachen, Germany
Department of Physics, RWTH Aachen University, 52074 Aachen, Germany
Department of Physics, RWTH Aachen University, 52074 Aachen, Germany
Department of Applied Physics, Aalto University School of Science, P.O.Box
11100, 00076 Aalto, Finland Department of Physics, RWTH Aachen University,
52074 Aachen, Germany

##  1 Introduction

The properties of semiconductors, especially atomically thin monolayer (ML)
semiconductors, depend strongly on the types and densities of defects in their
crystal lattices. The most technologically relevant defects are dopants, i.e.,
foreign atoms in substitutional positions in the crystal lattice. Shallow
dopants introduce free electrons or holes into the conduction or valence band
and change thus semiconductor conductivity. As such they facilitate the
fabrication of p-n junctions, which underpins most active optoelectronic
devices.

Doping with transition metal atoms has been shown to introduce ferromagnetic
order in p-doped semiconductors 1. Impurity atoms can also trap electrons or
holes or bind excitons. Radiative recombination involving such states can be
detected as sub-bandgap photoluminescence (PL). Single foreign atoms binding
excitons have been explored for single photon sources 2. Alternatively, if the
dopant atom has a functionality of a spin qubit, the bound excitons provide an
optical readout of its state 3, 4, 5. The binding of excitons to the dopant
atoms depends not only on electron and hole masses but also the dielectric
constant of the semiconductors. Because of that, excitonic effects in bulk
semiconductors are only observed at cryogenic temperatures. Foreign atoms can
also act as colour centres in semiconductors and insulators. Spin qubits based
on the colour centres have been realised in diamond 6, 7, 8, 9 or SiC 10, 11.

In two-dimensional (2D) semiconducting transition metal dichalcogenides
(TMDs), which feature weak electrostatic screening, substitutional atoms tend
to introduce deep levels in the bandgaps 12. While excitons have considerable
binding energies, they are predicted to be very weakly bound to individual
doping atoms 13. Optical transitions involving defect states have been
observed 14, with defects identified as vacancies 15, 16, 17, 14. The
transition responsible for the PL was found to occur between the hybridised
defect states and 2D lattice electronic states.

Among several methods of doping bulk semiconductors, ion implantation offers
the highest flexibility in choosing implanted elements. Ion energies of tens
of keV are used for implantation since functional layers can be even a hundred
nanometers below the surface. High-energy ion implantation has been used 18,
19, 20, 21, 22 to modify 2D materials, but its efficiency is low in this case,
as most atoms go through the 2D target 23. Moreover, the ions penetrating
through the ML can cause undesirable effects, e.g., trapped charges in the
substrate. Implantation into 2D materials has the highest implantation
efficiency with ion energies in the range of tens of eV. At these energies,
the implantation efficiency and threshold energy depend on the ions’ mass and
also chemical properties 24. Ultra-low energy ion implantation 25, 26 has
recently been demonstrated to be efficient in doping graphene using 40 eV Mn
ions 27, 28, or in Se ion implantation into MoS2 with the ion energy of 20 eV
29, 30. The ratio of the replaced S atoms with Se in the top sublattice was
sufficient to form a Janus compound MoS${}_{\text{2-2x}}$Se${}_{\text{2x}}$ as
indicated by Raman spectroscopy and the transmission electron microscopy
imaging.

Here, we study the optical properties of MoSe2 ML implanted with 25 eV 52Cr+
ions. Sub-bandgap defect-induced PL emission was observed only at the low
n-doping level and with saturation behaviour, characteristic of defects with
low density. Ab-initio molecular dynamics (MD) simulations of the implantation
process were performed, and possible configurations of the Cr atoms in the
MoSe2 ML lattice were outlined to understand the atomic structure of the
implanted MLs. The optical properties of the MoSe2 ML with such defects were
calculated using density functional theory (DFT). The most probable defect
configurations were identified by combining experimental data and theoretical
calculations.

##  2 Results

###  2.1 Sample preparation and ion implantation

A sample for ion implantation was prepared by mechanical exfoliation of the
MoSe2, graphene, and hBN flakes and their sequential transfer onto the Si/SiO2
substrate with pre-patterned Ti/Au contacts. The use of the dry-viscoelastic
transfer technique 31 ensured that the surface of the ML was sufficiently
clean for the implantation. The MoSe2 ML has to be grounded during the
implantation. An electric contact to the ML was provided by placing the
multilayer part of the exfoliated MoSe2 flake on a Ti/Au metal contact. The ML
was placed atop a graphite gate connected to another Ti/Au contact. The ML was
separated from the gate with an hBN flake. Once completed, the device was
implanted with 52Cr+ ions at 25 eV and a fluence of 3 $\times$ 1012 cm-2
(equivalent to 0.003 Cr per ML MoSe2 unit cell, using the MoSe2 ML in-plane
lattice constant 3.32 Å 32). The implantation was performed with the device
heated to 220 $\degree$C. Following the implantation and initial
characterisation, another hBN flake was deposited on the ML MoSe2, and the
device was annealed at 200 $\degree$C. The complete device is shown in figure
1. More details are available in the Methods section.

