English

• 0.   Introduction

  In 2004, Novoselov et al.^[1] prepared a single-layer graphene material and found that it has excellent optoelectronic properties. Graphene material is recognized as an ideal material for next-generation nanoelectronics^[2-4]. Since then, 2D materials have become one of the hot research directions. In addition to graphene, researchers have discovered phosphoranes^[5-6], nitrides^[7-9], transition metal carbides^[10], transition metal sulfides^[11-12], and other 2D materials. With the in-depth study of 2D materials, it has been found that 2D materials have excellent electrical, optical, and magnetic properties, which make 2D materials show endless potential in various aspects such as photocatalysis, solar cells, and optoelectronic devices and sensors^[13-17].

  2D GaSe is a new type of metal-sulfur compound material, which can be experimentally prepared by mechanical exfoliation, liquid-phase exfoliation, molecular-beam epitaxy, and chemical vapor deposition. 2D GaSe has the advantages of high switching ratios, high photoresponsivity, and good thermal stability^[18-21]. The 2D GaSe can be modulated through elemental doping, defects, and constructing heterojunctions to improve its properties, such as optoelectronic magnetism. Tang et al.^[22] modulated the electronic structure and magnetic properties of GaSe monolayers by the dual modulation of vacancy defects and electric field. It was found that the Ga vacancies in GaSe monolayers yielded 100% spin-polarized semi-metallicity because of the non-bonded 4p orbitals around the Se atoms. Under the critical electric field of 0.6 V·nm-1, the electric field causes the redistribution of the electronic states, and the switching magnetic field configuration of the Ga- vacancy monolayer GaSe is realized. Finally, it was found that charge transfer is the main reason for the controllable magnetic structure of the system. Hou et al.^[23] investigated the adsorption behavior of three toxic gases, Cl₂, NO, and SO₂, on GaSe monolayers doped with Cr₃ clusters. It was found that the doping of Cr₃ clusters greatly improved the adsorption capacity of the GaSe monolayer for the three toxic gases. Ke et al.^[24] presented a theoretical design for modulating magnetic properties of Fe-doped GaSe monolayers based on systematic density-functional theory calculations. It was found that under a critical electric field of 0.2 V·nm^-1, the ferromagnetic coupling between Fe and neighboring Ga atoms was modulated to anti-ferromagnetic coupling, accompanied by changes in magnetic moment and spin polarization. Pham et al.^[25] investigated the electrical properties of GaSe/MoS₂ and GaS/MoSe₂ heterojunctions using first-principles calculations. The results show that both heterojunction interfaces are weak van der Waals interactions. The band gaps of GaSe/MoS₂ and GaS/MoSe₂ heterojunctions are 1.91 and 1.23 eV, and they are both indirect band gaps. In addition, both heterojunctions are Type-Ⅱ heterojunctions, which can be used in applications such as optoelectronic devices. Ao et al.^[26] investigated the effect of 2D GaSe vacancies and chemical element doping on its electronic and magnetic properties. The results show that Mg, Al, Si, and transition metal atoms replace Ga sites, which are magnetic in most cases except for Sc, Cu, Al, and Si. Meanwhile, GaSe monolayers doped with V-Ga₂, V-GaSe₃, Ti, Cr, and Ni have semi-metallic characteristics and n-type GaSe monolayers can be obtained by replacing Ga with Si or Se with Cl. Therefore, 2D GaSe can be functionalized by vacancy and chemical element doping to get new electronic structures and magnetic properties.

  Liu et al.^[27] investigated the electronic, optical, and magnetic properties of ZnO doping with rare earth elements. The results show that the magnetic properties of ZnO doped with rare earth elements are significantly enhanced, and the optical absorption intensity is enhanced after Ce doping. Wang et al.^[28] investigated the effect of La, Ce doping on the electronic structure and optical properties of Mn₄Si₇. The results show that enhancing the static dielectric constant by doping rare earth elements enhanced the optical absorption performance of Mn₄Si₇. Tian et al.^[29] investigated the electronic, magnetic, and optical properties of phosphorene doping with rare earth metals (La, Ce, Nd). The results show that rare earth metals atom doping results in a blue shift of absorption peak, which enhances the absorption ability of optical intensity in visible and infrared regions. Therefore, doping rare earth affects the photoelectric properties of materials.

  There are few reports on the theoretical calculations of the optoelectronic properties of rare earth element doped 2D GaSe. The magnetic properties, electronic structure, and optical properties of 2D GaSe and those of 2D GaSe doped with rare earth elements Sc, Y, La, Ce, and Eu are investigated based on first-principles calculations.

