- Email: [email protected]
Magnetic properties of vanadium doped CdTe: Ab initio calculations
Author’s Accepted Manuscript Magnetic properties of Vanadium doped CdTe: abinitio calculations F. Goumrhar, L. Bahmad, O. Mounkachi, A. Benyoussef www.elsevier.com/locate/jmmm
PII: DOI: Reference:
S0304-8853(16)33381-9 http://dx.doi.org/10.1016/j.jmmm.2016.12.041 MAGMA62249
To appear in: Journal of Magnetism and Magnetic Materials Received date: 19 April 2016 Revised date: 30 November 2016 Accepted date: 17 December 2016 Cite this article as: F. Goumrhar, L. Bahmad, O. Mounkachi and A. Benyoussef, Magnetic properties of Vanadium doped CdTe: ab-initio calculations, Journal of Magnetism and Magnetic Materials, http://dx.doi.org/10.1016/j.jmmm.2016.12.041 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Magnetic properties of Vanadium doped CdTe : ab-initio calculations F.Goumrhara , L.Bahmadb, 1 , O.Mounkachic , A.Benyoussef b,c,d a
Laboratory of Physics of High Energy, Modeling & Simulations (LPHE-MS), Faculty of Sciences, Mohammed V University of Rabat, Av. Ibn Batouta, B. P. 1014 Rabat, Morocco b Laboratory of Magnetism and High Energy Physics (LMPHE-URAC12), Faculty of Sciences, Mohammed V University of Rabat, Av. Ibn Batouta, B. P. 1014 Rabat, Morocco c Material and Nanomaterial center, MAScIR Fondation, Rabat, Morocco d Hassan II Academy of Sciences and Technology, Rabat, Morocco
————————————————————————————————————
ABSTRACT In this paper, we are applying the ab-initio calculations to study the magnetic properties of Vanadium doped CdTe. This study is based on the Korringa-Kohn-Rostoker method (KKR) combined with the coherent potential approximation (CPA), within the Local Density Approximation (LDA). This method is called (KKR-CPA-LDA). We have calculated and plotted the density of states (DOS) in the energy diagram for different concentrations of dopants. We have also investigated the magnetic and half-metallic properties of this compound and shown the mechanism of exchange interaction. Moreover, we have estimated the Curie temperature Tc for different concentrations. Finally, we have shown how the crystal field and the exchange splittings vary as a function of the concentrations.
Keywords : CdTe, KKR-CPA, DMS, Ferromagnetism, Half-metal, Double exchange. 1. Introduction The diluted magnetic semiconductors (DMSs) are the compounds obtained by the substitution of a non-magnetic semiconductor by transition metal (TM) elements such as V, Ni, Cr, Mn, Ti and Fe [1]. One of their particularities is the appearance of localized magnetic moments generated by the electron-hole coupling. This gives rise to interesting properties, such as the increase of charge carriers. On the other hand, the ferromagnetism is rarely observed 1. corresponding author. E-mail address : [email protected]
in semiconductors due to of the low density of carriers. Also, because of the ascendancy of the superexchange between local magnetic moments. In addition, the magnetic semiconductors have low Curie temperature values. The diluted magnetic semiconductors (DMSs) are the basis of new materials for spintronic devices. This is due to their magnetic and electronic properties. The ferromagnetism in the DMSs was first observed in Mn-doped GaAs [2], but not at room temperature. These materials exhibit also half-metalic behavior. This half metalic behavior stands for metalic behavior in one spin direction, but shows an insulator behavior in the other spin direction. Some recent studies, of diluted magnetic semiconductors (DMSs), have shown interesting results for new generation of spintronics. These compounds showed high Curie temperatures TC and half-metalic behaviors. Many efforts have been devoted to investigate to study different semicondutors (III-V , II-VI , IV-VI and IV). The results found for these compounds are based on the DMSs properties. The specific compounds, DMS II- VI are the most intensively studied materials after Dietl’s work [3]. They are known by their magnetic properties which are dominated by the super-exchange antiferromagnetic interactions between the localized spins. This induces a paramagnetic character, or antiferromagnetic spin glass depending on the concentration of incorporated magnetic ions. On the other hand, recent results have shown a specific ferromagnetic phase induced by carriers (holes) [4]. Among the II-VI semiconductors, showing ferromagnetism at room temperature, the elements : Zn1−x Cox O and Zn1−x Crx O [5] exhibit Curie temperature values higher than room temperature. Recently, the Cadmium Telluride (CdTe), which stands for a semiconductor belonging to the II-VI group, has attracted much attention. Due to its potential application in the spintronic [6] and also in the photovoltaic devices [7]. This compound is used in many fields such as Infra-Red detectors, solar cells, visible, Infra-Red lasers, and in the electro-optic modulators [8]. The world