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Impact of vacancy defects on optoelectronic and magnetic properties of Mn-doped ZnSe
Computational Materials Science 174 (2020) 109493
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Impact of vacancy defects on optoelectronic and magnetic properties of Mndoped ZnSe ⁎
T
⁎
Muhammad Sheraz Khan, Lijie Shi , Bingsuo Zou
Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems and School of Physics, Beijing Institute of Technology, Beijing 100081, China
A R T I C LE I N FO
A B S T R A C T
Keywords: First principle calculation Spintronic Electronic properties Magnetism Optical absorption
Based on first principles calculations, we have investigated the electronic, magnetic and optical properties of Mndoped ZnSe with and without vacancy defects. We find that the incorporation of Mn at Zn site changes the nonmagnetic ground state of ZnSe to magnetic ground state with total magnetic moment 5 μB . From the investigation of magnetic coupling, it is found that the interaction between Mn spins in Mn-doped ZnSe is AFM which can be explained in term of super-exchange mechanism. The effect of vacancy defects such as Zn or Se vacancy on magnetic coupling between Mn spins were also analyzed and we found that Zn-vacancy promotes double exchange interaction which stabilizes the ferromagnetic state and room temperature ferromagnetism is expected while Se-vacancy doesn’t change magnetic ground state from AFM to FM states. The magnetic interactions in Mn-doped ZnSe system with and without Zn vacancy were explained using phenomenological band structure model. Moreover, optical absorptions for all systems were investigated at their stable magnetic states and we found that Mn doping causes the red shifted in absorption edge which is due to the spin forbidden d-d transitions (4T1-6A1) in Mn ions. The new peak in low energy range is related to the acceptor states introduced by Zn-vacancy in Mn-doped ZnSe system. The Se-vacancy generates peaks in visible region which is attributed to the donor states caused by Se-vacancy. Finally, the d-d transition (4T1-6A1) in FM and AFM coupled Mn ions were also studied and we found that the d-d transition peaks in AFM and FM coupled Mn ions are blue and red shifted respectively. Similarly, the blue and red shift in the energy bandgap of ZnSe are also observed in AFM and FM coupled Mn ions which support the agreement between the experimental and theoretical observations.
1. Introduction Dilute magnetic semiconductors (DMS), an alloy of magnetic impurities and semiconductors, has received much attraction in the area of material science and condensed matter physics due to potential application in the spintronic devices which employ a spin degree of freedom along with a charge of electrons to perform their multifunction. In a DMS, a fraction of magnetic ions is substituted at the cation site of the host II-VI or III-V semiconductors. The transition metals such as Cr, Mn, Fe, Co, etc have unpaired electrons in their dstates. These unpaired electrons, in term of their spin, are responsible to induce magnetic behavior in the systems. In DMS, the localized spin moments associated with transition metals couple with delocalize conduction band electrons and valence band holes. Generally, when transition metals are incorporated in the semiconductor, the resultant electronic structure is influenced by hybridization between d-state of transition metals and p-state of the anion of host semiconductor. This hybridization is responsible to exhibit magnetic behavior in the DMSs
⁎
[1,2]. For the practical application in spintronic, the DMSs must exhibit ferromagnetism at or above the room temperature. After the theoretical prediction of room temperature in p-type of Mn doped ZnO and GaN [3], it becomes a challenge for researchers to search DMSs with Curie temperature higher than room temperature (RT). Investigation of DMS plays an important role in the prospective applications of spintronic and spin-polarized magnetic-optic devices, and before that, it is essential to understand the origin of ferromagnetism in the DMS system. A number of DMSs with room temperature have been reported by magnetic ions doping such as Cr doped ZnTe [4], Cr doped ZnO and GaN [5], Mndoped GaN [6,7], Mn-doped ZnS [8] Co-doped ZnO [9], Ni-doped ZnS [10] and Mn-doped ZnO [11]. The origin of RT ferromagnetism in these materials are due to various phenomena such as structure defects, p-d, s,p-d and d-d coupling etc [12,13]. Among II-VI semiconductors, ZnSe is an important semiconductor with bulk wide bandgap of 2.7 eV and is an excellent material for the applications of lasers, light emitting diodes, solar cells and optoelectronic devices [14,15]. The optical properties such as absorption and
Corresponding authors. E-mail addresses: [email protected] (L. Shi), [email protected] (B. Zou).
https://doi.org/10.1016/j.commatsci.2019.109493 Received 15 October 2019; Received in revised form 12 December 2019; Accepted 16 December 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
Computational Materials Science 174 (2020) 109493
M.S. Khan, et al.
emission frequencies of II-VI semiconductors can be tuned by doping magnetic ions such as transition metal [16,17]. If the bandgap energy of the host semiconductor is greater than the excitation energy of dopant, then the photoluminescence of the doped system is determined by the dopant atoms. A large number of experimental and theoretical reports are present on magnetic and optical properties of transition metals doped ZnSe [18–22]. Among TMs doped ZnSe DMSs, Mn-doped ZnSe has gained much attraction in the application of spintronic and optoelectronic. Recently, Hou et al. [23] found the emission band at 585 nm which correspond to d-d transition of single Mn ion in ZnSe. Kamran et al. [24] studied the emission bands of FM and AFM Mn coupled ions in ZnS crystal and revealed that redshift and blue shift occur for FM and AFM coupled Mn-ions respectively. The ground state of Mn-doped ZnSe is antiferromagnetic under the superexchange mechanism [25]. In order to change the magnetic ground state of Mndoped ZnSe from antiferromagnetic to ferromagnetic, p-type co-doping such as N, C or Li at Zn site or Zn vacancy need to be introduced to make the Fermi level fall within the impurity levels in the bandgap [26]. The ferromagnetic behavior in Mn-doped ZnSe after p-type codoping or Zn vacancy is based on Zener’s double exchange mechanism [27]. Mn-doped II-VI based DMSs have widely investigated during the last few years, specially their semiconducting and magnetic properties. However, there exist controversies for the magnetism of Mn-doped II-VI semiconductor. For examples, paramagnetic behavior in CdS:Mn/ZnS core-shell nanoparticles was found by Yoshihiko Kanemitsu group [28]. In some literatures, ferromagnetic behaviors were reported [29–31], while in other literatures, antiferromagnetic behaviors were reported [32–34]. To avoid these controversies, several groups have found that vacancies play an important role in the stabilization of ferromagnetism in Mn-doped II-VI semiconductors. Therefore, these studies motivate us to investigate the effect of vacancies on magnetic and optical properties of Mn-doped ZnSe.
Table 1 Lattice constants (a), binding energy of Zn-3d state εd (eV), and bandgap Eg (eV) of pure ZnSe. Compound
ZnSe
Method
A(Å)
εd (eV)
Eg (eV)
Ref
GGA GGA + Ud (Ud = 8 eV) GGA + Ud + Up (Ud = 8.8 eV, Up = −18.8 eV) Expert
5.72 5.64 5.59
−6.41 −9.32 −9.374
1.14 1.71 2.70
This work This work This work
5.667
−9.37 eV
2.70
[23,39]
investigation of magnetic coupling between Mn spins, two Zn atoms are replaced by two Mn atoms, leading to 6.25% Mn concentrations. 2. Result and discussion 2.1. Optimized U parameters and electronic structure of pure ZnSe By optimizing the total energy of the crystal, the equilibrium lattice parameters for cubic ZnSe have been calculated using GGA method, and the results are listed in Table 1 with the experimental values. The GGA approximation overestimates the lattice constants relative to experimental values. Our calculated equilibrium structural parameters are in good agreement with experimental values within deviations of 5% in the lattice constants. A little difference in the lattice constants among experimental data is attributed to a different modification condition and characterization technique. First, the energy band structure and density of states (DOS) spectra (shown in Fig. 1) are calculated based on the optimized lattice parameters of ZnSe and found that minimum direct band gap was about 1.14 eV at Г point for GGA-PBE, which is significantly smaller than the experimental values (2.70 eV). The underestimation of the bandgap is due to well-known limitations in DFT. Especially, these results do not show the correct location of the Zn-3d states. It is found experimentally that the position of Zn-3d state is at −9.371 eV below the Fermi level [39]. The valence band (VB) has two separated energy regions below the Fermi level as shown in Fig. 1. The First energy region with width 4.1 eV mainly contributed by p-states of Se while the second energy region with width 1.2 eV is mainly contributed by d-state of Zn. The bottom of the conduction band is dominated by the Zn-4 s state. In GGA calculation, the high binding energy (−6.2 eV) of Zn-3d states overestimate the p-d hybridization, and as a result, the bandgap decreases. We use GGA + U method to reproduce the experimental bandgap of ZnSe and describe the correct bind energy of d-state of Zn atom. The use of GGA + U method would reduce hybridization effect and would lower the binding energy of Zn-3d state [40]. To study the impact of U for Zn-3d states on bandgap energy, the binding energy of Zn-3d states, and lattice constants, we have done several calculations for different tested U values (ranging from 0 to 12 eV)., as shown in Fig. 2. Our results for the calculations without the inclusion of Up (Up = 0) show that binding energy of Zn-d state is lowered with Ud as shown in Fig. 2(a). We find that for U = 8.8 eV, the binding energy of Zn-d state is −9.42 eV which is close to the experimental value (−9.37 eV). In Fig. 2(b), we present the variation of bandgap values and lattice constants with U values. It is found that the bandgap values of ZnSe increase from 1.1 eV to 2.0 eV and lattice constant decreases with increasing Ud from 0 to 12 eV. as shown in Fig. 1a, however, the bandgap energy is still smaller than the experimental value (2.70 eV). For U = 8.8 eV, the calculated binding energy of Zn-d state is −9.42 eV and improved bandgap is 1.81 eV. The problem of binding energy of Znd is resolved but the bandgap is still smaller than the experimental value. The decrease in lattice constant is due to the fact that the binding energy of Zn-3d state decreases with U. When Ud > 12 eV, then the self-consistent convergence cannot be completed at any accurate sets of
1.1. Computational methods The spin-polarized calculations reported here were performed by using density functional theory (DFT) using projector-augmented wave (PAW) potentials [35,36], executed in VASP package [35]. The Generalized Gradient Approximations (GGA) with Perdew–Burke–Ernzerhof (PBE) functional was employed to describe the exchange-correlation potential [37]. But GGA approximation gives underestimated band gap and don’t give the correct position of d or f states of transition metals or rare earth metals. Another approaches Hybrid functional [38] that include a fraction of Hartree–Fock exchange, and the quasi particle Green function formalism GW [39], shown a correction of electronic structure of semiconductor for some of severe limitations of the GGA and LDA approximations. However, these methods take much time to calculate electronic structure of large supercells containing large number of atoms. Therefore, the GGA + U method is a useful to solve the problem at reduced computational cost. This is the true for the highly correlated systems showing strong effective on-site Coulomb interactions (U) between localized elections. This method is used in the present. First we optimized the U parameters for Zn-d, and Se-p in order to reproduce the experimental bandgap of ZnSe. The energy change, kinetic energy cutoff and maximum force on each atom were set at 0.0001 eV, 500 eV, and 0.005 eVÅ−1 respectively in all the calculations. We used a Gamma-centered k-point mesh for sampling the Brillouin Zone (BZ) for structure relaxation, electronic and optical calculations. First we optimized the unit cell of ZnSe and then using optimized lattice constant of unit cell of ZnSe, we construct a supercell of 2 × 2 × 2 containing 64 atoms is used for investigation of the magnetic and optical properties in Mn-doped ZnSe with and without intrinsic defects. To study single Mn ion doped in ZnSe, we replace one Zn atom upon Mn atom which lead to 3.25% Mn concentration. For 2
Computational Materials Science 174 (2020) 109493
M.S. Khan, et al.