(a)

(b)

Figure 1: Cr-implanted MoSe2 ML with hBN encapsulation and graphite backgate.
(a) Micrograph of the finished device. The ML part of the exfoliated MoSe2
flake is encapsulated between two thin hBN flakes. The few-layer graphite back
gate and the thick part of MoSe2 flake make contacts with the two Ti/Au lines
to the right. (b) Schematic diagram of the device cross-section. Back gate
voltage $V_{g}$ can be applied to the graphite back gate via the Au contact,
while the MoSe2 flake is grounded via the other Au contact.

###  2.2 Optical spectroscopy data

Figure 2(a) shows PL spectra of weakly electron-doped pristine and Cr-
implanted MoSe2 MLs, measured at 10 K with the same laser power of 1 $\upmu$W.
Both spectra show similar features around the bandgap transitions, with an
emission line from neutral excitons (X) and negative trions (X-). The red
shift of these transitions in the Cr-implanted sample (figure 2(a)) is most
likely due to a difference in the dielectric environment or strain between the
samples. The level of implantation is too low to expect changes in the bandgap
33. Significant homogeneous broadening of the X line was determined by Voigt
function fitting. It resulted in the Lorentzian width of nearly 7 meV for the
implanted sample, compared to about 2 meV for the pristine sample, suggesting
a much shorter lifetime of the former. The most significant difference between
the samples is a broad emission at around 1.51 eV, which we label D.

(a)

(b)

(c)

(d)

Figure 2: PL of Cr-implanted MoSe2 ML at 10 K. (a) PL spectra of Cr-implanted
MoSe2 ML (red curve) at low n-doping ($V_{g}$ = 0.8 V), plotted with that of
pristine MoSe2 ML (black). In addition to the X- and X from MoSe2 ML, the Cr-
implanted sample also shows the broad D peak at around 1.51 eV. (b) PL spectra
of Cr-implanted ML under laser power ranging from 36 nW to 123 $\upmu$W.
Spectra are normalised to X-. Here the sample is slightly n-doped at $V_{g}$ =
0.8 V. (c) Power dependence of PL. Best fit lines (dashed), with their
standard deviations (shaded region around the lines), are plotted together
with extracted intensity from PL spectra (dots). Unless explicitly shown, the
error bars are smaller than the size of the data points. X- and X are fitted
with power law $I\propto P^{\alpha}$, and D is fitted with the saturation
curve described by equation (1). (d) Time-resolved PL of Cr-implanted MoSe2.
1/$e$ time is around 14 ns.

The relative intensity of the D peak compared to X- and X depends on the
excitation power $P$ (figure 2(b)). It is the most intense line at low laser
excitation powers ($P<1\,\upmu$W) but saturates as the laser power increases,
while X- and X continue to grow linearly. The saturating behaviour of D
intensity, shown in figure 2(c)), can be expressed phenomenologically as:

$I\propto\frac{P}{P+P_{sat}}$ (1)

with saturation power $P_{\text{sat}}$ $\approx$ 10 $\upmu$W. The saturating
behaviour is expected when the exciton generation rate exceeds the
recombination rate of the states responsible for D. The saturation threshold
depends on the density of states and the lifetime of the recombining carriers
16, 14. The low threshold for D is consistent with the low implantation level.
The lifetime of carriers was measured from time resolved PL. The decay of the
population of the excited states contributing to the D-peak after a pulsed
excitation can be seen in figure 2(d). As can be expected from measuring an
ensemble of emitters, the decay is not a single exponential. The very fast
initial decay of population by about 10%, which is faster than the time
resolution of the experiment, is followed by a slower decay with the 1/$e$
decay time of around 14 ns. These decay times are 2-3 orders of magnitude
longer than the lifetime of free excitons in MoSe2 MLs 34, 35, 36, 37 and one
order of magnitude longer than that from the isolated, confined excitons 38,
pointing to a low oscillator strength of the emitters.

The doping-dependent PL from neutral and charged excitons shown in figure 3(a)
is typical of MoSe2 MLs. When increasing the gate voltage, the D emission only
emerges after the signal from the positive trion, X+, entirely disappears. It
reaches the maximum intensity around 1 V, the gate voltage of the transition
between X and X- dominated spectra. The D line weakens strongly as the X- line
intensifies with a further gate voltage increase. This behaviour suggests a
competition between the exciton capture at the defect state and the formation
of an X-. This scenario is supported by PL excitation (PLE) spectroscopy
measurement (figure 3(b)), which shows that the intensity of D emission is
maximum when the excitation wavelength is resonant with the energy of X around
1.637 eV. D emission was not excited with laser resonant with X- (around 1.608
eV) even though the PL spectrum, measured at the same doping level, clearly
shows that the ML is doped with electrons (X- emission is the strongest PL
signal).

(a)

(b)

Figure 3: Doping level and excitation energy dependencies of PL. (a) Gate
dependent PL, where the back gate voltage $V_{g}$ was varied from -12 to 8 V
to tune the doping level in the ML from p- via neutral to n-doping. The
carrier concentration $n$ is calculated using the simple parallel plate
capacitor model (more details in supplementary note). (b) PLE of D peak, taken
at $V_{g}$ = 0.7 V. The D peak intensity was integrated around its PL emission
energy between 1.48 and 1.52 eV. Inset: PL spectrum under 688 nm (1.80 eV)
excitation under the gate voltage as applied for the PLE measurements.