record efficiency for the CdTe solar cell has been dramatically increased from 16.5 % to 21.5 % during the last four-years [9]. The CdTe compound has a direct energy band gap between the visible and the ultraviolet regions. This compound is a ferromagnetic material at room temperature. Its high thermal equilibrium stability is motivating a lot of work in the solar cell application. It is known that the CdTe doped by vanadium (V) has a high sensibility and attractive photorefractive (PR) gain [10, 11]. This compound is also becoming a real promising material for applications in optical telecommunication. In this work, we present results of magnetic properties of the material CdTe doped by Vanadium. We investigated the effect of doping on this material, for the doping concentrations : Cd1−x Vx T e (x=0.02, 0.06, 0.09, 0.12, 0.15, 0.20). 2. Crystal structure and calculation method In this paper, we perform calculations based on the Density Functional Theory (DFT), using the Korringa-Kohn-Rostoker (KKR) method combined with the coherent potential approximation (CPA)[12, 13]. This method has been developed by Akai and Dederichs in treating transition metal alloys [14], with the parameterization of Vosko, Wilk and Nusair (VWN) [15]. We used the program package MACHIKANEYAMA2002V09 produced by Akai of Osaka University, Japan [16]. In their calculations only the valence electrons were considered. The Local Density Approximation (LDA) is the most widely used approximation in the density functional theory (DFT). The LDA is based on the parameterization given by Moruzzi, Janak and Williams (MJW) [17]. Our calculations depend on the concetrations of the dopants. The pure compound CdTe Cd(Z=48) Te(Z=52) presents the zinc-blend crystal
structure. The lattice constant is a=6.4805 ˚ A. To improve the quality of our calculations, we added empty spheres (ES) with Z=0 at inter-sites, see Figure 1. The compound CdTe belongs to the F 43m space group, with eight atoms per unit cell : four Cadmium (Cd) taking the positions : (0 0 0) ; (0 12 21 ) ; ( 12 0 12 ) ;( 12 21 0) and four Tellurure (Te) placed at positions : ( 14 41 41 ) ; ( 14 43 43 ) ; ( 14 43 43 ) ; ( 34 43 41 ). Two empty-spheres ES are localised at the positions : ( 14 1 1 ) ; ( 12 21 21 ) as indicated in Figure 1. The electronic configurations considered are : 4 4 Cd : (1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 ) Te : (1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p4 ) V : (1s2 2s2 2p6 3s2 3p6 4s2 3d3).
Figure 1 – The unit cell of CdTe, with the Cd (purple), Te (green) and the empty spheres with x (white) between Cd atoms. 3. Results and discussion We begin our calculations by determining the electronic structure. Then we study the magnetic propreties of CdTe doped by Vanadium. We calculete two different energies : the Disordered Local Moment energy (EDLM ) and the Ferromagnetic energy (EF erro ). The DLM configuration can be defined as a random arrangement of two distinct magnetic states of the same atomic species in a metallic system. More precisely, half of the impurity ion spins point in the upward direction and the other spins point in the opposite direction. We also estimate the corresponding Curie temperature Tc . Besides, total, d and p projected densities of states (DOS) of the compound (Cd,V)Te for different doping concentrations are studied. First calculations were performed for the pure CdTe. It is known that all semiconductors of group II-VI present two structures : Wurtzite and Sphalerite. The properties of these two structures are different. Due to its stability, we chose the Sphalerite structure of CdTe without doping as illustrated in Figure 1. We found a direct band gap of Eg = 1.15eV , which is approximately equal to the value found in literature [18, 19], which is Eg = 1.2eV and
Eg = 1.45eV . The intrinsic CdTe is a N-type semiconductor. However when this compound is doped by Vanadium, it becomes of P-type with a typical concentration of holes. This behavior is caused by a deficit of electrons at the level of the peripheral layer. This lack of peripheral electrons does not allow us to restore all the initial covalent connections. This deficit is due to the appearance of a pseudo energy level situated above the valence band. The energy needed so that a valence electron cross this acceptor level is low. The migration of the electrons causes the appearance of holes in the valence band. The DOS of minority and majority spin states is equal because CdTe is not magnetic, hence the sum of the spin moments is zero (see Figure 2). To become magnetic, one must dope with magnetic impurities. Figure 2 reveals that the valence band (VB) contains two parts : the high VB band (in the energy range from -6 to -4.3 eV) and the short VB band (ranging from -4.3 to -1.15 eV). The conduction band (CB) contains many parts which come from the interactions between the Cd-d and Te-p electrons.
