# Electronic and magnetic properties of dopant atoms in SnSe monolayer: a
first-principles study

Qingxia Wang  International Laboratory for Quantum Functional Materials of
Henan, and School of Physics and Engineering, Zhengzhou University, Zhengzhou,
450001, China  Weiyang Yu  International Laboratory for Quantum Functional
Materials of Henan, and School of Physics and Engineering, Zhengzhou
University, Zhengzhou, 450001, China  School of Physics and Chemistry, Henan
Polytechnic University, Jiaozuo, 454000, China  Xiaonan Fu  Department of
Physics and School of Science, Henan University of Technology, Zhengzhou
450001, China  Chong Qiao  International Laboratory for Quantum Functional
Materials of Henan, and School of Physics and Engineering, Zhengzhou
University, Zhengzhou, 450001, China  Congxin Xia<EMAIL_ADDRESS>Department of Physics,Henan Normal University, Xinxiang, 453000, China  Yu Jia
<EMAIL_ADDRESS>International Laboratory for Quantum Functional Materials of
Henan, and School of Physics and Engineering, Zhengzhou University, Zhengzhou,
450001, China

###### Abstract

Abstract: SnSe monolayer with orthorhombic _Pnma_ GeS structure is an
important two-dimensional (2D) indirect band gap material at room temperature.
Based on first-principles density functional theory calculations, we present
systematic studies on the electronic and magnetic properties of X (X = Ga, In,
As, Sb) atoms doped SnSe monolayer. The calculated electronic structures show
that Ga-doped system maintains semiconducting property while In-doped SnSe
monolayer is half-metal. The As- and Sb- doped SnSe systems present the
characteristics of $n$-type semiconductor. Moreover, all considered
substitutional doping cases induce magnetic ground states with the magnetic
moment of 1$\mu_{B}$. In addition, the calculated formation energies also show
that four types of doped systems are thermodynamic stable. These results
provide a new route for the potential applications of doped SnSe monolayer in
2D photoelectronic and magnetic semiconductor devices.

Keywords: SnSe monolayer, substitutional doping, electronic properties,
magnetism

###### pacs:

73.20.At, 75.50.Pp, 75.75.+a

1\. Introduction

Along with the discovery of graphene, many new two-dimensional(2D) atomic
layered systems have attracted special attention for future electronics
applications.Novoselov ; Geim ; Rodin ; Brumme ; Sivek  Recently, more and
more researchers devote themselves on 2D atomic-layer materials, such as
silicene, germanane, stanene, phosphorene, and so on.Yu ; Zhu1 ; Vogt ; Xia ;
Zhu2  Just as the scope of group IV semiconductors such as graphene and
silicene have been broadened significantly by introducing isoelectronic III-V
compounds, phosphorene has been broadened by introducing isoelectronic IV-VI
compounds.Zhu3  IV-VI group semiconductors have layered structures which are
similar to phosphorene.Rarenteau ; Choi  For bulk Tin selenium (SnSe), it has
two most common crystal structures: one is cubic NaCl (rock salt) and the
other is orthorhombic GeS structure with an orthorhombic _Pnma_ space group at
room temperature.Lefebvre ; Chamberlain  Furthermore, bulk SnSe is an
important double layered binary IV-VI semiconductor with structural
orthorhombic symmetry and weak van der Waals force between double layers. In
addition, bulk SnSe has both a direct band gap of 1.30 eV and an indirect band
gap of 0.90 eV, just falling into the optimum band gap for solar cells.
Therefore, bulk SnSe is also considered as the most promising candidates for
solar cells.Antunez ; Liu ; Baumgardner  Especially, with the successfully
synthesizing of 2D SnSe experimentally, SnSe monolayer has attracted more and
more attention in monolayer IV-VI semiconductor.Li1  SnSe monolayer is
comprised of zigzag double-layered planes and exhibits strong anisotropic
properties.Antunez ; Pejova ; Xue1  As material of earth-abundance,
environment friendly and good chemical stability, SnSe can be applied in a
wide range of potential applications, e.g. optical devices, memory switching
devices, infrared optoelectronic devices and anode materials for rechargeable
lithium batteries.Chun ; Zhang1 ; Xiao ; Xue2 ; Zhang2