Figure 4(a) compares gate-dependent PL at 22 K and 108 K. While X- emission is
the most intense line in the spectra at the lower temperature, it is very weak
at the higher temperature. X becomes the strongest line, but D diminished less
than X- and remains up to room temperature (supplementary figure
LABEL:fig:RT_PL). We trace the change of PL signal counts from X- and D, both
normalised to X signal counts, on the Arrhenius plot shown in figure 4(b). X-
dissociates into higher energy X and an electron at higher temperature. Its
intensity can be fitted with the standard Arrhenius formula 39, 40, 41:

$I(T)=\frac{I(0)}{1+A\exp(\frac{-E_{a}}{k_{B}T})}$ (2)

where $I(0)$ is the PL intensity at temperature 0 K, $A$ is a proportionality
constant, $E_{a}$ is the activation energy for the dissociation of X-, and
$k_{B}$ is the Boltzmann constant. Fitting the formula to the data gives
$E_{a}$ $\approx$ 32 $\pm$ 5 meV, which is expected for a binding energy of
the trion 13, 42. D emission intensity first increased with temperature up to
around 34 K before diminishing. To account for this initial increase in
intensity, we assume that trapping of carriers that recombine requires
overcoming activation energy. We use a modified multi-level model for the
temperature dependence of D intensity 43, 44, 45, 46, 41:

$I(T)=I(0)\frac{1+A_{1}\exp(\frac{-E_{a1}}{k_{B}T})}{1+A_{2}\exp(\frac{-E_{a2}}{k_{B}T})}$
(3)

where $A_{1}$, $A_{2}$ are proportionality constants, and $E_{a1}$ and
$E_{a2}$ are activation energies for trapping and detrapping of carriers.
Fitting of the D peak yields $E_{a1}$ $\approx$ 1 $\pm$ 6 meV, and $E_{a2}$
$\approx$ 30 $\pm$ 9 meV.

(a)

(b)

(c)

Figure 4: Temperature dependence of PL emission. (a) Gate voltage-dependent PL
at 22 K and 108 K. (b) Arrhenius plot of X- and D (symbols). At each
temperature, the two peaks’ integrated intensities were acquired at the doping
levels, where each emission is the brightest. The intensities were then
normalised to that of X (at the voltage where X is most intense). Lines: the
best-fit line was according to equations (2) and (3). (c) The temperature-
dependent bandgap of X and D (symbols). Line: the best-fit line was according
to equation (4)

Temperature affects not only the intensity but also the D emission energy. The
temperature-dependent energy shift of X and D lines can be described by the
modified Varshni relation 47, 48, 16 as

$E_{g}(T)=E_{g}(0)-S\langle\hbar\omega\rangle[\mathrm{coth}\frac{\langle\hbar\omega\rangle}{2k_{B}T}-1]$
(4)

where $E_{g}(0)$ is the emission energy at 0 K, $S$ is the electron-phonon
coupling, and $\langle\hbar\omega\rangle$ is the average phonon energy.
Fitting gives $\langle\hbar\omega\rangle$ = 11.1 $\pm$ 1.3 meV and $S$ = 1.82
$\pm$ 0.14 for X, similar to the reported values ($\langle\hbar\omega\rangle$
$\approx$ 12 - 20 meV, $S$ $\approx$ 2 49, 50, 48, 51, 52). The fitted
$\langle\hbar\omega\rangle$ and $S$ for D emission are smaller, at 10.7 $\pm$
1.5 meV and 0.79 $\pm$ 0.09, respectively. Smaller $S$ constant compared to
excitonic lines has been reported for vacancy-induced PL emissions from TMD
MLs 16, 17, 53 and explained as a result of the defect being decoupled from
the conduction band, which varies with the temperature. Similar scenario is
also likely to be the case in our sample.

To gain further insight, we measured the PL emission from the sample under
out-of-plane magnetic field $B$ varying from -8 to 8 T. Figures 5(a) show the
splitting of X and X- spectra in two circular polarisation detection states
under applied $B$-field. The valley splitting, caused by the Zeeman effect
(54, 55, 56) and defined as

$\Delta E_{Z}=E_{\sigma^{+}}-E_{\sigma^{-}}=g\mu_{B}B$ (5)

(where $E_{\sigma^{+}}$ and $E_{\sigma^{-}}$ are the emission energy in the
detected circular polarisation basis $\sigma^{+}$ and $\sigma^{-}$
respectively, $g$ is the Landé $g$-factor, $\mu_{B}$ is the Bohr magneton)
changes linearly with the applied magnetic field (figures 5(b)). The
$g$-factors derived from the data are -3.69 $\pm$ 0.04 and -4.80 $\pm$ 0.03,
for X and X-, respectively. The $g$-factor value for X is close to the ones
from previous experimental work 56, 57, 58, 59, 55, 60, 61 which are between
-3.8 and -4.3 and well within the expected range from -3.22 to -3.82 predicted
by recent ab initio calculations 62, 63. The $g$-factor for X- is slightly
higher than for X but similar to the values observed for samples under higher
doping level 57, 58, 59. On the other hand, D emission shows little change
with the magnetic field (figure 5(c)). Comparing the energy of photons from D
peak in both circular polarisation gives $g$-factor of about -1.18 $\pm$ 0.06.
The peak position was determined by fitting the data with three Voigt
functions and then taking the maximum of the fitted line. The uncertainty here
is high, partly owing to the D peak’s large width.