Fig. 1. The calculated band structure (a) and TDOS and PDOS (b) of ZnSe using GGA method.
2.2. Electronic and magnetic properties of Mn-doped ZnSe
our calculations based on DFT and binding energy of Zn-3d state is much lower (lower than 11 eV) than that of experimental value. However, in addition to the Ud values for the 3d state of Zn, if the Up value is included for 4p-state of Se atom, an accurate bandgap is obtained. In GGA + Ud + Up calculations, we performed several tests to find the suitable U parameters for Se-4p state to reproduce the corrected energy band gap and Zn-3d DOS peak in ZnSe. In these calculations we keep the lattice constant relaxed. Fig. 2(c) shows that the Zn3d state is gradually delocalized and bandgap increases with Up < 0 eV. The optimum value for Ud and Up are 8.8 eV and −18.8 eV. For these value of Up and Ud, we obtained correct bandgap and correct the position of Zn-3d states. But the lattice constants are smaller than that calculated with GGA and experimental value due to the fact that application of U produces the Zn-3d state more localized. This is in line with the observation that, in the case of pseudopotentials with the dorbitals in the core, the calculated lattice constants for (II-VI)-semiconductors are much smaller than the experimental value [41]. Therefore, it can be recommended that GGA + U with Up = −18.8 eV and Ud = 8.8 eV will be appropriate for first-principles calculations for the electronic structure of ZnSe. Recently, we used large negative U for p-state of S to improve bandgap of ZnS [40]. The calculated band structure and density of state using Up = −18.8 eV and Ud = 8.8 eV in the GGA + U method are shown in the Fig. 3. We can see that the calculated bandgap for pure ZnSe is 2.70 eV which is in good agreement with the experimental value. It is clearly seen from DOS that Zn-3d state is localized at 9.35 eV which is also good agreement with the experimental value (−9.371 eV). Additionally, we calculate spin polarized density of state (see Fig. 3(c)) and found that spin up and spin down channel are symmetric, indicating that pure ZnSe is a non-magnetic semiconductor.
Next, we study the properties of Mn-doped ZnSe system with GGA + U method. First, the Hubbard parameter for Mn-3d states is optimized. For this, we did several calculations and compared our results for UMn-d with experimental optical results. We found that U = 1.1 eV gives a better result when compared with experimental d-d transition peak of single Mn ion in ZnSe (580 nm or 2.13 eV) [23]. In the following calculations, we used Ud = 8.8 eV, Up = −18.8 eV and Ud = 1.1 eV for Zn, Se, and Mn atoms respectively to study magnetic and optical properties of Mn-doped ZnSe system. As we discussed above that pure ZnSe is a non-magnetic semiconductor with calculated band gap 2.70 eV. Now in order to induce magnetism in ZnSe, one Mn atom is substituted at Zn site in 2 × 2 × 2 ZnSe supercell, which leads to 3.25% Mn concentration. Then we calculated the energy difference between spin polarized and non-spin polarized states. it is found that the total energy for spin polarized state is lower than that for the nonspin polarized state. This depicts that Mn-doped ZnSe is favorable in spin polarized state. The Mn doping at the Zn site gives total magnetic moment 5 μB per supercell. The major contribution to the total magnetic moment comes from Mn dopant while little parts come from nonmagnetic sites Zn and Se atoms. The appearance of small magnetic moment at non-magnetic sites Se atoms are due to the interaction of band of the host semiconductor and d-state of Mn dopant. This point is confirmed from the spin density distribution of Mn-doped ZnSe as shown in Fig. 4(a). We can see that large spin density is localized at Mn dopant which means that Mn contribution to the total magnetization is large. We can also see that Mn polarizes its neighboring Se atoms in the same direction, indicating the ferromagnetic interaction between Mn3d and Se-4p states. Now to study the magnetic behavior of ZnSe doped
Fig. 2. The variation of binding energies of Zn-3d state as a function of Ud (a) the variation of lattice constants and bandgap values of cubic ZnSe as a function of Ud (b), and the variation of bandgap energies and binding energies as function of Up at fixed Ud (8.8 eV) (c), The dotted line show U parameter corresponding to experimental value of band gap and binding energy of Zn-3d state. The lattice constants are expressed in the unit of Å and bandgap and binding energy are expressed in the unit of eV. 3
Computational Materials Science 174 (2020) 109493
M.S. Khan, et al.
Fig. 3. The non-spin polarized Band structure (a), non-spin polarized TDOS and PDOS (b) and spin polarized TDOS (c) of Pure ZnSe. The Horizontal/vertical dashed lines indicate the Fermi level.
positive, then the stable ground state is FM. If the energy difference is negative, then the ground state is AFM. Here, in this study, we consider two configurations (near and far) based on Mn-Mn separation. In near configuration, the separation between Mn ions is 3.92 Å while in far configuration, the separation is 7.85 Å. One is near configuration and other is far configuration. The calculated energy difference for each configuration is listed in the Table 2. We found that the energy difference in both configurations are negative, indicating that AFM is favored for both configurations. The large value ΔE in near configuration means that AFM interaction between Mn spin is strong. The total magnetic moment of supercell per Mn atom is 5 µB, signifying the magnetic semiconducting solution. The spin-polarized density of state for Mn-doped ZnSe with FM state in the near configuration is shown in Fig. 5(a). It gives as a reference point and will permit us for investigating the difference introduced by native defects such as Zn and Se-vacancies. We see that Mn ions doping does not introduce carriers, therefore, the system does not show polarization at the Fermi level. Thus, in the absence of any defects, Mndoped ZnSe shows the behavior of semiconductor with spin-up channel completely filled and spin-down channel completely empty. Clearly, it is found that near the Fermi level, the Mn-3d orbitals show spin-polarization, and hybridize strongly with 4p-state of neighboring Se atoms, indicative of the sp-d hybridization typical dilute magnetic semiconductors. We can see that the unoccupied states of Mn 3d in spin down channel exist at 1.98 eV above the Fermi level, which is in line
with Mn from its electronic properties, the spin-polarized band structure of Mn-doped ZnSe were calculated along high symmetry directions of the first Brillouin zone (BZ) as shown in Fig. 4(b). It is found that the Fermi level exists in the energy bandgap of both spin channels, which indicates that Mn-doped ZnSe shows semiconductor nature. The band edges splitting indicates the magnetic behavior of the system. The valence band edge splitting is due to p-d hybridization while conduction band edge splitting is due to s-d hybridization. The states near the Fermi level in the valence band are the hybridized states which are the mixture of d-state of Mn and p-state of Se atoms. These hybridized states are the results of interaction of valence band of host semiconductor and Mn dopant. The bands at 2.13 eV above the Fermi level in the spin down channel are unoccupied d-states of Mn dopant. The state at 2.43 eV just above the spin down unoccupied d-state is the s-state of Zn atoms. The Zn-s state in the conduction band in spin up channel is at 2.32 eV. Thus, the energy splitting of s-state of Zn is about 0.11 eV which is due to the s-d hybridization. 2.3. Magnetic coupling Now in order to study the stability of the magnetic state in Mndoped ZnSe, we calculate total energy for parallel spin orders (FM) and antiparallel spin orders (AFM). The energy difference between AFM and FM states is a measure of magnetic exchange coupling. The sign of ΔE indicates the stable magnetic ground state. If the energy difference is
Fig. 4. The spin density distribution (a) and spin polarized band structure of single Mn ion in ZnSe (b). The horizontal dotted line indicates the Fermi level. 4
Computational Materials Science 174 (2020) 109493
M.S. Khan, et al.
between FM and AFM state is given by the following equation [43].