Figure 2 – The total DOS of the pure compound CdTe and the partial DOS from Cd(d) and Te(p) states Doping CdTe with Vanadium (with a concentration of 2 %), leads to a spin polarization in the total density of states (T-DOS) and the partial Vanadium density of states (V-DOS) of the doped compound, see Figures 3.a and b. The doped CdTe becomes magnetic, because at the Fermi level EF new peaks appear but only for spins ”Up” electrons. For all concentrations of the magnetic impurities, the system exhibits a Ferromagnetic behavior (see figures 3 : a, b, c, d, e, and f ). The peaks in the T-DOS near EF are caused by the Vanadium spins up electrons. This reveals that this compound is half-metal (see figure 3). The total density of states (T-DOS) at EF increases with the Vanadium doping. However, the partial V-DOS (see figures 3 : b, d and f ) broadens and decreases due to an increased hybridization with the other valence states.
By comparing figures 3 (a, c and e) and figures 3 (b, d and f ), one can realize that there is a hybridization between the ”p” layer of Telluride (Te) and ”3d” layer of Vanadium (V). This result can be interpreted by a coupling of exchange responsible for the magnetism appearing in the doped compound Cd(V)Te, called double exchange interaction. This interaction is a short-range and can appear only when the carriers are induced.
Figure 3 – The influence of different V concentrations on Total DOS of our compound CdTe, and the partial DOS from Cd(d), Te(p) and V(d) states
Figure 4 shows how the density of states originating from the Vanadium 3d states vary with the concentration. The magnetic impurity (V) induces a peak in the band gap. This figure confirms the prediction of the double exchange mechanism , which can be explained by the fact that the density of states decreases while the peak widens when one increases the concentrations of vanadium. This is caused by the hybridization between d states. The impurity band is partially occupied due to this band broadening so stabilizing the the ferromagnetic configuration. The peaks in figure 4 from the atomic orbitals with eg and t2g symmetry are well separated. Hence, one can conclude that there is a crystal field. Furthermore, one finds that the atomic orbital peak eg is completely filled whereas the atomic orbital peak t2g is only partially filled.
Figure 4 – Partial DOS (from V-d states) as a function of V concentration
In order to compute the stability of magnetic fields we calculate the energy of the ferromagnetic and the DLM state (or spin-glass state) by the Akai-KKR code (see Table 1). We remark that they increase according to the concentrations. Then we estimate the total energy difference ΔE, between the DLM and ferromagnetic energy, according to : ΔE = EDLM − EF erro
(1)
This quantity describes the stability of the magnetic phase in the studied diluted magnetic semiconductor (CdTe). The variation of the total energy difference ΔE as a function of the concentration of V doped CdTe, is given in Table 1 and Figure 5. We found that ΔE is positive and increases with the concentration of V (see Figure 5). Thus the most stable phase of CdTe doped by Vanadium is the ferromagnetic one because its energy is lower.
V (%) 6 9 12 15 20
EF erro (µB ) (Ry) -24199.3413380 -23920.8095395 -23642.2777400 -23363.7459666 -22899.5264266
EDLM (Ry) -24199.3409988 -23920.8090227 -23642.2770162 -23363.7450132 -22899.5250459
ΔE (ev) 0.004624 0.006936 0.009928 0.012920 0.018768
Stability phase Ferro Ferro Ferro Ferro Ferro
Table 1 – Ferro energy, DLM energy, the total energy difference and stability phase for the compound Cd1−x Vx T e with different concentrations of V
By using the Mean Field Approximation (MFA), the transition from the ferromagnetic phase to DLM phase is given by the Curie temperature (Tc ). Which can be estimated from the total energy difference ΔE using the following equation :
Tc =
2 ΔE . 3KB C
(2)
where C is the doping concentration and KB is the Boltzmann constant. For a detailed formulation, we refer Refs. [20, 21]. According to our calculations we obtained the results represented in the Figure 5, which can shows that the Curie temperature increases with the doping concentration of Vanadium. The MFA overestimate Tc of DMS systems in particular for low concentrations.