  1.   Computational methods and models

  1.1   Computational methods

  The calculations were performed using the Vienna ab initio simulation package (VASP)^[30-32] software package based on the framework of density functional theory. The projector augmented wave (PAW)^[33-34] method was chosen for the calculations, and the Perdew-Burke-Ernzerhof (PBE)^[35] generalization under the generalized gradient approximation (GGA)^[36] was used to describe the exchange-correlation generalization of the system. Monkhorst-Pack^[37] schemed to generate a 5×5×1 K-point mesh, with the cut-off energy taken to be 500 eV, the force convergence accuracy set to 0.2 eV·nm^-1, and the energy convergence criterion to be set to 10^-5 eV. In the integration of the Brillouin zone, all calculations were carried out in reciprocal space. Since the GGA method and PBE function usually underestimate the bandgap value, the HSE06 hybrid functional was chosen to calculate the energy bands, so the calculated results of the energy bands were closer to the experimental values^[38].

  1.2   Theoretical models

  The monolayer GaSe has four atomic planes as shown in Fig. 1, the middle two layers of Ga atoms are wrapped by the top and bottom two layers of Se atoms, a Ga atom forms chemical bonds with three Se atoms, and one Ga atom, and a Se atom forms chemical bonds with three Ga atoms. A 3×3×1 GaSe monolayer supercell containing 36 atoms was constructed. The intrinsic 2D GaSe contains 18 Se atoms and 18 Ga atoms. For doping, a Ga atom was replaced by the rare earth elements X (X=Sc, Y, La, Ce, Eu). A 2 nm vacuum layer was used in the z-direction to avoid periodic boundary interaction. The valence electron configurations of the atoms involved in the work were Se (3d¹⁰4s²4p⁴), Ga (3d¹⁰4s²4p¹), Sc (3d¹4s²), Y (4d¹5s²), La (5d¹6s²), Ce (4f ¹5d¹6s²) and Eu (4f ⁷6s²).

  Figure 1

  

  Figure 1.  Structure of rare earth element X (X=Sc, Y, La, Ce, Eu) doped 2D GaSe: (a) top view, (b) side view

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  2.   Results and discussion

  2.1   Geometric optimization results

  Table 1 lists the lattice constants, bond lengths, and formation energies of the optimized 2D GaSe doped with Sc, Y, La, Ce, and Eu, where X represents the doped elements. The lattice constants of optimized 2D GaSe are a=b=0.375 6 nm, the bond lengths of Ga—Se are 0.249 7 nm, and the bond lengths of Ga—Ga are 0.247 0 nm, which is the same as that of the calculations of Ke et al.^[39-40], indicating that the calculation model is reasonable, and doping does not cause lattice distortion. With the doping of Sc, Y, La, Ce, and Eu atoms, the bond lengths of the 2D GaSe change, and from the analysis of the atomic radii, there is a difference in the radii of the doped atom X and the replaced Ga atom (0.122 nm for Ga, 0.161 nm for Sc, 0.181 nm for Y, 0.188 nm for La, 0.183 nm for Ce and 0.204 nm for Eu), thus the larger the atomic radius, the longer the bond lengths.

  Table 1

  

  Table 1.  Optimized lattice constants a, b, bond lengths d_X—Se, d_X—Ga, formation energy E_form of 2D GaSe before and after doping

  下载: 导出CSV

  System	a=b / nm	dX—Se / nm	dX—Ga / nm	Eform / eV
  GaSe	0.375 6	—	—	—
  Sc-GaSe	0.375 6	0.256 6	0.279 0	-2.349
  Y-GaSe	0.375 6	0.270 0	0.292 1	-2.436
  La-GaSe	0.375 6	0.282 6	0.305 23	-2.349
  Ce-GaSe	0.375 6	0.279 3	0.301 7	-2.114
  Eu-GaSe	0.375 6	0.284 1	0.306 9	-1.923

  The formation energy E_form represents the degree of atomic doping difficulty and the stability of the doping system, the lower the formation energy, the better the structural stability. To further observe the stability of the doped 2D GaSe, the formation energy is calculated, and the formation energy of the doped 2D GaSe is defined as follows^[41]:

  E_form = E_total - E_GaSe + μ_Ga - μ_x

  where E_total is the total energy of the doped 2D GaSe; E_GaSe is the total energy of intrinsic 2D GaSe; μ_Ga and μ_X represent the chemical potentials of the replaced atom Ga, and doped atoms, respectively, with the value of the average atomic energy of the corresponding bulk structure after full relaxation. The formation energies of the five doped 2D GaSe are shown in Table 1, and the formation energies are all negative, indicating that the doped 2D GaSe is structurally stable and theoretically easy to prepare.