Table 2 The calculated the energy difference between AFM and FM state for Near and Far configurations with and without vacancy defects. All energy units are represented in meV. Alloys
ΔE(Near)
ΔE(Far)
Zn30Mn2Se32 Zn30Mn2Se32+VZn Zn30Mn2Se32+VSe
−89 108 −71.2
−13 66 −11.59
EFM − EAFM = −mh Δ1dd + (6 − mh)Δ1,2 dd
Where between the spin up and spin down d states and the coupling between the two spin up d states and two spin down d states are represented by Δ1dd and Δ2dd respectively. mh in the above equation shows the number of holes. The first term Δ1dd indicates the double exchange and second term Δ1,2 dd indicates the super-exchange mechanisms. If the number of holes (mh ) in the system is zero (e.g. Mn-doped ZnSe), then according to the above equation, the first term vanish and only second term left, thus TM with occupied d-states such as Co, Mn etc interact antiferromagnetically. For mh > 0, then the system interact ferromagnetically. From Fig. 6(a), we can see that in FM state, there are three electrons in anti-bond state and three electrons in bond state i.e. mh = 0 therefore, there is no energy gain. However, when Mn ions are in antiferromagnetic order, the spin up t2g states (with three electrons) of Mn1 interact with spin up t2g states (with zero electrons) of Mn2, therefore the energy gain is 3Δ1,2 dd . Similarly, spin down t2g state (with three electrons) of Mn1 interact with the spin down t2g (with zero electron) of Mn2, the energy gain is 1,2 3Δ1,2 dd . For the whole system, the total energy gain is 6Δdd . During AFM interaction between Mn spins, the hoping of electrons from one Mn to another Mn atom is impossible, indicating super-exchange mechanism (SE). We, therefore, concluded that Mn-doped ZnSe without vacancy defects show antiferromagnetic behavior via SE mechanism. Experimentally, the antiferromagnetic ground state of ZnSe:Mn is reported in Ref. [32]. The above calculations were performed when there are no additive defects such as Zn vacancy defect or Se vacancy defect other than Mn doping. To study the vacancy defects in Mn doped ZnSe system, we insert Zn and Se vacancies in Zn30Mn2Se32 system by removing one Zn atom and one Se atom. Two possible positions for vacancy are considered: one with the Se vacancy (VSe ) between the Mn dopants (near configuration) and other with the Se vacancy far away Mn dopants (far configuration) Similarly, two positions for Zn vacancy are chosen: one with the Zn vacancy near the Mn dopants (near configuration) and other Zn vacancy (VZn ) far away Mn dopants (far configuration). We have calculated the energy difference between FM and AFM states in the presence of Zn and Se vacancies. The calculated results are shown in the Table-2. We can see that Mn ions interact ferromagnetically under double exchange mechanism in the presence of Zn vacancy while interacting antiferromagnetically under the effect of super-exchange in the presence of Se vacancy. In Fig. 7(b), we present the total density of the state of Zn30Mn2Se32 with Se-vacancy (VSe ) in AFM configuration. It is found that material still shows magnetic semiconducting in the
DOS (states/eV)
with the experimental results d-d transition in FM coupled Mn paired in ZnSe nanobelts NB insert Ref. [23]. Thus, the d-d transition occurs between spin-down Mn-d states and p-d hybridized states of Mn-d and S-p states. According to the optical selection rule, the d-d transitions of Mn ion in the ZnSe lattice are spin forbidden. However, the p-d hybridization breaks the optical selection rule and makes the spin-forbidden d-d transition possible. During this process, spin-orbit coupling (SOC) plays a relative minor role in the d-d transitions of Mn ions in ZnSe crystal [23,42]. In Fig. 5(b), the spin-polarized DOS of Mn; ZnSe for AFM configuration is shown. It can be seen that the Fermi level is in vanishing state regions. The states below and above the Fermi level are mainly composed of Mn-d states which indicates that Mn; ZnSe in AFM configuration show magnetic insulating behavior. Magnetically the upspin and down-spin channel of Mn-d and Se-p are all degenerate with zero exchange splitting which suggest that antiferromagnetic exchange interaction exist between Mn ions in ZnSe which is due to super-exchange mechanism via connecting Se atoms in this system. The unoccupied states of Mn ions in spin up and spin down channels are located at 2.25 eV. Therefore, during AFM coupling, the d-d transition energy (2.25 eV) of Mn ions during absorption is higher in energy as compared to the d-d transition energy (1.98 eV) during FM coupling. As there are no impurity states around the Fermi level, therefore, the system without any other defects should be AFM, which agree with the model proposed by Dalpian et al. [43]. In FM configuration, the spin up electrons interact with spin down electrons therefore, during the ferromagnetic interaction, the electrons flip from spin up to spin down channel. In AFM configuration, the spin up occupied state of one Mn ion interact with spin up of unoccupied state of another Mn ion. The antiferromagnetic behavior in pure Mn-doped ZnSe can be explained using phenomenological band structure model suggested by Gustavo et al. [43,44]. This model is based on the repulsions between the host semiconductor band and d-states of transition metal. Fig. 6 illustrates the schematic model of band coupling and level repulsion of Mn-3d states in FM and AFM configurations. The energy difference
40 (a) 20 0 -20 -40
TDOS
60 40 20 0 -20 -40 -60
Se-p
0.4
0.4 0.0
0.0
-0.4
-0.4
1.5 0.0
0.0
-1.5
-1.5
-4
-2
0
2
Energy(eV)
4
(b)
TDOS
Se-p
1.5
Mn-d
-6
(1)
Δ1,2 dd is the coupling Δ1dd and Δ2dd indicate
6
Mn-d
-6
-4
-2
0
2
Energy(eV)
4
6
Fig. 5. The TDOS and PDOS of Mn-3d and Se-4p states for (a) FM (b) AFM configurations in Mn-doped ZnSe. The Fermi level is shown by vertical dotted line. 5
Computational Materials Science 174 (2020) 109493
M.S. Khan, et al.
Fig. 6. Schematic band coupling Models and level of repulsions of Mn-3d states in FM and AFM configurations of (a) pure Mn;ZnSe and (b) Mn; ZnSe with Znvacancy.
super-exchange mechanism dominate over the double exchange mechanism and therefore, the system is antiferromagnetically stable [45]. Thus the electrons from Se-vacancy do not change the magnetic ground state from antiferromagnetic state to ferromagnetic state. Next, we also calculated the density of state of double Mn-doped ZnSe with Zn vacancy as shown in Fig. 7(a). From the TDOS, it is clearly seen that impurity states are available around the Fermi level, indicating the half-metallicity of the material. From PDOS, we see that spin up dz2 and dx2 states of Mn are occupied so it is located below the Fermi level while spin up dxy, dyz, and dxz states are partially occupied so these are located around the Fermi level. Thus holes produced by Zn vacancy affect the occupancy of 3d-state of Mn ions. Before Zn vacancy
presence of Se vacancy. From the PDOS of d-state of Mn, all spin up 3d states of one Mn ion (spin up-dxy, dyz, dxz, dz2 and dx2) and spin down 3d of another Mn ion (spin down-dxy, dyz, dxz, dz2 and dx2) are occupied and located below the Fermi level. While spin up of 3d-states (dxy, dyz, dxz, dz2 and dx2) of one Mn ion and spin down of 3d-states (dxy, dyz, dxz, dz2 and dx2) of another Mn ion are unoccupied and located above the Fermi Level. Thus, Se vacancy does not affect the occupancy of d-states of Mn ion. The calculated magnetic moment per Mn ion in the presence of Se vacancy is 4.18 which is approximately equal to the magnetic moment (4.16 μB ) for Mn ion without Se vacancy. This means that the two electrons produced by Se-vacancy do not fill the dstates of Mn ions. As there is no impurity states at the Fermi level, then
Fig. 7. The calculated TDOS Mn-doped ZnSe and PDOS of Mn-3d and Se-4p states with (a) Zn vacancy for FM state (b) Se vacancy for AFM state. The vertical dotted line shows the Fermi level. 6
Computational Materials Science 174 (2020) 109493
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doping, d-state of Mn is half filled and material shows magnetic insulating nature. When Zn vacancy is introduced, then two holes are generated. These holes are filled by the electrons from 3d-states Mn ions. Thus the number of electrons in d-state is decreased which, in turn, decrease the magnetic moment. The calculated magnetic moment of Mn ion with Zn vacancy is 3.66 μB which is smaller than magnetic moment of Mn without Zn vacancy. It is found that the Fermi energy shifts into valence band for Zn vacancy because Zn vacancy as acceptor provides two holes which promote double exchange interaction and stabilize the ferromagnetic state. From the band coupling model for Zn-vacancy in Mn-ZnSe, as shown in Fig. 6(b), we find that there are two holes exist in t2g states. Therefore, the energy gain to stabilize FM states is a 2Δ1dd according to the above equation (1). The energy gain is 4Δ1,2 dd for stabilizing the antiferromagnetic state. It implies that there is a competition between FM and AFM couplings and ground state depends over the relative strength between 2Δ1dd and 4Δ1,2 dd . Ferromagnetic ground state will be governed by the value of ΔE ' = −2Δ1dd + 4Δ1,2 dd . Actually, FM coupling dominates in this competition because of the level repulsion Δ1dd in spin up channel is much larger than Δ1,2 dd , which is consistent with our first principle calculations. Our Result proved the FM stability when Zn vacancy is injected in Mn;ZnSe.
seen clearly that the absorption edge in single Mn ion in ZnSe is at 2.13 eV as shown in the inset of Fig. 8(a) which is assigned to the d-d transition in Mn ion. This spin forbidden d-d transition is slightly allowed by SOC effect [42]. The d-d transition energy of single Mn ion doped ZnSe is in good agreement with the experimental result [25]. In Fig. 8(b), the results of double Mn ions doped in ZnSe with and without intrinsic vacancy defects are shown. The d-d transition in double Mn ions system (shown in the inset of Fig. 8(b)) occur at about 2.24 eV which is higher in energy as compared to single Mn ion doped system. This blue shift of d-d transition energy is due to the anti-ferromagnetic coupling between Mn ions in double Mn ion system. We can see sharp peaks in Mn-doped ZnSe with Zn vacancy doping in the infrared region as shown in Fig. 8(b), which are attributed to the acceptor states introduced by Zn vacancy. No such a peak is observed in the infrared region in pure Mn-doped ZnSe with and without Se vacancy because it is an insulator. After introducing Se vacancy in Mn-ZnSe, a peak is observed at near infrared region (1.68 eV) which is attributed to donor states introduced by Se vacancy. The appearance of the absorption peaks in the infrared region in Mn;ZnSe with Zn vacancy makes them applicable for energy harvesting devices. Finally, the d-d transitions during optical absorption in FM and AFM ordered systems were also investigated and the results are shown in Fig. 9. As we discussed above that d-d transition (4T1-6A1) in single Mn ion in ZnSe is 2.13 eV. During d-d transition in Mn ion, the spin of electron flipped from spin up to spin down channel in the lowest excited state. If two Mn ions in the lattice of ZnSe are in FM order, then the absorption edge is at 1.97 eV which is due to d-d transition in FM coupled Mn ions in ZnSe which is lower than optical d-d transition in single Mn ion in ZnSe (paramagnetic state). Our calculations show that in FM coupled Mn ions pair system, the energy range from 1.98 to 2.23 eV is due to electronic intra-band transition within d-states (d-d transition) of Mn ions. In AFM coupled Mn ions, d-d (4T1-6A1) transition is from 2.24 to 2.46 eV which is also in good agreement with the experimental report [23]. Thus, we concluded that the d-d transition during optical absorption is red and blue shifted for FM and AFM coupled Mn ions pair system respectively which support the agreement between theoretical and experimental observations [23,48,8]. Most of previous II-VI:Mn DMS structure contain AFM coupled dopants inside the host semiconductor lattice which widens the bandgap of host semiconductor, as obtained here (Eg = 2.77 eV see in Fig. 9). But if the Mn ions are doped in low concentration, there are some of them staying at ferromagnetic coupling. In such a situation the bandgap would have redshift due to the phonon coupling enhancement [49] to form excitonic-magnetic polaron EMP, which need to be discussed here theoretically. In Mn-doped ZnSe without any other p-type defects such as Zn vacancy, Mn spins couple antiferromagnetic and the separation between 4T1 and 4A1 increase because of repulsion of up-spin occupied state of one Mn ion and up-spin unoccupied state of another Mn ion which widen the bandgap energy of ZnSe semiconductor. Therefore, the bandgap of ZnSe increases with AFM coupled Mn ions (Eg = 2.77 eV).