(a)

(b)

(c)

(d)

Figure 5: Magneto-PL measurement of Cr-implanted MoSe2 ML at 1.8 K. PL spectra
acquired with out-of-plane magnetic field $B$ (varying between -8 and 8 T)
applied to the sample and excited with an H-polarised laser. The detection is
set to measure either $\upsigma^{+}$ (black) or $\upsigma^{-}$ (red)
polarisation states. The figure shows the polarisation-resolved PL spectra of
(a) X and X-, (c) D, with their Zeeman splitting $\Delta E_{Z}$ shown in (b)
and (d). The splitting was calculated from the peak positions (extracted from
fitting Voigt functions to the PL spectra), with the error bars representing
the propagated standard deviation of the fit procedure. The Zeeman splitting
of the three emissions reveals expected $g$-factors around -4 for X and X-,
only around -1.18 for D.

###  2.3 First-principles molecular dynamics simulation of Cr ion implantation
into MoSe2 ML

To get insights into the defect formation process and types of defects which
can appear upon impacts of energetic Cr ions, we carried out DFT MD
simulations, as described below. The atomic structure of a free-standing MoSe2
rectangular slab containing 90 atoms was fully optimised, then a Cr atom was
placed 6 Å above its surface, figure 6(a) and kinetic energy of 25 eV was
assigned to the atom. Normal incidence was simulated; that is, the initial
velocity vector of the projectile was oriented perpendicular to the surface of
the ML. The projectile was assumed to be a neutral atom, as at such low
energies and low charge states, its neutralisation must occur well before it
reaches the surface. We note that DFT MD on the Born-Oppenheimer surface
cannot describe the evolution of charge transfer anyway, and the Ehrenfest
dynamics 64, 65 should be used. 21 impact points were selected in the
irreducible area of the primitive cell of MoSe2, figure 6(b), and the outcomes
of the simulations were averaged with the corresponding weights. The MD runs
continued until the kinetic energy brought up by the projectile was
distributed over the whole supercell (normally after a few picoseconds), then
the system’s temperature was quenched to zero, and the atomic structure was
analysed. Although the effects of substrate on defect generation in a 2D
system can be significant for ions with much higher (keV range) energies 66,
67, 68, the role of the substrate should be minimal for impacts of 25 eV Cr
ions onto MoSe2, so that a free-standing slab was simulated. Spin-polarised
calculations were carried out. Although computationally more efficient non-
spin-polarised method with a correction for isolated atom polarisation
energies can be used to simulate irradiation effects 24, the account for spin
effects is particularly important for Cr, as it is magnetic, which affects the
energetics of defect configurations.

Figure 6: First-principles MD simulation of ion implantation process into ML
MoSe2. (a) The setup for simulations of ion impacts. (b) Impact sites used in
the simulation. (c) Atomic structures of the defects likely to appear upon
impacts of energetic Cr ions.

Figure 6(c) shows the most common atomic configurations which appear after Cr
atom impacts. These are Cr adatoms, X-sub configuration (Cr at Se sites with a
Se adatom 69), interstitials (the Cr atom between Mo atoms) and substitutional
defects in Mo and Se sites, which are Cr@Mo and Cr@Se respectively. Table 1
lists the probabilities for the defects to appear. Ion irradiation also gives
rise to the sputtering of Se atoms, that is the formation of Se vacancies
(V${}_{\text{Se}}$), but these events were not so common.

Table 1: Results of DFT MD simulations of 25 eV Cr ion irradiation on single layer MoSe2. The probabilities $p$ of likely defect configurations to appear along with the formation energies $E_{f}$ of these configurations are listed.  | $p$ |  $E_{f}$ [eV]
---|---|---
adatom | 0.16 | -0.85
X-sub | 0.41 | -0.76
interstitial | 0.08 | -0.25
Cr@Mo | 0.21 | 3.03
Cr@Se | 0.04 | 2.57
V${}_{\text{Se}}$ | 0.01 | 5.41
passed through | 0.09 | 0.00