SnSe monolayer has the similar structure to phosphorene. Sn and Se atoms
present a puckered surface due to the $sp^{2}$ hybridization.Li2  Each Sn atom
forms three covalent bonds with Se, and the same as Se atom. The synthesis and
properties of SnSe monolayer have attracted much attention.Antunez ; Li1  As
we know, 2D material have many special properties due to their unique
dimension-dependent properties comparing with 3D material.Rogers  Whereas
there is few literature about 2D SnSe monolayer,Zhu3  the electronic and
magnetic properties of substitutional doping of SnSe monolayer have not been
done. In this work, using first-principles density functional theory (DFT)
calculations, we present a systematic study of the electronic and magnetic
properties of Ga-, In-, As-, and Sb- doped SnSe monolayer. Firstly, we
calculate the electronic and magnetic properties of the doped systems. And
then, we calculate the formation energy $E_{f}$ and find that the formation
energy of Ga-doped system is lowest than the other three systems,indicating
that Ga-doped system is apt to be realized in experiment.

2\. Computational Details

The present first-principles DFT Kohn  calculations were performed using
Perdew-Burke-Ernzerh (PBE)Perdew  in the projector augmented wave (PAW) Blochl
within Vienna _ab initio_ Simulation Package (VASP) .Kresse  The reciprocal
space was sampled with a fine grid of 3$\times$3$\times$3 $k$-points in the
Brillouin zone of the primitive unit cell for bulk SnSe, and
1$\times$3$\times$3 $k$-points for the SnSe monolayer and the doped systems.
The wave functions were expanded in a plane-wave basis with an energy cutoff
of 500 eV. The maximum force of each atom was less than 0.01 eV/Å.The
geometrical structure was employed with a 3$\times$3 supercell including 36
atoms with doping concentration of 2.78%. A vacuum spacing perpendicular to
the plane was employed to be at least 15Å in the unit cell to avoid the
coupling between neighboring cells. The spin-polarized was considered to
analyze the magnetism of the doped systems.

3\. Results and discussion

Fig. 1 presents the geometrical structure and electronic band structure of
bulk SnSe. The calculated optimal lattice parameters of bulk SnSe are a=11.50Å
b=4.16Å, and c=4.45Å, which are in agreement with the experiment
valuesFranzman  and previous theoretical valuesKutorasinski ; Huang . The bond
lengths of Sn-Se are $d_{1}$=2.81Å and $d_{2}$=2.78Å, which are coincided with
the previous reported values,Lefebvre  as seen in Fig. 1 (a). The calculated
band gap is 0.50 eV, which is smaller than experimental value and the previous
theoretical calculation,Huang  on account of the DFT-PBE method which
underestimates the band gap of semiconductor. Even though the fundamental band
gaps are typically underestimated in DFT-PBE approach, the prediction of the
indirect semiconductor system is correct.Lu ; Krasheninnikov ; Ramasubramaniam
; Cheng  In Fig. 1 (b), we can see that the valence band maximum (VBM) of bulk
SnSe is at M point, while conduction band minimum (CBM) is located at the
middle of $\Gamma$-M, indicating an indirect band gap. Moreover, the bulk SnSe
has no magnetism according to our calculation.

The structure of SnSe monolayer is displayed in Fig. 2, along with the similar
structure of phosphorene. As seen in Fig. 2 (a) and (b), Sn and Se atoms form
three covalent bonds with each other in a puckered surface, which is similar
to that of phosphorene,Yu ; Zhu1  as shown in Fig. 2 (c) and (d). However, it
is obvious to perceive that the structure of phosphorene is of higher symmetry
than SnSe monolayer, so they appear some different properties, e.g. SnSe
monolayer is an indirect band gap semiconductor, while phosphorene has a
direct band gap.Yu

Figure 1: (a) The geometric and (b) electronic structures of bulk SnSe.

To investigate the electronic and magnetic properties of substitutional doping
in SnSe monolayer, the band structure, total density of states (DOS) and
partial density of states (PDOS) of the doping systems
$Sn_{17}$$Se_{18}$$X_{Sn}$ (X=Ga, In, As, Sb) are calculated, along with the
pure SnSe monolayer for comparison.

Figure 2: (a) Top and (b) side views of SnSe monolayer with 3$\times$3
supercell cell, indicating the black dashed rectangle. The dark atom denotes
Sn atom substituted by a dopant atom, and navy balls denote Sn atoms and
prasinous balls denote Se atoms. (c) Top and (d) side views of black
phosphorene (pink balls denote P atoms).