2.4. Optical absorption The absorption coefficient is important parameter for designing optical device. The optical absorption spectrum is related to the probabilities of inter-band transition [46]. The VASP package can calculate the frequency-dependent real and imaginary part of the dielectric after the electronic ground state have been determined. The optical absorption coefficient can be obtained from the known imaginary ε (ω)2 and real ε (ω)1 parts of dielectric using the following relation 1
α (ω) = ω [2 ε (ω)12 + ε (ω)22 − 2ε1 (ω)] 2
(2)
The computed results of absorption coefficients for pure ZnSe and single Mn-doped ZnSe are shown in Fig. 8(a). The peaks in absorption spectra are generated because of the electronic transition between occupied and unoccupied states in the materials. For the pure ZnSe, the absorption edge around 2.70 eV correspond to the bandgap energy and is due to the band edge (BE) excitonic transition of ZnSe (transition between Se-4p state at the top of valence band and Zn-4 s state at bottom of conduction band). The peak at 5.77 eV comes from the electronic transition between deep lying Se-4p in VB and Zn-s states in bottom of CB. The transition between Se-s state and Zn-3d within the valence band produces the peak at 7.0 eV. The main peak around 9.1 eV corresponding to strong absorption occur in pure ZnS and may be due to the transition between Zn-3d state and Zn-4 s state. There is no absorption peak at low energy side (0 to 2.7) which shows that ZnSe crystal has no Zn/Se vacancies [47]. We can see that the intensity of the absorption spectra of pure ZnSe is slightly reduced after Mn-doping. It is
Fig. 8. The calculated Absorption coefficients for (a) Pure ZnSe and single Mn ion in ZnSe (b) double Mn ions doped in ZnSe with and without vacancy defects. The black, blue, red, pink and green colors indicate the results of pure ZnSe, single Mn ion doped, double Mn ions doped, double Mn ions doped with Se vacancy and double Mn ions with Zn vacancy defects.
7
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Acknowledgment This work was supported by the 973 Project of China (No.2014CB920903), National Natural Science Foundation of China (No. 11004009). References [1] J.K. Furdyna, J. Appl. Phys. 64 (1988). [2] R.D. Mcnorton, T.M. Schuler, J.M. Maclaren, R.A. Stern, Phys. Rev. B 78 (2008) 1. [3] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Science (80-.) 287 (2000) 1019. [4] H. Saito, V. Zayets, S. Yamagata, K. Ando, Phys. Rev. Lett. 90 (2003) 20. [5] C. Liu, F. Yun, H. Morkoc, J. Mater. Sci. Mater. Electron. 6 (2005) 555. [6] M.E. Overberg, C.R. Abernathy, S.J. Pearton, N.A. Theodoropoulou, K.T. McCarthy, A.F. Hebard, Appl. Phys. Lett. 79 (2001) 1312. [7] S. Sonoda, S. Shimizu, T. Sasaki, Y. Yamamoto, J. Cryst. Growth 239 (2002) 1358. [8] M.S. Khan, L. Shi, H. Ullah, X. Yang, B. Zou, J. Phys. Condens. Matter 31 (2019) 485706. [9] K. Ueda, H. Tabata, T. Kawai, Appl. Phys. Lett. 79 (2001) 988. [10] S. Kumar, C.L. Chen, C.L. Dong, Y.K. Ho, J.F. Lee, T.S. Chan, R. Thangavel, T.K. Chen, B.H. Mok, S.M. Rao, M.K. Wu, J. Alloy. Compd. J. 554 (2013) 357. [11] V.M. De Almeida, A. Mesquita, A.O. De Zevallos, N.C. Mamani, P.P. Neves, X. Gratens, V.A. Chitta, W.B. Ferraz, A.C. Doriguetto, A.C.S. Sabioni, H.B. De Carvalho, J. Alloys Compd. 655 (2015) 406. [12] R. Long, N.J. English, Phys. Rev. B 80 (2009) 1. [13] B. Poornaprakash, S. Sambasivam, D. Amaranatha Reddy, G. Murali, R.P. Vijayalakshmi, B.K. Reddy, Ceram. Int. 40 (2013) 2677. [14] C. Wen, Z. Zhu, W. Li, J. Zhang, L. Wu, B. Li, G. Zeng, W. Wang, J. Alloys Compd. 718 (2017) 197. [15] H. Zhang, Y. Fang, J. Alloys Compd. 781 (2019) 201. [16] X. Zhai, Y. Gong, W. Yang, H. Kang, X. Zhang, RSC Adv. 5 (2015) 63458. [17] Q. Mahmood, S.M. Alay-e-abbas, M. Hassan, N.A. Noor, J. Alloys Compd. 688 (2016) 899. [18] B.T. Huy, M.H. Seo, A.P. Kumar, H. Jeong, Y.I. Lee, J. Alloys Compd. 588 (2014) 127. [19] V. Wood, J.E. Halpert, M.J. Panzer, M.G. Bawendi, V. Bulović, Nano Lett. 9 (2009) 2367. [20] W. Benstaali, S. Bentata, A. Abbad, A. Belaidi, Mater. Sci. Semicond. Process. 16 (2013) 231. [21] S. Khatta, S.K. Tripathi, S. Prakash, J. Magn. Magn. Mater. 460 (2018) 354. [22] X. Ge, Y. Zhang, J. Magn. Magn. Mater. 321 (2008) 198. [23] L. Hou, W. Zhou, B. Zou, Y. Znang, J. Han, X. Yang, Z. Gong, J. Li, S. Xie, L.J. Shi, Nanotechnology 28 (2017) 105202. [24] M.A. Kamran, A. Majid, T. Alharbi, M.W. Iqbal, M.W. Amjad, G. Nabi, S. Zou, B. Zou, J. Mater. Chem. C 5 (2017) 8749. [25] T. Fukushima, H. Katayama-Yoshida, K. Sato, H. Fujii, E. Rabel, R. Zeller, P.H. Dederichs, W. Zhang, R. Mazzarello, Phys. Rev. B – Condens. Matter Mater. Phys. 90 (2014) 1. [26] K. Sato, L. Bergqvist, J. Kudrnovský, P.H. Dederichs, O. Eriksson, I. Turek, B. Sanyal, G. Bouzerar, H. Katayama-Yoshida, V.A. Dinh, T. Fukushima, H. Kizaki, R. Zeller, Rev. Mod. Phys. 82 (2010) 1633. [27] Y. Pan, Y. Zhu, D.N. Shi, X.Y. Wei, C.L. Ma, K.C. Zhang, J. Alloys Compd. 644 (2015) 341. [28] S. Taguchi, A. Ishizumi, T. Tayagaki, Y. Kanemitsu, Appl. Phys. Lett. 94 (2009) 20. [29] M. Ragam, G. Kalaiselvan, S. Arumugam, N. Sankar, K. Ramachandran, J. Alloys Compd. 541 (2012) 222. [30] P.V.B. Lakshmi, K.S. Raj, K. Ramachandran, Cryst. Res. Technol 158 (2009) 153. [31] K.W. Nielsen, J.B. Philipp, M. Opel, A. Erb, J. Simon, L. Alff, R. Gross, Superlattices Microstruct. 37 (2005) 327. [32] V.P. Sirkeli, D.D. Nedeoglo, N.D. Nedeoglo, I.V. Radevici, R.L. Sobolevskaia, K.D. Sushkevich, E. Lähderanta, A.V. Lashkul, R. Laiho, J.P. Biethan, O. Yilmazoglu, D. Pavlidis, H.L. Hartnagel, Phys. B Condens. Matter 407 (2012) 3802. [33] L.M. Sandratskii, P. Bruno, Phys. Rev. B 73 (2006) 1. [34] N. Tsujii, H. Kitazawa, G. Kido, N. Tsujii, H. Kitazawa, G. Kido, J. Appl. Phys. 6957 (2003) 1. [35] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [36] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953. [37] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [38] J. Heyd, G.E. Scuseria, M. Ernzerhof, J. Chem. Phys. 118 (2003) 8207. [39] A. Fleszar, W. Hanke, Phys. Rev. B 71 (2005) 1. [40] M.S. Khan, L. Shi, X.-T. Yang, S. Ali, H. Ullah, B. Zou, J. Phys. Condens. Matter 31 (2019) 395702. [41] S.H. Wei, A. Zunger, Phys. Rev. B 37 (1988) 15. [42] R. Beaulac, P.I. Archer, D.R. Gamelin, J. Solid State Chem. 181 (2008) 1582. [43] G.M. Dalpian, S. Wei, X.G. Gong, Solid State Commun. 138 (138) (2006) 353. [44] G. M. Dalpian, S. Wei, 2187, 2170 (2006). [45] K. Sato, P. H. Dederichs, K.-Y. H, and J. Kudrnovsk, J. Phys. Condens. MATTER 5491, (2004). [46] S.Z. Karazhanov, P. Ravindran, A. Kjekshus, H. Fjellvåg, B.G. Svensson, Phys. Rev. B 75 (2007) 1. [47] M.A. Kamran, Nanotechnology 29 (2018) 435702. [48] B.B. Liang, L.P. Hou, S.Y. Zou, L. Zhang, Y.C. Guo, Y.T. Liu, M.U. Farooq, L.J. Shi, R.B. Liu, B.S. Zou, RSC Adv. 8 (2018) 3133. [49] S. Zou, M.A. Kamran, L.J. Shi, R. Liu, S. Guo, A. Kavokin, B. Zou, ACS Photonics 3 (2016) 1809. [50] M.S. Khan, L. Shi, B. Zou, Mater. Res. Express 6 (2019) 116126.
Fig. 9. The absorption during d-d transitions for FM and AFM coupled Mn ions in ZnSe.