  2.2   Magnetic properties and electronic structure

  2.2.1   Magnetic properties

  Table 2 lists the total magnetic moments M_tot of the intrinsic 2D GaSe and X-doped 2D GaSe, the local magnetic moments M_Ga of the Ga atoms, the local magnetic moments M_Se of the Se atoms, and the local magnetic moments M_X of the X atoms. From Table 2, the intrinsic 2D GaSe has no magnetism and is a nonmagnetic semiconductor. In the doped 2D GaSe, the Sc-, Y-, and La-doped 2D GaSe have no magnetism. The total magnetic moment of Ce-doped 2D GaSe is 0.908μ_B, the total magnetic moment of Ce-doped 2D GaSe is mainly contributed by Ce atoms, and the local magnetic moment of Ce atoms is 0.927μ_B. The total magnetic moment of the Eu-doped 2D GaSe is 7.163μ_B, the total magnetic moment of Eu-doped 2D GaSe is mainly contributed by Eu atoms, and the local magnetic moment of the Eu atoms is 6.818μ_B.

  Table 2

  

  Table 2.  M_tot, M_Ga, M_Se, and M_X of 2D GaSe before and after doping

  下载: 导出CSV

  System	Mtot / μB	MGa / μB	MSe / μB	MX / μB
  GaSe	0	0	0	0
  Sc-GaSe	0	0	0	0
  Y-GaSe	0	0	0	0
  La-GaSe	0	0	0	0
  Ce-GaSe	0.908	0.010	-0.026	0.927
  Eu-GaSe	7.163	0.179	0.165	6.818

  2.2.2   Electronic structure

  The energy band structure of doped 2D GaSe is shown in Fig. 2, the calculation was carried out under the consideration of spin polarization conditions, so the energy bands of the doped 2D GaSe are divided into two parts, spin-up and spin-down.

  Figure 2

  

  Figure 2.  Band structures of (a) intrinsic 2D GaSe, (b) Sc-, (c) Y-, (d) La-, (e) Ce-, and (f) Eu-doped 2D GaSe

  The blue lines represent the spin-up band structure, and the red lines represent the spin-down band structure.

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  Fig. 2a shows the energy band of intrinsic 2D GaSe, the spin-up and spin-down energy bands of intrinsic 2D GaSe are completely symmetrical. The conduction band minimum (CBM) of intrinsic 2D GaSe is located between the G points and M points in the Brillouin zone, the valence band maximum (VBM) of intrinsic 2D GaSe is located at the K point, and the Fermi energy level of intrinsic 2D GaSe is closer to the VBM, which indicates that the intrinsic 2D GaSe is a p-type semiconductor with indirect bandgap. The bandgap value of intrinsic 2D GaSe is 2.661 1 eV, which is consistent with the calculation results of previous literature^[42-43].

  Fig. 2b-2d show the energy bands of Sc-, Y- and La-doped 2D GaSe, the spin-up and spin-down energy bands of the doped 2D GaSe are completely symmetric, and the bandgap values of the doped 2D GaSe are 2.688 6, 2.695 1, and 2.467 3 eV, respectively, which indicates that the doped 2D GaSe are nonmagnetic semiconductors. Fig. 2e and 2f show the energy bands of Ce-, Eu-doped 2D GaSe, the spin-up and spin-down energy bands of the doped 2D GaSe are asymmetric, indicating that Ce-, Eu-doped 2D GaSe are magnetic semiconductors. In addition, impurity levels appear in the spin-up and spin-down energy bands of Eu-doped 2D GaSe, which increases the probability of electron transition.