Firstly, band structures, DOS and PDOS of SnSe monolayer are calculated in
Fig. 3. As shown in Fig. 3 (a), the indirect band gap is 0.78 eV, which is
bigger than that of bulk SnSe ($E_{g}$=0.50 eV). From the PDOS of SnSe
monolayer , as shown in Fig. 3 (b), we can clearly see that it is
${5s}$-orbitals of Sn and ${4p}$-orbitals of Se that contribute mostly to the
total DOS below Fermi level from -1.50 eV to -0.11 eV. While above Fermi
level, ${5p}$-orbitals of Sn and ${4s}$-orbitals of Se contribute mostly to
the total DOS. In detail, it is the hybridization of ${5s}$-orbital of Sn and
${4p}$-orbital of Se that forms the valence band, and ${5p}$-orbital of Sn and
${4s}$-orbital of Se hybridize to comprise the conduction band. The spin-
polarized calculations show that pristine SnSe monolayer is of non-magnetism.

Figure 3: (a) Electronic band structure along $\Gamma$-M-N-$\Gamma$ direction
and corresponding total DOS, (b) PDOS of SnSe monolayer. The energy zero
represents the Fermi level.  Figure 4: Calculated band structures of (a) Ga-
and (b) In-doped systems, along $\Gamma$-M-N-$\Gamma$ direction. The energy
zero represents the Fermi level. Figure 5: DOS and PDOS of (a) Ga-doped and
(b) In-doped systems. The energy zero represents the Fermi level.

Now we turn to investigate the doping effects on electronic structures of SnSe
monolayer. As we know that the electronic structure of SnSe monolayer can be
tuned in a widely range by substitutional doping with Sn atom replaced by
other atoms because the outer electron valence configuration of Sn is
$4d^{10}$$5s^{2}$$5p^{2}$. There are two $5p^{2}$ electrons of Sn which join
in bonding, and two $5s^{2}$ electrons left to form a lone pair. As a result,
Sn atom can form s$p^{2}$ bonding with a lone pair of valence
electrons.Chamberlain  In the doped system $Sn_{17}$$Se_{18}$$X_{Sn}$ (X=Ga,
In, As, Sb), X dopant atom is neighborhood with Sn in the periodic table of
elements, which can avoid of lattice distortion, giving rise to the impurity
states always appear either above valence band or below conduction band, or
the middle of band gap. To explore the underlying electronic and magnetic
properties of the doped monolayer $Sn_{17}$$Se_{18}$$X_{Sn}$ (X=Ga, In, As,
Sb). We divide the related figures into two parts: spin up and spin down,
which makes us to have a clear insight to the substitutional doping systems.

Fig. 4 (a) presents the split band structure of Ga-doped system. The impurity
state is split into spin-up and spin-down cases, and the impurity energy level
appears either above valence band (spin-up) or below conduction bands (spin-
down). Furthermore, the band gap is 0.66 eV for spin-up and 0.43 eV for spin-
down, indicating semiconductor properties. The _Eg_ values of spin-up and
spin-down are both smaller than that of pure SnSe monolayer. Since Ga is the
acceptor, leading to the band gap decreasing both for spin-up and spin-down.
When Ga atom is doped, the doped system has a red shift, giving rise to a
relatively wide application in electron devices. However, for In-dpoed system,
it is exceptive that the VBM rises for spin-up, while the CBM goes down cross
the Fermi level for spin-down, which lead to a half-metal property, as shown
in Fig. 4 (b). For the Ga- and In-doped systems, because Ga and In belong to
the same group IIIA, they present different properties. The intriguing
phenomenon can be explained by the nearly equal electronegativity
(Ga$\sim$1.81, Sn$\sim$1.96, In$\sim$1.78), and we know that the difference
between Sn and In is slightly bigger than that between Sn and Ga. To have a
further insight into the underlying mechanism of the dopant systems, the total
DOS and PDOS of Ga- and In-doped system are shown in Fig. 5.

Figure 6: Spin charge density ($\rho$up-$\rho$down) of (a) Ga- and (b) In-
doped system (dark blue ball denotes Ga atom, light pink ball denotes In
atom),respectively. The value of isosurfaces is 0.03 e/${\AA^{3}}$.