But the bandgap (2.63 eV) of ZnSe decreases with FM coupled Mn ions. These observations support experimental and theoretical reports [23,50,8]. 3. Conclusion In summary, we have investigated the effect of vacancy defects on optoelectronic and magnetic properties of Mn-doped ZnSe crystal using first principle method. It has been found that the experimental bandgap of ZnSe can be reproduced by employing positive U on Zn-d state and negative U on Se-p state in GGA + U method. The antiferromagnetic behavior in Mn-doped ZnSe can be explained on the basis of superexchange mechanism. It has been concluded that Zn-vacancy defect changes the ground state of Mn-doped ZnS from AFM to FM state and Se-vacancy defect has no effect on the ground state of Mn-doped ZnSe. The optical absorption edge of Mn-doped systems is due to the spin forbidden d-d transitions of Mn ions. The peak in low energy side is related to the acceptor states introduced by Zn-vacancy in Mn-doped ZnSe system. The absorption peaks in the near infra-red region are attributed to the donor states caused by Se-vacancy in the Mn-doped ZnSe. The red and blue shift of d-d transitions of Mn ions are observed in FM and AFM configurations, respectively, which supports the agreement between experimental and theoretical observations. Similarly, the red and blue shift of fundamental bandgap are also observed in FM and AFM configurations respectively. CRediT authorship contribution statement Muhammad Sheraz Khan: Data curation, Investigation, Visualization, Writing - original draft, Writing - review & editing. Lijie Shi: Conceptualization, Formal analysis, Validation, Writing - original draft. Bingsuo Zou: Conceptualization, Methodology, Project administration, Writing - review & editing. Chinese Government: Funding acquisition. Beijing Institute of Technology: Resources. Commercial VASP: Software. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 8
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Impact of vacancy defects on optoelectronic and magnetic properties of Mndoped ZnSe ⁎
T
⁎
Muhammad Sheraz Khan, Lijie Shi , Bingsuo Zou
Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems and School of Physics, Beijing Institute of Technology, Beijing 100081, China
A R T I C LE I N FO
A B S T R A C T
Keywords: First principle calculation Spintronic Electronic properties Magnetism Optical absorption
Based on first principles calculations, we have investigated the electronic, magnetic and optical properties of Mndoped ZnSe with and without vacancy defects. We find that the incorporation of Mn at Zn site changes the nonmagnetic ground state of ZnSe to magnetic ground state with total magnetic moment 5 μB . From the investigation of magnetic coupling, it is found that the interaction between Mn spins in Mn-doped ZnSe is AFM which can be explained in term of super-exchange mechanism. The effect of vacancy defects such as Zn or Se vacancy on magnetic coupling between Mn spins were also analyzed and we found that Zn-vacancy promotes double exchange interaction which stabilizes the ferromagnetic state and room temperature ferromagnetism is expected while Se-vacancy doesn’t change magnetic ground state from AFM to FM states. The magnetic interactions in Mn-doped ZnSe system with and without Zn vacancy were explained using phenomenological band structure model. Moreover, optical absorptions for all systems were investigated at their stable magnetic states and we found that Mn doping causes the red shifted in absorption edge which is due to the spin forbidden d-d transitions (4T1-6A1) in Mn ions. The new peak in low energy range is related to the acceptor states introduced by Zn-vacancy in Mn-doped ZnSe system. The Se-vacancy generates peaks in visible region which is attributed to the donor states caused by Se-vacancy. Finally, the d-d transition (4T1-6A1) in FM and AFM coupled Mn ions were also studied and we found that the d-d transition peaks in AFM and FM coupled Mn ions are blue and red shifted respectively. Similarly, the blue and red shift in the energy bandgap of ZnSe are also observed in AFM and FM coupled Mn ions which support the agreement between the experimental and theoretical observations.
1. Introduction Dilute magnetic semiconductors (DMS), an alloy of magnetic impurities and semiconductors, has received much attraction in the area of material science and condensed matter physics due to potential application in the spintronic devices which employ a spin degree of freedom along with a charge of electrons to perform their multifunction. In a DMS, a fraction of magnetic ions is substituted at the cation site of the host II-VI or III-V semiconductors. The transition metals such as Cr, Mn, Fe, Co, etc have unpaired electrons in their dstates. These unpaired electrons, in term of their spin, are responsible to induce magnetic behavior in the systems. In DMS, the localized spin moments associated with transition metals couple with delocalize conduction band electrons and valence band holes. Generally, when transition metals are incorporated in the semiconductor, the resultant electronic structure is influenced by hybridization between d-state of transition metals and p-state of the anion of host semiconductor. This hybridization is responsible to exhibit magnetic behavior in the DMSs
⁎
[1,2]. For the practical application in spintronic, the DMSs must exhibit ferromagnetism at or above the room temperature. After the theoretical prediction of room temperature in p-type of Mn doped ZnO and GaN [3], it becomes a challenge for researchers to search DMSs with Curie temperature higher than room temperature (RT). Investigation of DMS plays an important role in the prospective applications of spintronic and spin-polarized magnetic-optic devices, and before that, it is essential to understand the origin of ferromagnetism in the DMS system. A number of DMSs with room temperature have been reported by magnetic ions doping such as Cr doped ZnTe [4], Cr doped ZnO and GaN [5], Mndoped GaN [6,7], Mn-doped ZnS [8] Co-doped ZnO [9], Ni-doped ZnS [10] and Mn-doped ZnO [11]. The origin of RT ferromagnetism in these materials are due to various phenomena such as structure defects, p-d, s,p-d and d-d coupling etc [12,13]. Among II-VI semiconductors, ZnSe is an important semiconductor with bulk wide bandgap of 2.7 eV and is an excellent material for the applications of lasers, light emitting diodes, solar cells and optoelectronic devices [14,15]. The optical properties such as absorption and
Corresponding authors. E-mail addresses: [email protected] (L. Shi), [email protected] (B. Zou).
https://doi.org/10.1016/j.commatsci.2019.109493 Received 15 October 2019; Received in revised form 12 December 2019; Accepted 16 December 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
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emission frequencies of II-VI semiconductors can be tuned by doping magnetic ions such as transition metal [16,17]. If the bandgap energy of the host semiconductor is greater than the excitation energy of dopant, then the photoluminescence of the doped system is determined by the dopant atoms. A large number of experimental and theoretical reports are present on magnetic and optical properties of transition metals doped ZnSe [18–22]. Among TMs doped ZnSe DMSs, Mn-doped ZnSe has gained much attraction in the application of spintronic and optoelectronic. Recently, Hou et al. [23] found the emission band at 585 nm which correspond to d-d transition of single Mn ion in ZnSe. Kamran et al. [24] studied the emission bands of FM and AFM Mn coupled ions in ZnS crystal and revealed that redshift and blue shift occur for FM and AFM coupled Mn-ions respectively. The ground state of Mn-doped ZnSe is antiferromagnetic under the superexchange mechanism [25]. In order to change the magnetic ground state of Mndoped ZnSe from antiferromagnetic to ferromagnetic, p-type co-doping such as N, C or Li at Zn site or Zn vacancy need to be introduced to make the Fermi level fall within the impurity levels in the bandgap [26]. The ferromagnetic behavior in Mn-doped ZnSe after p-type codoping or Zn vacancy is based on Zener’s double exchange mechanism [27]. Mn-doped II-VI based DMSs have widely investigated during the last few years, specially their semiconducting and magnetic properties. However, there exist controversies for the magnetism of Mn-doped II-VI semiconductor. For examples, paramagnetic behavior in CdS:Mn/ZnS core-shell nanoparticles was found by Yoshihiko Kanemitsu group [28]. In some literatures, ferromagnetic behaviors were reported [29–31], while in other literatures, antiferromagnetic behaviors were reported [32–34]. To avoid these controversies, several groups have found that vacancies play an important role in the stabilization of ferromagnetism in Mn-doped II-VI semiconductors. Therefore, these studies motivate us to investigate the effect of vacancies on magnetic and optical properties of Mn-doped ZnSe.
Table 1 Lattice constants (a), binding energy of Zn-3d state εd (eV), and bandgap Eg (eV) of pure ZnSe. Compound
ZnSe
Method
A(Å)
εd (eV)
Eg (eV)
Ref
GGA GGA + Ud (Ud = 8 eV) GGA + Ud + Up (Ud = 8.8 eV, Up = −18.8 eV) Expert
5.72 5.64 5.59
−6.41 −9.32 −9.374
1.14 1.71 2.70
This work This work This work
5.667
−9.37 eV
2.70
[23,39]
investigation of magnetic coupling between Mn spins, two Zn atoms are replaced by two Mn atoms, leading to 6.25% Mn concentrations. 2. Result and discussion 2.1. Optimized U parameters and electronic structure of pure ZnSe By optimizing the total energy of the crystal, the equilibrium lattice parameters for cubic ZnSe have been calculated using GGA method, and the results are listed in Table 1 with the experimental values. The GGA approximation overestimates the lattice constants relative to experimental values. Our calculated equilibrium structural parameters are in good agreement with experimental values within deviations of 5% in the lattice constants. A little difference in the lattice constants among experimental data is attributed to a different modification condition and characterization technique. First, the energy band structure and density of states (DOS) spectra (shown in Fig. 1) are calculated based on the optimized lattice parameters of ZnSe and found that minimum direct band gap was about 1.14 eV at Г point for GGA-PBE, which is significantly smaller than the experimental values (2.70 eV). The underestimation of the bandgap is due to well-known limitations in DFT. Especially, these results do not show the correct location of the Zn-3d states. It is found experimentally that the position of Zn-3d state is at −9.371 eV below the Fermi level [39]. The valence band (VB) has two separated energy regions below the Fermi level as shown in Fig. 1. The First energy region with width 4.1 eV mainly contributed by p-states of Se while the second energy region with width 1.2 eV is mainly contributed by d-state of Zn. The bottom of the conduction band is dominated by the Zn-4 s state. In GGA calculation, the high binding energy (−6.2 eV) of Zn-3d states overestimate the p-d hybridization, and as a result, the bandgap decreases. We use GGA + U method to reproduce the experimental bandgap of ZnSe and describe the correct bind energy of d-state of Zn atom. The use of GGA + U method would reduce hybridization effect and would lower the binding energy of Zn-3d state [40]. To study the impact of U for Zn-3d states on bandgap energy, the binding energy of Zn-3d states, and lattice constants, we have done several calculations for different tested U values (ranging from 0 to 12 eV)., as shown in Fig. 2. Our results for the calculations without the inclusion of Up (Up = 0) show that binding energy of Zn-d state is lowered with Ud as shown in Fig. 2(a). We find that for U = 8.8 eV, the binding energy of Zn-d state is −9.42 eV which is close to the experimental value (−9.37 eV). In Fig. 2(b), we present the variation of bandgap values and lattice constants with U values. It is found that the bandgap values of ZnSe increase from 1.1 eV to 2.0 eV and lattice constant decreases with increasing Ud from 0 to 12 eV. as shown in Fig. 1a, however, the bandgap energy is still smaller than the experimental value (2.70 eV). For U = 8.8 eV, the calculated binding energy of Zn-d state is −9.42 eV and improved bandgap is 1.81 eV. The problem of binding energy of Znd is resolved but the bandgap is still smaller than the experimental value. The decrease in lattice constant is due to the fact that the binding energy of Zn-3d state decreases with U. When Ud > 12 eV, then the self-consistent convergence cannot be completed at any accurate sets of
1.1. Computational methods The spin-polarized calculations reported here were performed by using density functional theory (DFT) using projector-augmented wave (PAW) potentials [35,36], executed in VASP package [35]. The Generalized Gradient Approximations (GGA) with Perdew–Burke–Ernzerhof (PBE) functional was employed to describe the exchange-correlation potential [37]. But GGA approximation gives underestimated band gap and don’t give the correct position of d or f states of transition metals or rare earth metals. Another approaches Hybrid functional [38] that include a fraction of Hartree–Fock exchange, and the quasi particle Green function formalism GW [39], shown a correction of electronic structure of semiconductor for some of severe limitations of the GGA and LDA approximations. However, these methods take much time to calculate electronic structure of large supercells containing large number of atoms. Therefore, the GGA + U method is a useful to solve the problem at reduced computational cost. This is the true for the highly correlated systems showing strong effective on-site Coulomb interactions (U) between localized elections. This method is used in the present. First we optimized the U parameters for Zn-d, and Se-p in order to reproduce the experimental bandgap of ZnSe. The energy change, kinetic energy cutoff and maximum force on each atom were set at 0.0001 eV, 500 eV, and 0.005 eVÅ−1 respectively in all the calculations. We used a Gamma-centered k-point mesh for sampling the Brillouin Zone (BZ) for structure relaxation, electronic and optical calculations. First we optimized the unit cell of ZnSe and then using optimized lattice constant of unit cell of ZnSe, we construct a supercell of 2 × 2 × 2 containing 64 atoms is used for investigation of the magnetic and optical properties in Mn-doped ZnSe with and without intrinsic defects. To study single Mn ion doped in ZnSe, we replace one Zn atom upon Mn atom which lead to 3.25% Mn concentration. For 2
Computational Materials Science 174 (2020) 109493
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Fig. 1. The calculated band structure (a) and TDOS and PDOS (b) of ZnSe using GGA method.