  To further investigate the microscopic properties of the materials, the total density of states (TDOS) and partial density of states (PDOS) of intrinsic 2D GaSe and Sc-, Y-, La-, Ce-, Eu-doped 2D GaSe were calculated, the selection range of energy is -5-5 eV. Fig. 3a shows the density of states (DOS) of intrinsic 2D GaSe, the valence band of intrinsic 2D GaSe is mainly contributed by Ga4p and Se4p orbitals, with Se4p orbitals contributing the most. The conduction bands of intrinsic 2D GaSe mainly contributed to Ga4s, Ga4p, and Se4p orbitals. The spin-up and spin-down state densities of intrinsic 2D GaSe are entirely symmetric, showing the characteristics of non-magnetic semiconductors that are consistent with the results of energy band analysis. Fig. 3b-3d shows the DOS of Sc-, Y- and La-doped 2D GaSe, doped atoms have a weak effect on the valence band of the doped 2D GaSe, which is mainly contributed by the Ga4p and Se4p orbitals. The conduction band of the doped 2D GaSe is involved in the contribution of Sc3d, Y4d, and La5d orbitals in addition to Ga4s, Ga4p, and Se4p orbitals contributions. The spin-up and spin-down DOS of the doped 2D GaSe are completely symmetric, showing the characteristics of non-magnetic semiconductors. Fig. 3e and 3f show the DOS of Ce-, Eu-doped 2D GaSe, spin splitting can be seen to occur in the spin-up and spin-down DOS of Ce-, Eu-doped 2D GaSe, which results in the formation of uncanceled spontaneous magnetic moments in Ce4f, Eu4f orbitals, and hence spontaneous magnetization, leading to a net magnetic moment of Ce-, Eu-doped 2D GaSe, and thus Ce-, Eu-doped 2D GaSe exhibits the properties of magnetic semiconductors. The TDOS of Ce-doped 2D GaSe is mainly contributed by Ga4s, Ga4p, Se4p, and Ce4f orbitals, and the TDOS of Eu-doped 2D GaSe contributed by Ga4s, Ga4p, Se4p and Eu4f orbitals. The Eu-doped 2D GaSe appears impurity energy levels at the valence band and the conduction band, where the impurity energy levels at the valence band are mainly contributed by the Eu4f orbitals, and those at the conduction band are primarily contributed by the Ga4p and Se4p orbitals.

  Figure 3

  

  Figure 3.  DOS of (a) intrinsic 2D GaSe, (b) Sc-, (c) Y-, (d) La-, (e) Ce-, (f) Eu-doped 2D GaSe

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  2.3   Optical properties

  To further investigate the optical properties of Sc-, Y-, Ce-, La- and Eu-doped 2D GaSe, the complex dielectric function, absorption coefficient, and reflection coefficient of 2D GaSe before and after doping were calculated, and the effects caused by different doping atoms on 2D GaSe were analyzed.

  Fig. 4a represents the real part ε₁(ω) of the complex dielectric function for the doped 2D GaSe. The larger the real part, the stronger the electron binding ability, indicating a higher degree of polarization of the material.

  Figure 4

  

  Figure 4.  Optical properties of 2D GaSe before and after doping: (a) ε₁(ω), (b) ε₂(ω)

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  The value of ε₁(ω) when there is no incident optical (zero photon energy) corresponds to the static dielectric constant. As shown in Fig. 4a, the static dielectric constant of intrinsic 2D GaSe is 4.514, and that of Sc-, Y-, La-, Ce-, Eu-doped 2D GaSe are 4.591, 4.624, 4.749, 4.850 and 8.686, respectively. Compared with intrinsic 2D GaSe, the static dielectric constants of the doped 2D GaSe are all improved, indicating the enhanced polarizability of the doped 2D GaSe and high utilization of light.

  Fig. 4b represents the imaginary part ε₂(ω) of the complex dielectric function for the doped 2D GaSe. The larger the imaginary part, the greater the number of electrons in the excited state and the greater the chance of generating energy level transition. The intrinsic 2D GaSe of ε₂(ω) shows a strong peak at 4.271 eV, the peaks of ε₂(ω) of the Sc-, Y-, La-, Ce-doped 2D GaSe are at 4.311, 4.326, 4.304, 4.306 eV, respectively, and the Eu-doped 2D GaSe shows three peaks at 0.592, 2.369 and 4.023 eV, respectively. Among them, the ε₂(ω) of Eu-doped 2D GaSe is red-shifted. The ε₂(ω) of the Eu-doped 2D GaSe has the largest peak, according to the analysis of the energy band and state density, it can be seen that the strong peak is attributed to impurity energy level caused by the 4f orbital of Eu, and the number of electrons that can transition near the Fermi level is more than that of other doped 2D GaSe, resulting in a greater probability of transition in the Eu-doped 2D GaSe.

  Fig. 5a shows the optical absorption coefficients of the doped 2D GaSe, the absorption spectrum of the doped 2D GaSe shifts towards the low-energy, and the red-shift phenomenon occurs, which extends the absorption spectral range. The optical absorption coefficients of the doped 2D GaSe are larger than that of intrinsic 2D GaSe in the low energy region. Among them, the red shift is the most obvious for Eu-doped 2D GaSe, and the absorption coefficient of Eu-doped 2D GaSe shows a peak at 2.394 and 4.147 eV.