Figure 5 – The energy difference between the disordered local moment (DLM) and ferromagnetic state and the Curie temperature as function of V concentrations A Vanadium atom (with its 3d-orbitals) are surrounded by the tetrahedral environment. Due to the crystal field splitting ΔCR : 0.408 eV (see Table 2), the orbitals are divided into ”eg ” and ”t2g ” ones (see Figure 4). The impurity states show a variation of exchange splitting ΔEx from 1.496 to 1.906 eV (see Table 2), which leads to the high-spin configuration of d-electrons. The exchange splitting is defined as the separation between the corresponding spin-up and spin-down peaks due to the effective V-3d states [22]. Considering the local symmetry of the Cd-substitutional site, it is concluded that 3dα orbitals, which have the same symmetry as the functions xy, yz and zx, hybridize well with the p orbitals of the valence bands. On the other hand, 3dβ orbital’s, which have the same symmetry as the functions x2 − y 2 and 3z 2 − r 2 ; point to the interstitial region making nonbonding states (eg ). It was already proposed that the origin of the ferromagnetism in DMSs was the double exchange mechanism [23].
V (%) 2 6 9 12 15 20
M V (µB ) -2.56844 -2.57227 -2.57420 -2.57601 -2.57946 -2.58011
ΔEx (eV ) 1.496 1.632 1.632 1.768 1.768 1.906
ΔCR (eV ) 0.408 0.408 0.408 0.408 0.408 0.408
Table 2 – The magnetic moment, the exchange splitting and crystal-field splitting calculations for different concentration of Vanadium
4. Conclusion In this work, we have investigated the magnetism of Vanadium doped CdTe. This coumpond is found to show a half-metal behavior. It is worth mentioning that the Curie temperature Tc increases is proportional to the energy difference divided by concentration. By doping more and more the ferromagnetic phase stabilises. The energy difference between the ferromagnetic and the disorder local moment states increases more than the concentration. As a result, the Curie temperature Tc increases. Furthermore, the mechanism of the double exchange interaction is also investigated.
Bibliographie [1] V.K. Sharma, R. Xalxo, G.D. Varma, Structural and magnetic studies of Mn-doped ZnO, Cryst. Q6 Res. Technol. 42 (2007) 34. [2] H. Ohno, A. Shen, F. Matsukura, A. Oiwa, A. Endo, S. Katsumoto and Y. Iye, (Ga,Mn)As : A new diluted magnetic semiconductor based on GaAs, Appl. Phys. Lett. 69, 363 (1996). [3] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Zener Model Description of Ferromagnetism in Zinc-Blende Magnetic Semiconductors, Science 287,1019,(2000). [4] K. H. J. Buschow, Handbook of Magnetic Materials, Volume 14, (2002). [5] K. Sato, et al., Stabilization of ferromagnetic states by electron doping in Fe-, Co- or Ni-doped ZnO, Jpn. J. Appl. Phys. Part 2-Lett. 40 (4A) (2001) L334–L336, APR 1. [6] K. Sato, et al., First-principles theory of dilute magnetic semiconductors, Rev.Modern Phys. 82 (2010) 1633–1690, MAY 20. [7] T. Myers, S. Edwards, J. Schetzina, Optical properties of polycrystalline CdTe films, J. Appl. Phys. 52 (1981) 4231-4237. [8] J.K. Furdyna, Diluted magnetic semiconductors, J. Appl. Phys. 64 (1988) 29. [9] M.Green, K. Emery, Y.Hishikawa, W. Warta, E. Dunlop, Solar cell efficiency tables (Version 46), Prog , Photovolt. : Res. Appl. 23 (2015) 805-812. [10] M. Ziari, W. H. Steier, P . Ranon, M. B. Klein, S. Trivedi, Enhancement of the photorefractive gain at 1.3–1.5 micro-metre in CdTe using alternating electric fields, Opt. Soc. Am. b 9 (1992) 1461. [11] J. Y. Moisan, N. Wolffer, O. Moine, P. Gravey, G. Martel, A. Aoudia, E. Repka , Y. Marfaing, R. Triboulet, Characterization of photorefractive CdTe :V : high two-wave mixing gain with an optimum low-frequency periodic external electric field, J. Opt. Soc. Am. B 11 (1994) 1655. ´ Nagy, Density functional. Theory and application to atoms and molecules, Physics Reports [12] A. 298(1998)1–79. [13] H. Akai, Fast Korringa-Kohn-Rostoker