2.2. Electronic and magnetic properties of Mn-doped ZnSe
our calculations based on DFT and binding energy of Zn-3d state is much lower (lower than 11 eV) than that of experimental value. However, in addition to the Ud values for the 3d state of Zn, if the Up value is included for 4p-state of Se atom, an accurate bandgap is obtained. In GGA + Ud + Up calculations, we performed several tests to find the suitable U parameters for Se-4p state to reproduce the corrected energy band gap and Zn-3d DOS peak in ZnSe. In these calculations we keep the lattice constant relaxed. Fig. 2(c) shows that the Zn3d state is gradually delocalized and bandgap increases with Up < 0 eV. The optimum value for Ud and Up are 8.8 eV and −18.8 eV. For these value of Up and Ud, we obtained correct bandgap and correct the position of Zn-3d states. But the lattice constants are smaller than that calculated with GGA and experimental value due to the fact that application of U produces the Zn-3d state more localized. This is in line with the observation that, in the case of pseudopotentials with the dorbitals in the core, the calculated lattice constants for (II-VI)-semiconductors are much smaller than the experimental value [41]. Therefore, it can be recommended that GGA + U with Up = −18.8 eV and Ud = 8.8 eV will be appropriate for first-principles calculations for the electronic structure of ZnSe. Recently, we used large negative U for p-state of S to improve bandgap of ZnS [40]. The calculated band structure and density of state using Up = −18.8 eV and Ud = 8.8 eV in the GGA + U method are shown in the Fig. 3. We can see that the calculated bandgap for pure ZnSe is 2.70 eV which is in good agreement with the experimental value. It is clearly seen from DOS that Zn-3d state is localized at 9.35 eV which is also good agreement with the experimental value (−9.371 eV). Additionally, we calculate spin polarized density of state (see Fig. 3(c)) and found that spin up and spin down channel are symmetric, indicating that pure ZnSe is a non-magnetic semiconductor.
Next, we study the properties of Mn-doped ZnSe system with GGA + U method. First, the Hubbard parameter for Mn-3d states is optimized. For this, we did several calculations and compared our results for UMn-d with experimental optical results. We found that U = 1.1 eV gives a better result when compared with experimental d-d transition peak of single Mn ion in ZnSe (580 nm or 2.13 eV) [23]. In the following calculations, we used Ud = 8.8 eV, Up = −18.8 eV and Ud = 1.1 eV for Zn, Se, and Mn atoms respectively to study magnetic and optical properties of Mn-doped ZnSe system. As we discussed above that pure ZnSe is a non-magnetic semiconductor with calculated band gap 2.70 eV. Now in order to induce magnetism in ZnSe, one Mn atom is substituted at Zn site in 2 × 2 × 2 ZnSe supercell, which leads to 3.25% Mn concentration. Then we calculated the energy difference between spin polarized and non-spin polarized states. it is found that the total energy for spin polarized state is lower than that for the nonspin polarized state. This depicts that Mn-doped ZnSe is favorable in spin polarized state. The Mn doping at the Zn site gives total magnetic moment 5 μB per supercell. The major contribution to the total magnetic moment comes from Mn dopant while little parts come from nonmagnetic sites Zn and Se atoms. The appearance of small magnetic moment at non-magnetic sites Se atoms are due to the interaction of band of the host semiconductor and d-state of Mn dopant. This point is confirmed from the spin density distribution of Mn-doped ZnSe as shown in Fig. 4(a). We can see that large spin density is localized at Mn dopant which means that Mn contribution to the total magnetization is large. We can also see that Mn polarizes its neighboring Se atoms in the same direction, indicating the ferromagnetic interaction between Mn3d and Se-4p states. Now to study the magnetic behavior of ZnSe doped
Fig. 2. The variation of binding energies of Zn-3d state as a function of Ud (a) the variation of lattice constants and bandgap values of cubic ZnSe as a function of Ud (b), and the variation of bandgap energies and binding energies as function of Up at fixed Ud (8.8 eV) (c), The dotted line show U parameter corresponding to experimental value of band gap and binding energy of Zn-3d state. The lattice constants are expressed in the unit of Å and bandgap and binding energy are expressed in the unit of eV. 3
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Fig. 3. The non-spin polarized Band structure (a), non-spin polarized TDOS and PDOS (b) and spin polarized TDOS (c) of Pure ZnSe. The Horizontal/vertical dashed lines indicate the Fermi level.
positive, then the stable ground state is FM. If the energy difference is negative, then the ground state is AFM. Here, in this study, we consider two configurations (near and far) based on Mn-Mn separation. In near configuration, the separation between Mn ions is 3.92 Å while in far configuration, the separation is 7.85 Å. One is near configuration and other is far configuration. The calculated energy difference for each configuration is listed in the Table 2. We found that the energy difference in both configurations are negative, indicating that AFM is favored for both configurations. The large value ΔE in near configuration means that AFM interaction between Mn spin is strong. The total magnetic moment of supercell per Mn atom is 5 µB, signifying the magnetic semiconducting solution. The spin-polarized density of state for Mn-doped ZnSe with FM state in the near configuration is shown in Fig. 5(a). It gives as a reference point and will permit us for investigating the difference introduced by native defects such as Zn and Se-vacancies. We see that Mn ions doping does not introduce carriers, therefore, the system does not show polarization at the Fermi level. Thus, in the absence of any defects, Mndoped ZnSe shows the behavior of semiconductor with spin-up channel completely filled and spin-down channel completely empty. Clearly, it is found that near the Fermi level, the Mn-3d orbitals show spin-polarization, and hybridize strongly with 4p-state of neighboring Se atoms, indicative of the sp-d hybridization typical dilute magnetic semiconductors. We can see that the unoccupied states of Mn 3d in spin down channel exist at 1.98 eV above the Fermi level, which is in line
with Mn from its electronic properties, the spin-polarized band structure of Mn-doped ZnSe were calculated along high symmetry directions of the first Brillouin zone (BZ) as shown in Fig. 4(b). It is found that the Fermi level exists in the energy bandgap of both spin channels, which indicates that Mn-doped ZnSe shows semiconductor nature. The band edges splitting indicates the magnetic behavior of the system. The valence band edge splitting is due to p-d hybridization while conduction band edge splitting is due to s-d hybridization. The states near the Fermi level in the valence band are the hybridized states which are the mixture of d-state of Mn and p-state of Se atoms. These hybridized states are the results of interaction of valence band of host semiconductor and Mn dopant. The bands at 2.13 eV above the Fermi level in the spin down channel are unoccupied d-states of Mn dopant. The state at 2.43 eV just above the spin down unoccupied d-state is the s-state of Zn atoms. The Zn-s state in the conduction band in spin up channel is at 2.32 eV. Thus, the energy splitting of s-state of Zn is about 0.11 eV which is due to the s-d hybridization. 2.3. Magnetic coupling Now in order to study the stability of the magnetic state in Mndoped ZnSe, we calculate total energy for parallel spin orders (FM) and antiparallel spin orders (AFM). The energy difference between AFM and FM states is a measure of magnetic exchange coupling. The sign of ΔE indicates the stable magnetic ground state. If the energy difference is
Fig. 4. The spin density distribution (a) and spin polarized band structure of single Mn ion in ZnSe (b). The horizontal dotted line indicates the Fermi level. 4
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between FM and AFM state is given by the following equation [43].