According to the DFT MD simulations, the most probable defects which appear
upon 25 eV Cr ion irradiation are Cr adatoms, Cr@Mo, and X-sub defects. The Cr
atoms which pass through the MoSe2 sheet will likely form adatoms attached to
the bottom of MoSe2. Self-annealing of defects at finite temperatures at which
irradiation was carried out in the experiment can affect their concentrations
in the implanted samples. To get insight into the possible evolution of
defects, we assessed the defect formation energies $E_{f}$, as done previously
69. For adatoms, interstitials and X-sub defects, $E_{f}$ was calculated as
the energy difference between the system with Cr atom and the pristine system
plus isolated Cr atom. For the Cr@Mo, Cr@Se and V${}_{\text{Se}}$
configurations, the energies of isolated Mo and Se atoms were also taken as a
reference. We note that the listed defect formation energies for the Cr@Mo,
Cr@Se, and V${}_{\text{Se}}$ cannot be used to assess the equilibrium
concentrations of these defects, as the chemical potentials were chosen to
match isolated, that is sputtered, atoms. This can be done, though, if the
chemical potentials of the displaced Se and Mo atoms are chosen in such a way
that they reflect the actual experimental conditions that the potential can be
anywhere between the values corresponding to the Se or Mo-rich limits. This
would result in lower formation energies, as the sputtered atoms would be
incorporated in the lattice. It can also be assumed that the displaced Se
atoms form Se clusters at the surface, which would give rise the lowering of
Cr@Se defect energies.

As evident from Table 1, $E_{f}$ for adatoms is lower than for the
interstitials, so that at finite temperatures, the interstitials will most
likely be ’pushed away’ from the Mo plane and form adatoms. We note that this
result was obtained for a relatively small 90-atom supercell, and in the
larger system, the difference between these energies is smaller, as reported
earlier 69. Nevertheless, even for equal formation energies at zero
temperature, with account for the entropic term in the Gibbs energy, the
probabilities for the adatoms should be higher due to a larger configurational
space. Some X-sub defects may also be converted to Cr@Se configurations,
especially in the Mo-rich limit, when Se vacancies are present, but the
energetics of this process naturally depends on the experimental conditions,
that is, the choice of Se chemical potential. The Cr@Se defects can also
appear due to the adsorption of Cr atoms on Se vacancies, as this is
energetically favourable due to the saturation of dangling bonds. Thus one can
expect that the most prolific defects in the samples are Cr adatoms (or Cr
clusters on top of MoSe2), X-sub, as well as Cr@Mo and Cr@Se substitutional
configurations.

###  2.4 DFT calculations of optical properties

To investigate if Cr defects introduce states in the bandgap of the MoSe2 ML
that are optically active we have simulated optical absorption spectra for
MoSe2 with Cr defects in various positions. The simulations are based on a 5x5
supercell. Each supercell hosts one Cr defect. The unfolded band structures
are shown in the supplementary figure LABEL:fig:DFT_band. All defects give
rise to states in the bandgap. The absorption spectrum
$\imaginary[\varepsilon(\omega)]$ with the energy dependent macroscopic
dielectric function $\varepsilon(\omega)$ has been calculated within the
random-phase approximation in the limit $\mathbf{k}\rightarrow\mathbf{0}$.
Optical matrix elements and local-field effects are taken into account. It
should be pointed out that self-energy corrections (such as $GW$) or electron-
hole interactions (as described by the Bethe-Salpeter equation) are neglected.
Self-energy corrections and electron-hole interactions are known to have a
partially compensating effect on the bandgap 70: While the former tends to
increase the bandgap, the electron-hole interactions make the optical bandgap
smaller. Due to this compensating effect, the present theoretical results can
be seen as approximate spectra specifically showing the impact of the defects.
However, quantitative differences between theory and experiment should be
expected due to the neglect of many-body effects and also due to the
difference in the dielectric environment. The theoretical spectra are shown in
figure 7. Absorption below the bandgap (around 1.6 eV) is present for all
defects and originates from transitions involving the defect states.

Figure 7: Comparison of calculated absorption functions for pristine MoSe2 ML
(black line) and MoSe2 ML with Cr in various positions of the crystal
structure: Cr at interstitial position (red), Cr at Mo position (Cr@Mo -
blue), Cr at Se position with additional Se adatom (X-sub - green) and Cr at
Se position (Cr@Se - purple). Spectra are offset vertically for clarity. The
vertical dotted line at about 1.6 eV marks the calculated bandgap of pristine
MoSe2 ML.

There is an optical transition for X-sub at 1.5 eV, which is in the same
energy range of D emission from the PL spectra, between the valence band and
an acceptor state of X-sub. This state results from the coupling of the
conduction band at the K point with the Cr defect state. The energy of this
transition is similar to that of the MoSe2 ML with a vacancy 71, 72, 73, 74.

The weak transition involving a deep acceptor state at 0.9 eV is outside the
spectral range of our experiments. We note that the coupling between the
conduction band and the defect state shifts the conduction band minimum from K
towards the $\Gamma$ point (supplementary figure LABEL:fig:DFT_band). However,
the resulting suppression of PL would not be visible in the experiment due to
the low density of defects and only the local opening of the bandgap.

Well-defined spin-degenerate acceptor levels are also introduced by Cr
substituting the Mo atom in the lattice (Cr@Mo). Optical transitions from this
defect state into the valence band states can be seen in figure 7 in the range
between 1.4 and 1.5 eV, which is also in a similar energy range to D peak PL
emission. The band-to-band transition is shifted to higher energy compared to
the pristine MoSe2 ML because of the coupling between the conduction band and
the defect state. However, similar to the X-sub configuration discussed above,
it is unlikely to observe this blueshift in the PL spectra due to the low
defect density.