From the PDOS of Ga-doped system, as seen in Fig. 5 (a), we can see that it is
obvious that 4$s$-, 4$p$-orbital of Ga and 4$p$-orbital of Se play an
important role for the VBM and CBM, and make the main contribution to the
total DOS. Similarly, the In-doped system presents the almost same phenomenon:
5$s$-, 5$p$-orbital of In and 4$p$-orbital of Se play an important role for
VBM, CBM, and the total DOS. Comparing to the semiconductor property of Ga-
doped system, it is obvious that the 5$p$-orbits of In atom presents
hybridization at the Fermi level. Consequently, the doping system presents a
half-metallic property, which is consistent with the band structure. Moreover,
we know that the total DOS is up and down asymmetry nearby the Fermi level,
indicating that Ga- and In-doped system present magnetism with the values
about 1.00 $\mu_{B}$ and 0.99 $\mu_{B}$, respectively, which are close to
their free atoms (Ga$\sim$1.00 $\mu_{B}$; In$\sim$1.00 $\mu_{B}$).
Furthermore, from Fig. 5 (a), it is obvious that the majority of magnetism is
induced by Ga atom while Se atom contributes minority to the magnetism. But in
In-doped system, the magnetism is mainly induced by the In dopant, as seen in
Fig. 5 (b).

In order to get a clear explanation of magnetism, the spin charge density of
Ga- and In- doped systems are calculated in Fig. 6. From Fig. 6 (a) and (b) we
can obviously see that the magnetism is induced by the dopant Ga atom and In
atom, respectively. The phenomena are coincide well with the results of DOS
and PDOS. And in the Ga-doped system, the majority of magnetism distributes
around the Ga atom while the minority scatters around Se atom. Comparing to
Ga-doped system, the magnetism is mainly induced by the dopant atom in In-
doped system. The reason of the magnetism is that when Ga and In replaced Sn
in SnSe monolayer, the system will exist a hole because of the formed covalent
band. Hence, the hole will induce the magnetism. As a result, both Ga and In
dopant atoms lead to an acceptor level which gives rise to $p$-type doping
systems with band gap decreasing.

Figure 7: Calculated band structures of (a) As- and (b) Sb-doped systems,
along $\Gamma$-M-N-$\Gamma$ direction. The energy zero represents the Fermi
level. Figure 8: DOS and PDOS of (a) As- and (b) Sb-doped systems. The energy
zero represents the Fermi level. Figure 9: Spin charge
density($\rho$up-$\rho$down) of (a) As- and (b) Sb-doped system (red ball
denotes As atom, brown ball denotes Sb atom), respectively. The value of
isosurface is 0.03 e/${\AA}^{3}$.

In addition, we calculate the electronic band structure of As- and Sb-doped
systems in Fig. 7. From Fig. 7 we can see that the impurity level appears in
valence bands leading to the VBM rise for spin-up, while in conduction bands
resulting in the CBM declining for spin-down. However, the impurity level does
not cross the Fermi level, so the system maintains the semiconductor property
for As- and Sb-doped systems. In detail, for the As-doped system, as seen in
Fig. 7 (a), the band gap is divided into two parts: 0.48 eV for spin-up and
0.88 eV for spin-down. At the same time the band gap of Sb-doped system is
0.26 eV for spin-up and 0.84 eV for spin-down, as seen in Fig. 7 (b).
Otherwise, comparing to the band gap of SnSe monolayer, we find that the value
of Sb-doped system has a less change than that of As-doped system. This
phenomenon can be explained by electronegativity (As$\sim$2.18; Sn$\sim$1.96;
Sb$\sim$2.05). It is visible that the electronegativity difference between Sn
and As is larger than that between Sn and Sb. In order to have a further
penetration into the electronic property of dopant systems, the total DOS and
PDOS of As- and Sb-doped are shown in Fig. 8.

From Fig. 8 (a) we can obviously see that 4$p$-orbitals of As makes the
contribution to not only VBM and CBM, but also the total DOS. In other words,
the main contribution is from 4$p$-orbitals of the dopant As, which is
coincide with the explanation by band structure. Furthermore, there is a flat-
level for the band structure in spin-up, leading to a large density of states
in that region, as shown in PDOS of As. In addition, we find that the system
is not symmetry at the Fermi level in total DOS, which exhibits the system is
of magnetism. Obviously, the magnetism is mainly induced by As atom. Then we
calculated the magnetic value (1.00 $\mu_{B}$), which is smaller than its free
atom (As$\sim$3.00 $\mu_{B}$). On the other hand, for Sb-doped system, as seen
in Fig. 8 (b), it shows up the similar properties to As-doped system that
4$p$-orbitals of Sb play an important role for VBM, CBM and total DOS. The
total DOS appears asymmetry at the Fermi level, indicating the Sb-doped system
is of magnetism. Obviously, the magnetism is mainly derived from the Sb atom,
and the value of calculated magnetism is 1.00$\mu_{B}$, which is also smaller
than its free atom (Sb$\sim$3.00$\mu_{B}$). From Fig. 8, we obtain the same
explanation with that of the band structures. Finally, in order to explain the
magnetic mechanism, we calculated the spin charge density of As- and Sb-doped
systems as shown in Fig. 9.