Table 2 The calculated the energy difference between AFM and FM state for Near and Far configurations with and without vacancy defects. All energy units are represented in meV. Alloys
ΔE(Near)
ΔE(Far)
Zn30Mn2Se32 Zn30Mn2Se32+VZn Zn30Mn2Se32+VSe
−89 108 −71.2
−13 66 −11.59
EFM − EAFM = −mh Δ1dd + (6 − mh)Δ1,2 dd
Where between the spin up and spin down d states and the coupling between the two spin up d states and two spin down d states are represented by Δ1dd and Δ2dd respectively. mh in the above equation shows the number of holes. The first term Δ1dd indicates the double exchange and second term Δ1,2 dd indicates the super-exchange mechanisms. If the number of holes (mh ) in the system is zero (e.g. Mn-doped ZnSe), then according to the above equation, the first term vanish and only second term left, thus TM with occupied d-states such as Co, Mn etc interact antiferromagnetically. For mh > 0, then the system interact ferromagnetically. From Fig. 6(a), we can see that in FM state, there are three electrons in anti-bond state and three electrons in bond state i.e. mh = 0 therefore, there is no energy gain. However, when Mn ions are in antiferromagnetic order, the spin up t2g states (with three electrons) of Mn1 interact with spin up t2g states (with zero electrons) of Mn2, therefore the energy gain is 3Δ1,2 dd . Similarly, spin down t2g state (with three electrons) of Mn1 interact with the spin down t2g (with zero electron) of Mn2, the energy gain is 1,2 3Δ1,2 dd . For the whole system, the total energy gain is 6Δdd . During AFM interaction between Mn spins, the hoping of electrons from one Mn to another Mn atom is impossible, indicating super-exchange mechanism (SE). We, therefore, concluded that Mn-doped ZnSe without vacancy defects show antiferromagnetic behavior via SE mechanism. Experimentally, the antiferromagnetic ground state of ZnSe:Mn is reported in Ref. [32]. The above calculations were performed when there are no additive defects such as Zn vacancy defect or Se vacancy defect other than Mn doping. To study the vacancy defects in Mn doped ZnSe system, we insert Zn and Se vacancies in Zn30Mn2Se32 system by removing one Zn atom and one Se atom. Two possible positions for vacancy are considered: one with the Se vacancy (VSe ) between the Mn dopants (near configuration) and other with the Se vacancy far away Mn dopants (far configuration) Similarly, two positions for Zn vacancy are chosen: one with the Zn vacancy near the Mn dopants (near configuration) and other Zn vacancy (VZn ) far away Mn dopants (far configuration). We have calculated the energy difference between FM and AFM states in the presence of Zn and Se vacancies. The calculated results are shown in the Table-2. We can see that Mn ions interact ferromagnetically under double exchange mechanism in the presence of Zn vacancy while interacting antiferromagnetically under the effect of super-exchange in the presence of Se vacancy. In Fig. 7(b), we present the total density of the state of Zn30Mn2Se32 with Se-vacancy (VSe ) in AFM configuration. It is found that material still shows magnetic semiconducting in the
DOS (states/eV)
with the experimental results d-d transition in FM coupled Mn paired in ZnSe nanobelts NB insert Ref. [23]. Thus, the d-d transition occurs between spin-down Mn-d states and p-d hybridized states of Mn-d and S-p states. According to the optical selection rule, the d-d transitions of Mn ion in the ZnSe lattice are spin forbidden. However, the p-d hybridization breaks the optical selection rule and makes the spin-forbidden d-d transition possible. During this process, spin-orbit coupling (SOC) plays a relative minor role in the d-d transitions of Mn ions in ZnSe crystal [23,42]. In Fig. 5(b), the spin-polarized DOS of Mn; ZnSe for AFM configuration is shown. It can be seen that the Fermi level is in vanishing state regions. The states below and above the Fermi level are mainly composed of Mn-d states which indicates that Mn; ZnSe in AFM configuration show magnetic insulating behavior. Magnetically the upspin and down-spin channel of Mn-d and Se-p are all degenerate with zero exchange splitting which suggest that antiferromagnetic exchange interaction exist between Mn ions in ZnSe which is due to super-exchange mechanism via connecting Se atoms in this system. The unoccupied states of Mn ions in spin up and spin down channels are located at 2.25 eV. Therefore, during AFM coupling, the d-d transition energy (2.25 eV) of Mn ions during absorption is higher in energy as compared to the d-d transition energy (1.98 eV) during FM coupling. As there are no impurity states around the Fermi level, therefore, the system without any other defects should be AFM, which agree with the model proposed by Dalpian et al. [43]. In FM configuration, the spin up electrons interact with spin down electrons therefore, during the ferromagnetic interaction, the electrons flip from spin up to spin down channel. In AFM configuration, the spin up occupied state of one Mn ion interact with spin up of unoccupied state of another Mn ion. The antiferromagnetic behavior in pure Mn-doped ZnSe can be explained using phenomenological band structure model suggested by Gustavo et al. [43,44]. This model is based on the repulsions between the host semiconductor band and d-states of transition metal. Fig. 6 illustrates the schematic model of band coupling and level repulsion of Mn-3d states in FM and AFM configurations. The energy difference
40 (a) 20 0 -20 -40
TDOS
60 40 20 0 -20 -40 -60
Se-p
0.4
0.4 0.0
0.0
-0.4
-0.4
1.5 0.0
0.0
-1.5
-1.5
-4
-2
0
2
Energy(eV)
4
(b)
TDOS
Se-p
1.5
Mn-d
-6
(1)
Δ1,2 dd is the coupling Δ1dd and Δ2dd indicate
6
Mn-d
-6
-4
-2
0
2
Energy(eV)
4
6
Fig. 5. The TDOS and PDOS of Mn-3d and Se-4p states for (a) FM (b) AFM configurations in Mn-doped ZnSe. The Fermi level is shown by vertical dotted line. 5
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Fig. 6. Schematic band coupling Models and level of repulsions of Mn-3d states in FM and AFM configurations of (a) pure Mn;ZnSe and (b) Mn; ZnSe with Znvacancy.
super-exchange mechanism dominate over the double exchange mechanism and therefore, the system is antiferromagnetically stable [45]. Thus the electrons from Se-vacancy do not change the magnetic ground state from antiferromagnetic state to ferromagnetic state. Next, we also calculated the density of state of double Mn-doped ZnSe with Zn vacancy as shown in Fig. 7(a). From the TDOS, it is clearly seen that impurity states are available around the Fermi level, indicating the half-metallicity of the material. From PDOS, we see that spin up dz2 and dx2 states of Mn are occupied so it is located below the Fermi level while spin up dxy, dyz, and dxz states are partially occupied so these are located around the Fermi level. Thus holes produced by Zn vacancy affect the occupancy of 3d-state of Mn ions. Before Zn vacancy
presence of Se vacancy. From the PDOS of d-state of Mn, all spin up 3d states of one Mn ion (spin up-dxy, dyz, dxz, dz2 and dx2) and spin down 3d of another Mn ion (spin down-dxy, dyz, dxz, dz2 and dx2) are occupied and located below the Fermi level. While spin up of 3d-states (dxy, dyz, dxz, dz2 and dx2) of one Mn ion and spin down of 3d-states (dxy, dyz, dxz, dz2 and dx2) of another Mn ion are unoccupied and located above the Fermi Level. Thus, Se vacancy does not affect the occupancy of d-states of Mn ion. The calculated magnetic moment per Mn ion in the presence of Se vacancy is 4.18 which is approximately equal to the magnetic moment (4.16 μB ) for Mn ion without Se vacancy. This means that the two electrons produced by Se-vacancy do not fill the dstates of Mn ions. As there is no impurity states at the Fermi level, then
Fig. 7. The calculated TDOS Mn-doped ZnSe and PDOS of Mn-3d and Se-4p states with (a) Zn vacancy for FM state (b) Se vacancy for AFM state. The vertical dotted line shows the Fermi level. 6
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doping, d-state of Mn is half filled and material shows magnetic insulating nature. When Zn vacancy is introduced, then two holes are generated. These holes are filled by the electrons from 3d-states Mn ions. Thus the number of electrons in d-state is decreased which, in turn, decrease the magnetic moment. The calculated magnetic moment of Mn ion with Zn vacancy is 3.66 μB which is smaller than magnetic moment of Mn without Zn vacancy. It is found that the Fermi energy shifts into valence band for Zn vacancy because Zn vacancy as acceptor provides two holes which promote double exchange interaction and stabilize the ferromagnetic state. From the band coupling model for Zn-vacancy in Mn-ZnSe, as shown in Fig. 6(b), we find that there are two holes exist in t2g states. Therefore, the energy gain to stabilize FM states is a 2Δ1dd according to the above equation (1). The energy gain is 4Δ1,2 dd for stabilizing the antiferromagnetic state. It implies that there is a competition between FM and AFM couplings and ground state depends over the relative strength between 2Δ1dd and 4Δ1,2 dd . Ferromagnetic ground state will be governed by the value of ΔE ' = −2Δ1dd + 4Δ1,2 dd . Actually, FM coupling dominates in this competition because of the level repulsion Δ1dd in spin up channel is much larger than Δ1,2 dd , which is consistent with our first principle calculations. Our Result proved the FM stability when Zn vacancy is injected in Mn;ZnSe.
seen clearly that the absorption edge in single Mn ion in ZnSe is at 2.13 eV as shown in the inset of Fig. 8(a) which is assigned to the d-d transition in Mn ion. This spin forbidden d-d transition is slightly allowed by SOC effect [42]. The d-d transition energy of single Mn ion doped ZnSe is in good agreement with the experimental result [25]. In Fig. 8(b), the results of double Mn ions doped in ZnSe with and without intrinsic vacancy defects are shown. The d-d transition in double Mn ions system (shown in the inset of Fig. 8(b)) occur at about 2.24 eV which is higher in energy as compared to single Mn ion doped system. This blue shift of d-d transition energy is due to the anti-ferromagnetic coupling between Mn ions in double Mn ion system. We can see sharp peaks in Mn-doped ZnSe with Zn vacancy doping in the infrared region as shown in Fig. 8(b), which are attributed to the acceptor states introduced by Zn vacancy. No such a peak is observed in the infrared region in pure Mn-doped ZnSe with and without Se vacancy because it is an insulator. After introducing Se vacancy in Mn-ZnSe, a peak is observed at near infrared region (1.68 eV) which is attributed to donor states introduced by Se vacancy. The appearance of the absorption peaks in the infrared region in Mn;ZnSe with Zn vacancy makes them applicable for energy harvesting devices. Finally, the d-d transitions during optical absorption in FM and AFM ordered systems were also investigated and the results are shown in Fig. 9. As we discussed above that d-d transition (4T1-6A1) in single Mn ion in ZnSe is 2.13 eV. During d-d transition in Mn ion, the spin of electron flipped from spin up to spin down channel in the lowest excited state. If two Mn ions in the lattice of ZnSe are in FM order, then the absorption edge is at 1.97 eV which is due to d-d transition in FM coupled Mn ions in ZnSe which is lower than optical d-d transition in single Mn ion in ZnSe (paramagnetic state). Our calculations show that in FM coupled Mn ions pair system, the energy range from 1.98 to 2.23 eV is due to electronic intra-band transition within d-states (d-d transition) of Mn ions. In AFM coupled Mn ions, d-d (4T1-6A1) transition is from 2.24 to 2.46 eV which is also in good agreement with the experimental report [23]. Thus, we concluded that the d-d transition during optical absorption is red and blue shifted for FM and AFM coupled Mn ions pair system respectively which support the agreement between theoretical and experimental observations [23,48,8]. Most of previous II-VI:Mn DMS structure contain AFM coupled dopants inside the host semiconductor lattice which widens the bandgap of host semiconductor, as obtained here (Eg = 2.77 eV see in Fig. 9). But if the Mn ions are doped in low concentration, there are some of them staying at ferromagnetic coupling. In such a situation the bandgap would have redshift due to the phonon coupling enhancement [49] to form excitonic-magnetic polaron EMP, which need to be discussed here theoretically. In Mn-doped ZnSe without any other p-type defects such as Zn vacancy, Mn spins couple antiferromagnetic and the separation between 4T1 and 4A1 increase because of repulsion of up-spin occupied state of one Mn ion and up-spin unoccupied state of another Mn ion which widen the bandgap energy of ZnSe semiconductor. Therefore, the bandgap of ZnSe increases with AFM coupled Mn ions (Eg = 2.77 eV).