The coupling of the defect and conduction band results in a gradual increase
of the above-bandgap absorption for Cr substitution into the Se site (Cr@Se).
This defect type also introduces a donor state at the Fermi level and two
single-spin, deep defect levels. The signal from the donor state merges with
the band-to-band absorption. Otherwise, the Cr defect at the Se site hardly
affects the MoSe2 band structure. Several weak optical transitions are present
at a large range of energies (down to 500 meV below the bandgap).

Interstitial Cr introduces several deep defect levels in the bandgap, and
again the highest state couples to the conduction band shifting the conduction
band minimum to the $\Lambda$ point. The absorption spectrum does not contain
discrete absorption lines but a gradually increasing absorption from 1.2 eV.

##  3 Discussion

Radiative recombination of an electron (e-) bound to a defect state with the
valence band hole (h+) can explain the measured PL. Considering that our DFT
calculations do not show donor states at high enough energy, the electron here
is likely to occupy an acceptor. In this scenario, an exciton bound to a
negatively charged acceptor (A-X) dissociates into A-h+ and a free electron in
the conduction band. Following radiative recombination, A-h+ becomes neutral
acceptor A0. Theoretical modelling of A-X indicated a binding energy of only a
few meV compared with A0 \+ e- state 13, which is of the same order of
magnitude as the activation energy of the D-line determined from the Arrhenius
plot. Among the potential defects identified by MD calculations, Cr@Mo, X-sub,
and Cr@Se have non-zero matrix elements for optical transitions between
acceptor states and valence band. Other configurations, e.g. interstitial Cr
or Se vacancies, are unlikely to be present. Besides, neither would explain
the data (see figure 7 and supplementary information note 4).

The measured 1/$e$ recombination time is longer than the lifetimes reported
for band-to-band and localised states recombination in MoSe2. Low oscillator
strength of the transition can result from the spatial separation of electrons
and holes, as for Cr@Se or X-sub. However, since this lifetime is longer than
that of the spin dark states in WSe2, which is only a few ns 75, this
transition could also be from a spin forbidden state. Such a state would
correspond to the charge configuration of A0 for Cr@Se defect in the absence
of exchange interactions between electrons in the conduction band.

The $g$-factor of D emission is negative but much smaller than the ones for X
or X-. With large $g$-factors for electrons in the valence band, it implies
either a large $g$-factor for an electron on the acceptor level near the
conduction band (e.g. in Cr@Mo or X-sub configuration) and valley-selective
transitions or reduced $g$-factor of holes in the valence band. The latter
could be caused by the hybridisation of the valence band with the defect level
as in the Cr@Se configuration. Further insight would require higher magnetic
field measurements and theoretical input.

##  4 Conclusion

In conclusion, we demonstrated the ultra-low energy ion implantation of Cr
ions (at 25 eV) into a MoSe2 ML. The implantation was performed with ions at
25 eV and the ion fluence of 3 $\times$ 1012 cm-2, the resultant material
retains high optical quality as evidenced by clear excitonic PL. Implanted Cr
ions introduce an additional low energy PL signal at around 1.51 eV visible at
the onset of n-doping. Molecular dynamics calculations identified defects that
can be generated by implantation. We found that Cr atoms can substitute for
both Mo and Se atoms. In the latter case, the Cr atom is slightly more likely
to bind an additional Se atom than not. The defects’ stability, including
interstitial Cr, depends on the post-implantation treatment and the final
configuration of Se and Mo, which are not in the lattice. DFT calculations
revealed that all the probable defects introduce one or more defect states in
the MoSe2 bandgap with non-zero matrix elements for optical transitions. It is
impossible to identify with certainty which defect is the origin of D-line, Cr
at Se site with Se adatom (X-sub), and perhaps Cr at Mo (Cr@Mo) seem to fit
best with the measured data. Further experiments, for example, implantation of
Cr only into the Se sub-lattice or implantation through the hBN protective
layer to avoid environmental changes, could be considered to distinguish
between the cases.

More generally, this study shows that while implantation of heavier elements
into metal sub-lattice of TMD MLs is possible without a visible loss of the
material quality, the implantation process is complex, and simulations of the
possible outcomes are necessary to identify material systems of the desired
properties. In the search for single photon emitting sites, it is also worth
noting that upon implantation with a very low fluence, it should be possible
to address individual Cr atoms at different lattice sites.

##  5 Methods

###  5.1 Atomistic simulation

We used DFT-MD as implemented in the VASP code 76, 77. The Perdew-Burke-
Ernzerhof (PBE) exchange and correlation functional was employed 78. The
evolution of the system was modelled using the microcanonical ensemble. A
cutoff value of 300 eV was chosen for DFT MD, and sampling over the Brillouin
zone was done using a $3\times 3\times 1$ k-point mesh. The time step was
chosen to be 0.1 fs, which provided energy conservation better than 0.1 eV.