  Figure 5

  

  Figure 5.  Optical properties of 2D GaSe before and after doping: (a) absorption coefficient, (b) reflection coefficient

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  Fig. 5b shows the optical reflection coefficients of the doped 2D GaSe. At the energy of 0 eV, the reflection coefficient of intrinsic 2D GaSe is 0.129, and the reflection coefficients of Sc-, Y-, La-, Ce- and Eu-doped 2D GaSe are 0.132, 0.133, 0.137, 0.141 and 0.243, respectively. Compared with the intrinsic 2D GaSe, the static optical reflection coefficient of the doped 2D GaSe is improved, and Eu-doped 2D GaSe is the most obvious.

  3.   Conclusions

  The magnetic, electronic structure and optical properties of intrinsic 2D GaSe and rare earth element X (X=Sc, Y, La, Ce, Eu) doped 2D GaSe have been calculated and investigated by using the first-principles plane wave method based on density functional theory.

  Intrinsic 2D GaSe is a p-type nonmagnetic semiconductor with an indirect band gap of 2.661 1 eV, with the valence band near the Fermi energy level mainly contributed by Ga4p and Se4p orbitals and the conduction band mainly contributed by Ga4s, Ga4p and Se4p orbitals. The stability of the structure was analyzed utilizing the formation energies, and the formation energies of the Sc-, Y-, La-, Ce- and Eu-doped 2D GaSe are -2.349, -2.436, -2.349, -2.114 and -1.923 eV, respectively. The formation energies of the doped 2D GaSe are all negative, indicating that the doped 2D GaSe has good structural stability. The Sc-, Y-, and La-doped 2D GaSe are non-magnetic semiconductors; the Ce- and Eu-doped 2D GaSe transforms into a magnetic semiconductor with magnetic moments of 0.908μ_B and 7.163μ_B. Compared with the intrinsic 2D GaSe, the static dielectric constant of the doped 2D GaSe increases, and the polarization ability is enhanced. The absorption spectrum of the doped 2D GaSe shifts in the low-energy direction, and the red-shift phenomenon occurs, which extends the absorption spectral range. The optical reflection coefficient of the doped 2D GaSe is improved in the low energy region, and the improvement of Eu-doped 2D GaSe is the most obvious.

  
  
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  Figure 1  Structure of rare earth element X (X=Sc, Y, La, Ce, Eu) doped 2D GaSe: (a) top view, (b) side view

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  Figure 2  Band structures of (a) intrinsic 2D GaSe, (b) Sc-, (c) Y-, (d) La-, (e) Ce-, and (f) Eu-doped 2D GaSe

  The blue lines represent the spin-up band structure, and the red lines represent the spin-down band structure.

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  Figure 3  DOS of (a) intrinsic 2D GaSe, (b) Sc-, (c) Y-, (d) La-, (e) Ce-, (f) Eu-doped 2D GaSe

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  Figure 4  Optical properties of 2D GaSe before and after doping: (a) ε₁(ω), (b) ε₂(ω)

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  Figure 5  Optical properties of 2D GaSe before and after doping: (a) absorption coefficient, (b) reflection coefficient

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  Table 1.  Optimized lattice constants a, b, bond lengths d_X—Se, d_X—Ga, formation energy E_form of 2D GaSe before and after doping

  System	a=b / nm	dX—Se / nm	dX—Ga / nm	Eform / eV
  GaSe	0.375 6	—	—	—
  Sc-GaSe	0.375 6	0.256 6	0.279 0	-2.349
  Y-GaSe	0.375 6	0.270 0	0.292 1	-2.436
  La-GaSe	0.375 6	0.282 6	0.305 23	-2.349
  Ce-GaSe	0.375 6	0.279 3	0.301 7	-2.114
  Eu-GaSe	0.375 6	0.284 1	0.306 9	-1.923

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  Table 2.  M_tot, M_Ga, M_Se, and M_X of 2D GaSe before and after doping

  System	Mtot / μB	MGa / μB	MSe / μB	MX / μB
  GaSe	0	0	0	0
  Sc-GaSe	0	0	0	0
  Y-GaSe	0	0	0	0
  La-GaSe	0	0	0	0
  Ce-GaSe	0.908	0.010	-0.026	0.927
  Eu-GaSe	7.163	0.179	0.165	6.818

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