2.4. Optical absorption The absorption coefficient is important parameter for designing optical device. The optical absorption spectrum is related to the probabilities of inter-band transition [46]. The VASP package can calculate the frequency-dependent real and imaginary part of the dielectric after the electronic ground state have been determined. The optical absorption coefficient can be obtained from the known imaginary ε (ω)2 and real ε (ω)1 parts of dielectric using the following relation 1
α (ω) = ω [2 ε (ω)12 + ε (ω)22 − 2ε1 (ω)] 2
(2)
The computed results of absorption coefficients for pure ZnSe and single Mn-doped ZnSe are shown in Fig. 8(a). The peaks in absorption spectra are generated because of the electronic transition between occupied and unoccupied states in the materials. For the pure ZnSe, the absorption edge around 2.70 eV correspond to the bandgap energy and is due to the band edge (BE) excitonic transition of ZnSe (transition between Se-4p state at the top of valence band and Zn-4 s state at bottom of conduction band). The peak at 5.77 eV comes from the electronic transition between deep lying Se-4p in VB and Zn-s states in bottom of CB. The transition between Se-s state and Zn-3d within the valence band produces the peak at 7.0 eV. The main peak around 9.1 eV corresponding to strong absorption occur in pure ZnS and may be due to the transition between Zn-3d state and Zn-4 s state. There is no absorption peak at low energy side (0 to 2.7) which shows that ZnSe crystal has no Zn/Se vacancies [47]. We can see that the intensity of the absorption spectra of pure ZnSe is slightly reduced after Mn-doping. It is
Fig. 8. The calculated Absorption coefficients for (a) Pure ZnSe and single Mn ion in ZnSe (b) double Mn ions doped in ZnSe with and without vacancy defects. The black, blue, red, pink and green colors indicate the results of pure ZnSe, single Mn ion doped, double Mn ions doped, double Mn ions doped with Se vacancy and double Mn ions with Zn vacancy defects.
7
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Acknowledgment This work was supported by the 973 Project of China (No.2014CB920903), National Natural Science Foundation of China (No. 11004009). References [1] J.K. Furdyna, J. Appl. Phys. 64 (1988). [2] R.D. Mcnorton, T.M. Schuler, J.M. Maclaren, R.A. Stern, Phys. Rev. B 78 (2008) 1. [3] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Science (80-.) 287 (2000) 1019. [4] H. Saito, V. Zayets, S. Yamagata, K. Ando, Phys. Rev. Lett. 90 (2003) 20. [5] C. Liu, F. Yun, H. Morkoc, J. Mater. Sci. Mater. Electron. 6 (2005) 555. [6] M.E. Overberg, C.R. Abernathy, S.J. Pearton, N.A. Theodoropoulou, K.T. McCarthy, A.F. Hebard, Appl. Phys. Lett. 79 (2001) 1312. [7] S. Sonoda, S. Shimizu, T. Sasaki, Y. Yamamoto, J. Cryst. Growth 239 (2002) 1358. [8] M.S. Khan, L. Shi, H. Ullah, X. Yang, B. Zou, J. Phys. Condens. Matter 31 (2019) 485706. [9] K. Ueda, H. Tabata, T. Kawai, Appl. Phys. Lett. 79 (2001) 988. [10] S. Kumar, C.L. Chen, C.L. Dong, Y.K. Ho, J.F. Lee, T.S. Chan, R. Thangavel, T.K. Chen, B.H. Mok, S.M. Rao, M.K. Wu, J. Alloy. Compd. J. 554 (2013) 357. [11] V.M. De Almeida, A. Mesquita, A.O. De Zevallos, N.C. Mamani, P.P. Neves, X. Gratens, V.A. Chitta, W.B. Ferraz, A.C. Doriguetto, A.C.S. Sabioni, H.B. De Carvalho, J. Alloys Compd. 655 (2015) 406. [12] R. Long, N.J. English, Phys. Rev. B 80 (2009) 1. [13] B. Poornaprakash, S. Sambasivam, D. Amaranatha Reddy, G. Murali, R.P. Vijayalakshmi, B.K. Reddy, Ceram. Int. 40 (2013) 2677. [14] C. Wen, Z. Zhu, W. Li, J. Zhang, L. Wu, B. Li, G. Zeng, W. Wang, J. Alloys Compd. 718 (2017) 197. [15] H. Zhang, Y. Fang, J. Alloys Compd. 781 (2019) 201. [16] X. Zhai, Y. Gong, W. Yang, H. Kang, X. Zhang, RSC Adv. 5 (2015) 63458. [17] Q. Mahmood, S.M. Alay-e-abbas, M. Hassan, N.A. Noor, J. Alloys Compd. 688 (2016) 899. [18] B.T. Huy, M.H. Seo, A.P. Kumar, H. Jeong, Y.I. Lee, J. Alloys Compd. 588 (2014) 127. [19] V. Wood, J.E. Halpert, M.J. Panzer, M.G. Bawendi, V. Bulović, Nano Lett. 9 (2009) 2367. [20] W. Benstaali, S. Bentata, A. Abbad, A. Belaidi, Mater. Sci. Semicond. Process. 16 (2013) 231. [21] S. Khatta, S.K. Tripathi, S. Prakash, J. Magn. Magn. Mater. 460 (2018) 354. [22] X. Ge, Y. Zhang, J. Magn. Magn. Mater. 321 (2008) 198. [23] L. Hou, W. Zhou, B. Zou, Y. Znang, J. Han, X. Yang, Z. Gong, J. Li, S. Xie, L.J. Shi, Nanotechnology 28 (2017) 105202. [24] M.A. Kamran, A. Majid, T. Alharbi, M.W. Iqbal, M.W. Amjad, G. Nabi, S. Zou, B. Zou, J. Mater. Chem. C 5 (2017) 8749. [25] T. Fukushima, H. Katayama-Yoshida, K. Sato, H. Fujii, E. Rabel, R. Zeller, P.H. Dederichs, W. Zhang, R. Mazzarello, Phys. Rev. B – Condens. Matter Mater. Phys. 90 (2014) 1. [26] K. Sato, L. Bergqvist, J. Kudrnovský, P.H. Dederichs, O. Eriksson, I. Turek, B. Sanyal, G. Bouzerar, H. Katayama-Yoshida, V.A. Dinh, T. Fukushima, H. Kizaki, R. Zeller, Rev. Mod. Phys. 82 (2010) 1633. [27] Y. Pan, Y. Zhu, D.N. Shi, X.Y. Wei, C.L. Ma, K.C. Zhang, J. Alloys Compd. 644 (2015) 341. [28] S. Taguchi, A. Ishizumi, T. Tayagaki, Y. Kanemitsu, Appl. Phys. Lett. 94 (2009) 20. [29] M. Ragam, G. Kalaiselvan, S. Arumugam, N. Sankar, K. Ramachandran, J. Alloys Compd. 541 (2012) 222. [30] P.V.B. Lakshmi, K.S. Raj, K. Ramachandran, Cryst. Res. Technol 158 (2009) 153. [31] K.W. Nielsen, J.B. Philipp, M. Opel, A. Erb, J. Simon, L. Alff, R. Gross, Superlattices Microstruct. 37 (2005) 327. [32] V.P. Sirkeli, D.D. Nedeoglo, N.D. Nedeoglo, I.V. Radevici, R.L. Sobolevskaia, K.D. Sushkevich, E. Lähderanta, A.V. Lashkul, R. Laiho, J.P. Biethan, O. Yilmazoglu, D. Pavlidis, H.L. Hartnagel, Phys. B Condens. Matter 407 (2012) 3802. [33] L.M. Sandratskii, P. Bruno, Phys. Rev. B 73 (2006) 1. [34] N. Tsujii, H. Kitazawa, G. Kido, N. Tsujii, H. Kitazawa, G. Kido, J. Appl. Phys. 6957 (2003) 1. [35] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [36] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953. [37] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [38] J. Heyd, G.E. Scuseria, M. Ernzerhof, J. Chem. Phys. 118 (2003) 8207. [39] A. Fleszar, W. Hanke, Phys. Rev. B 71 (2005) 1. [40] M.S. Khan, L. Shi, X.-T. Yang, S. Ali, H. Ullah, B. Zou, J. Phys. Condens. Matter 31 (2019) 395702. [41] S.H. Wei, A. Zunger, Phys. Rev. B 37 (1988) 15. [42] R. Beaulac, P.I. Archer, D.R. Gamelin, J. Solid State Chem. 181 (2008) 1582. [43] G.M. Dalpian, S. Wei, X.G. Gong, Solid State Commun. 138 (138) (2006) 353. [44] G. M. Dalpian, S. Wei, 2187, 2170 (2006). [45] K. Sato, P. H. Dederichs, K.-Y. H, and J. Kudrnovsk, J. Phys. Condens. MATTER 5491, (2004). [46] S.Z. Karazhanov, P. Ravindran, A. Kjekshus, H. Fjellvåg, B.G. Svensson, Phys. Rev. B 75 (2007) 1. [47] M.A. Kamran, Nanotechnology 29 (2018) 435702. [48] B.B. Liang, L.P. Hou, S.Y. Zou, L. Zhang, Y.C. Guo, Y.T. Liu, M.U. Farooq, L.J. Shi, R.B. Liu, B.S. Zou, RSC Adv. 8 (2018) 3133. [49] S. Zou, M.A. Kamran, L.J. Shi, R. Liu, S. Guo, A. Kavokin, B. Zou, ACS Photonics 3 (2016) 1809. [50] M.S. Khan, L. Shi, B. Zou, Mater. Res. Express 6 (2019) 116126.
Fig. 9. The absorption during d-d transitions for FM and AFM coupled Mn ions in ZnSe.
But the bandgap (2.63 eV) of ZnSe decreases with FM coupled Mn ions. These observations support experimental and theoretical reports [23,50,8]. 3. Conclusion In summary, we have investigated the effect of vacancy defects on optoelectronic and magnetic properties of Mn-doped ZnSe crystal using first principle method. It has been found that the experimental bandgap of ZnSe can be reproduced by employing positive U on Zn-d state and negative U on Se-p state in GGA + U method. The antiferromagnetic behavior in Mn-doped ZnSe can be explained on the basis of superexchange mechanism. It has been concluded that Zn-vacancy defect changes the ground state of Mn-doped ZnS from AFM to FM state and Se-vacancy defect has no effect on the ground state of Mn-doped ZnSe. The optical absorption edge of Mn-doped systems is due to the spin forbidden d-d transitions of Mn ions. The peak in low energy side is related to the acceptor states introduced by Zn-vacancy in Mn-doped ZnSe system. The absorption peaks in the near infra-red region are attributed to the donor states caused by Se-vacancy in the Mn-doped ZnSe. The red and blue shift of d-d transitions of Mn ions are observed in FM and AFM configurations, respectively, which supports the agreement between experimental and theoretical observations. Similarly, the red and blue shift of fundamental bandgap are also observed in FM and AFM configurations respectively. CRediT authorship contribution statement Muhammad Sheraz Khan: Data curation, Investigation, Visualization, Writing - original draft, Writing - review & editing. Lijie Shi: Conceptualization, Formal analysis, Validation, Writing - original draft. Bingsuo Zou: Conceptualization, Methodology, Project administration, Writing - review & editing. Chinese Government: Funding acquisition. Beijing Institute of Technology: Resources. Commercial VASP: Software. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 8