###  5.2 Band structure and absorption spectra calculation

Density functional theory (DFT) simulations were performed in supercells of
5$\times$5 primitive unit cells. Each constructed with lattice constants of
$a=3.28\,$\mathrm{\SIUnitSymbolAngstrom}$$ and
$c=12.918\,$\mathrm{\SIUnitSymbolAngstrom}$$ of the hexagonal lattice. An
internal structure parameter of $z=0.125$ was used. The defect systems were
spatially relaxed using FLEUR 79 until the residual atomic forces had fallen
below 5 $\times$ 10-2 eV/$\mathrm{\SIUnitSymbolAngstrom}$. The subsequent
calculation of the macroscopic dielectric function in SPEX 80, 81 is based on
the random-phase approximation 82, 83 and includes local-field effects.
Calculations of 2D materials with 3D periodic boundary conditions are
computationally expensive because the decoupling of neighbouring layers in the
$z$ direction requires large supercells in this direction. In the case of 2D
systems with defects, the computational cost grows considerably, particularly
in the case of low defect concentrations, because suppressing the unwanted
defect-defect coupling requires large supercells in the $x$ and $y$
directions. To facilitate the calculations of the dielectric function, we had
to reduce the reciprocal cutoff radius from $4.1$ to $3.6$ Bohr-1 in the case
of the X-sub defect system. However, this should not affect the form of the
respective spectrum shown in figure 7.

The band structures presented in the Supplementary Information are made up of
320 $\mathbf{k}$ points along the unfolded high-symmetry path
$\Gamma-\text{M}-\text{K}-\Gamma$. Here, ”unfolded” means that the high-
symmetry points refer to the ones of the defect-free MoSe2 ML. The necessary
unfolding of the band structures of the defect systems has been carried out
with a new implementation 71 in the FLEUR code adapting the technique
described in Ref. 84 to the LAPW basis 85. In this technique, a spectral
weight is assigned to each state plotted in the band structure. The weight
$w_{n}(\mathbf{k})$ for the $n$-th state at $\mathbf{k}$ of the unfolded path
is given by

$\displaystyle
w_{n}(\mathbf{k})=\sum_{\tilde{\mathbf{G}},\mathbf{G}^{\prime}}C^{*}_{\mathbf{k}^{\prime}n}({\tilde{\mathbf{G}}})\cdot
C_{\mathbf{k}^{\prime}n}(\mathbf{G}^{\prime})\cdot
S_{{\tilde{\mathbf{G}}}\mathbf{G}^{\prime}}(\mathbf{k}^{\prime})$ (6)

where $\mathbf{k}^{\prime}=\mathbf{k}+\mathbf{G}^{\prime\prime}$ with a
suitable reciprocal lattice vector $\mathbf{G}^{\prime\prime}$ that folds
$\mathbf{k}$ back into the (smaller) Brillouin zone of the defect system. The
$\mathbf{G}^{\prime}$ sum runs over the set of all reciprocal lattice vectors
(of the defect system) at $\mathbf{k}^{\prime}$, and the $\tilde{\mathbf{G}}$
sum runs over the set of reciprocal lattice vectors (of the pristine system)
at $\mathbf{k}$. The latter is a subset of the former. The wave functions are
represented in the LAPW basis $\\{\chi_{\mathbf{kG}}(\mathbf{r})\\}$ with
coefficients $C_{\mathbf{k}n}(\mathbf{G})$ and overlap matrix
$S_{\mathbf{G}\mathbf{G}^{\prime}}(\mathbf{k})=\bra{\chi_{\mathbf{k}\mathbf{G}}}\ket{\chi_{\mathbf{k}\mathbf{G}^{\prime}}}$
71.

###  5.3 Sample preparation

Si with 90 nm thick dry-thermally grown SiO2 chips with 60 nm thick Ti/Au
contacts (pre-patterned by electron beam lithography) were used as the
substrate. Before flake transfer, the chips were cleaned in acetone and
isopropanol (IPA) under bath sonication, blown dry with N2 and treated with
oxygen plasma (300 W, 200 sccm for 10 minutes). Few-layer graphite, MoSe2
(from 2D Semiconductors) MLs, and hBN (from Takashi Taniguchi and Kenji
Watanabe) multilayers were mechanically exfoliated from bulk crystal using
polydimethylsiloxane (PDMS) stamps (Gel-pak DGL X4 films) and transferred onto
the substrate using dry viscoelastic transfer process 31. The process was
performed in a N2 filled glovebox. After transferring the graphite (5.5 nm
thick) and bottom-hBN (20 nm thick) flakes, the sample was annealed in H2/Ar
(1:10 ratio) atmosphere at 300 $\degree$C for 3 hours to improve the top
surface for the subsequent MoSe2 ML transfer. After transferring the top-hBN
(15 nm thick), the sample was annealed in low vacuum (5 $\times$ 10-3 mbar) at
200 $\degree$C for 2 hours to improve interfaces in the vdW stack. Electrical
contacts, provided by the Ti/Au lines, were made to the MoSe2 flake and the
graphite back gate. After each transfer, the heterostructure surface was
checked with atomic force microscopy to ensure a sufficiently flat area in the
stack and to obtain the flakes’ thickness. MoSe2 ML’s quality was confirmed
with Raman and PL spectroscopy at room temperature 86.