From Fig. 9 (a) and (b), we can distinctly see that the magnetism is mainly
induced by As atom and Sb atom for As- and Sb-doped systems, respectively. For
the As-doped system, the magnetism mainly gathers around the As atom, and
minority scatters around Se atoms. Similarly, the magnetism is mainly induced
by the dopant atom in Sb-doped system. The phenomena are in line with the
results of DOS and PDOS. The reason of the magnetism is that when As and Sb
replaced Sn in SnSe monolayer, the system will exist an extra electron. Hence,
the extra electron will induce the magnetism. As a result, both As and Sb
dopant atoms lead to an donor level resulting in $n$-type doped systems.

Generally, the X-doped (X=Ga, In, As, Sb) systems with either half-metal or
semiconductor properties can be explained by the $sp^{2}$ bonding character of
Sn atoms with a lone pair of valence electrons and their strong hybridizations
with the _sp_ orbitals of dopants. We can conclude that the doped systems
$Sn_{17}$$Se_{18}$$X_{Sn}$ (X=Ga, In, As, Sb) are ferromagnetic states from
the spin charge density. Considering our work, we are aware that the
electronic properties can be tuned by substitutional doping.

Table 1: Calculated structural and magnetic properties for single atoms doping on SnSe monolayer. Formation energy ($E_{f}$); the magnetic moments($\mu$); minimum dopants-Se (D-Se) distance($d_{2}$). Dopant |  $E_{f}$(eV/atom) |  $\mu$ ($\mu_{B}$) |  $d_{2}$ (D-Se) (Å)
---|---|---|---
SnSe |  -4.13 |  0 |  2.81
Ga |  -2.57 |  1.00 |  2.55
In |  -2.54 |  0.99 |  2.79
As |  -1.87 |  1.00 |  3.08
Sb |  -1.91 |  1.00 |  3.17

Finally, we calculate the formation energy of the substitutional system in
order to verify the stability of X-doped SnSe monolayer. The formation energy
($E_{f}$) is defined as $E_{f}$ = $E_{dh}$ \- $E_{d}$ \- $E_{h}$, where
$E_{dh}$, $E_{d}$, and $E_{h}$ are the total energies of the doped system
$Sn_{17}$ $Se_{18}$ $X_{Sn}$ (X=Ga, In, As, Sb), the energy of monolayer
$Sn_{17}$ $Se_{18}$ and single Sn atom and isolated X atoms, respectively.
From our definition, the negative value of $E_{f}$ shows that a system is
stable. The large absolute value of $E_{f}$ energy means strong interaction
between dopants and Sn. A summary of the results is shown in Table 1. From
Table 1, we find that the formation energy of Ga-doped system is minimum,
which demonstrates Ga atom is easy to be doped and the Ga-doped system is the
most stable than other three systems. In general, the doped systems can be
realized in experiment.

4\. Conclusions

In summary, using first-principles calculations, we present the geometrical
structure, electronic and magnetic properties of monolayer SnSe
substitutionally doped by Ga, In, As, and Sb atoms, respectively. We find that
the electron structure can be tuned by substitutional doping. When Ga or In is
doped, the system presents semiconductor and half-metal properties,
respectively; while As or Sb substitute Sn, the systems display semiconductor
properties. In Ga-doped system, due to the band gap declining, the system
exhibits red shift, which makes the system to have a wide application in
optoelectronic devises. When Sn atom is replaced by Ga atom or In atom,
inducing a hole, so the systems belong to $p$-type doping; on the other hand,
if As or Sb replace Sn, the system has an unpaired electron, resulting
$n$-type doping. No matter whether Ga and In as dopant atoms, or As and Sb,
there is an unpaired electron which can induce about 1$\mu_{B}$ magnetism.
Finally, comparing to the formation energy of $Sn_{17}$$Se_{18}$$X_{Sn}$
(X=Ga, In, As, Sb), we find that Ga is easy to be doped and the Ga-doped
system of is the most stable, whereas the four types of doped systems are
thermodynamic stable. The results of substitutional doping make the
application of SnSe monolayer more extensive.

5\. Acknowledgements

This work is supported by financial support from the National Basic Research
Program of China (No.2012CB921300) and the National Natural Science Foundation
of China (Grant Nos.11274280).

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