###  5.4 Ion implantation

Bronze tips were used to fix the sample on a holder, making contact with the
sample’s Au pads and, thus, the ML. To remove volatile contamination from the
sample, the sample chamber was then evacuated to 10-9 mbar for several hours.
The sample was heated to 150 $\degree$C for 10 minutes to remove residual
volatile adsorbates, then to 220 $\degree$C during the implantation. A foil is
used as the feedstock to provide 52Cr+ ions. After extraction, the ions are
decelerated from 30 keV to 25 eV directly in front of the sample. Since the
deceleration voltage is set relative to the potential of the source anode,
this energy represents the upper limit, with a tail towards lower energies.
The fluence of the ions was set to 3 $\times$ 1012 cm-2. The fluence was
verified by test implantations using Rutherford backscatter spectrometry (more
information in Supplementary information LABEL:section:RBS). A detailed
description of the source and the implantation system can be found in the
references 26, 25.

###  5.5 Optical measurements

PL spectroscopy was performed at 10 K (unless otherwise specified) in a He-
cooled cold-finger cryostat (Cryoindustries) with a heating element (allowing
a sample temperature range from 10 to 300 K). For PL measurements, the laser
beam - 688 nm (1.80 eV) from a Ti:Sa laser - is passed through a 680 $\pm$ 5
nm band-pass filter before being focused by an aspheric lens (NA = 0.47) into
a spot of 1.6 $\upmu$m in diameter on the sample. Unless otherwise specified,
the laser power on the sample was at 1 $\upmu$W for PL experiments. PL signal
is collected by the same lens and passed through a 700-nm low pass filter
before being focused by an achromatic doublet (NA = 0.24) through the entrance
slit of a Czerny-Turner spectrometer, dispersed by a 600 l/mm grating onto a
CCD camera. For gate dependence and temperature dependence PL, the laser power
was kept at 1 $\upmu$W. For PLE, excitation power ranged from 2 to 5 $\upmu$W,
and PL intensity is normalised to the power density for final data.

For time-resolved PL, the excitation was done using a pulsed laser at 660 nm
(1.88 eV) with 200ps pulse length, 2.5 MHz repetition rate and 2.8 $\upmu$W
average power. The PL signal is directed through an 800 nm (1.55 eV) low-pass
filter on the detection path before entering an avalanche photodiode with 30
ps time resolution. The histogram of the time difference between the laser
pulses and PL emission was acquired with a time tagger.

The sample was mounted on an x-y-z Attocube stage in a He flow cryostat
(attoDRY2100) for magneto-optics measurement at temperature T = 1.8 K. A
magnetic field up to $\pm$8 T was applied perpendicularly to the sample
(Faraday configuration). The excitation laser beam (688 nm, i.e. 1.80 eV at 4
$\upmu$W) was passed through a 680 nm bandpass filter and a linear polariser
in an H-configuration. The laser was focused by an aspheric lens (NA = 0.47)
into a spot of $\approx$ 1.6 $\upmu$m in diameter on the sample. The emitted
PL was collected by the same objective. It was passed through a combination of
$\uplambda$/4, $\uplambda$/2 waveplates, and a linear polariser set to pass
$\upsigma^{\pm}$ polarised light. It was then propagated via a single mode
optical fiber towards the entrance slit of a Czerny-Turner spectrometer, where
it was dispersed by a 600 l/mm grating onto a CCD camera. A long pass filter
(with 700 nm band edge) was inserted between the fiber output and the
spectrometer entrance to remove any remaining laser light.

## Data availability

The data supporting the findings of this study are available within the paper
and its supplementary information files. Data are also available from the
corresponding author upon reasonable request.

## Code availability

All scripts used to generate the results in this study are available from the
corresponding author upon reasonable request.

## Acknowledgement

This project is supported by the “Integration of Molecular Components in
Functional Macroscopic Systems” initiative of Volkswagen Foundation. We would
like to thank the staff at the Helmholtz Nano Facility 87 of Forschungszentrum
Jülich for helping with substrate fabrication, and Felix Junge (II. Institute
of Physics, University of Göttingen, Göttingen, Germany) for organizing the
RBS data. We acknowledge the computing time granted through JARA-HPC on the
supercomputer JURECA at Forschungszentrum Jülich. A.V.K. acknowledges funding
from the German Research Foundation (DFG), project KR 4866/8-1 and the
collaborative research center “Chemistry of Synthetic 2D Materials”
SFB-1415-417590517. Generous grants of computer time from the Technical
University of Dresden computing cluster (TAURUS) and the High Performance
Computing Center (HLRS) in Stuttgart, Germany, are gratefully appreciated.
K.W. and T.T. acknowledge support from the JSPS KAKENHI (Grant Numbers
19H05790 and 20H00354).

## Author contribution

B.E.K., H.C.H., and M.N.B conceived and designed the experiments. S.K. and
A.V.K. performed MD simulations. S.R., C.F. and S.B. performed DFT
calculations for band structures and absorption spectra. T.T. and K.W. grew
hBN crystals. L.Z. processed the Si/SiO2 substrate with patterned markers and
metal contacts. M.N.B. prepared the samples on Si/SiO2 substrate. M.A. and
H.C.H. performed ion implantation. M.N.B. acquired and analysed PL and Raman
data. All authors discussed the results and contributed to the writing of this
manuscript.

## Competing interests

The authors declare that there are no competing interests.

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