coherent potential approximation and its application to FCC Ni-Fe systems, J. Phys. Condens. Matter 1 (1989) 8045. [14] A.D. Becke, Phys. Rev. A , 38 (1988) 3098. [15] S.H. Vosko, L. Wilk, M. Nusair, Accurate spin-dependent electron liquid correlation energies for local spin density calculations : a critical analysis, Can. J. Phys. 58 (1980) 1200. [16] MACHIKANEYAMA2002v08 : H. Akai, Departement of Physics, Graduate School of Science, Osaka University, Machikaneyama 1-1,Toyonaka 560-0043, Japan, [email protected]. [17] V. L. Mouruzzi, J. F. Janak, A. R. Williams, Properties of Metals, Pergramon. New york, 1998. [18] A. Ait Raiss, Y. Sbai, L. Bahmad, A. Benyoussef, Magnetic and magneto-optical properties of doped and co-doped CdTe with (Mn, Fe) : Ab-initio study, J. Magn. Magn. Mater. Volume 385 (1 July 2015) 295–301. 11
[19] K. Durose, P.R. Edwards, D.P. Halliday, Materials aspects of CdTe/CdS solar cells, J.Crys.Growth197(1999)733–742. [20] K. Sato, H. Katayama-Yoshida, Electronic structure and magnetism of IV–VI compound based magnetic semiconductors, J.Non-Cry.Sol, 358 (2012) 2377–2380. [21] K. Sato, P. H. Dederics,H. Katayama-Yoshida, Curie temperatures of III–V diluted magnetic semiconductors calculated from first principles, Europhys. Lett.,61,(2003)403–408. [22] U.P. Verma, , Sonu Sharma, Nisha Devi, P.S. Bisht, P. Rajaram, Spin polarized structural, electronic and magnetic properties of diluted magnetic semiconductors (Cd,Mn)Te in zinc blende phase, J. Magn. Magn. Mater. Volume 323, March 2011, Pages 394–399. [23] H. Akai, Phys. Rev. Lett. 81 (1998) 3002.
PII: DOI: Reference:
S0304-8853(16)33381-9 http://dx.doi.org/10.1016/j.jmmm.2016.12.041 MAGMA62249
To appear in: Journal of Magnetism and Magnetic Materials Received date: 19 April 2016 Revised date: 30 November 2016 Accepted date: 17 December 2016 Cite this article as: F. Goumrhar, L. Bahmad, O. Mounkachi and A. Benyoussef, Magnetic properties of Vanadium doped CdTe: ab-initio calculations, Journal of Magnetism and Magnetic Materials, http://dx.doi.org/10.1016/j.jmmm.2016.12.041 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Magnetic properties of Vanadium doped CdTe : ab-initio calculations F.Goumrhara , L.Bahmadb, 1 , O.Mounkachic , A.Benyoussef b,c,d a
Laboratory of Physics of High Energy, Modeling & Simulations (LPHE-MS), Faculty of Sciences, Mohammed V University of Rabat, Av. Ibn Batouta, B. P. 1014 Rabat, Morocco b Laboratory of Magnetism and High Energy Physics (LMPHE-URAC12), Faculty of Sciences, Mohammed V University of Rabat, Av. Ibn Batouta, B. P. 1014 Rabat, Morocco c Material and Nanomaterial center, MAScIR Fondation, Rabat, Morocco d Hassan II Academy of Sciences and Technology, Rabat, Morocco
————————————————————————————————————
ABSTRACT In this paper, we are applying the ab-initio calculations to study the magnetic properties of Vanadium doped CdTe. This study is based on the Korringa-Kohn-Rostoker method (KKR) combined with the coherent potential approximation (CPA), within the Local Density Approximation (LDA). This method is called (KKR-CPA-LDA). We have calculated and plotted the density of states (DOS) in the energy diagram for different concentrations of dopants. We have also investigated the magnetic and half-metallic properties of this compound and shown the mechanism of exchange interaction. Moreover, we have estimated the Curie temperature Tc for different concentrations. Finally, we have shown how the crystal field and the exchange splittings vary as a function of the concentrations.
Keywords : CdTe, KKR-CPA, DMS, Ferromagnetism, Half-metal, Double exchange. 1. Introduction The diluted magnetic semiconductors (DMSs) are the compounds obtained by the substitution of a non-magnetic semiconductor by transition metal (TM) elements such as V, Ni, Cr, Mn, Ti and Fe [1]. One of their particularities is the appearance of localized magnetic moments generated by the electron-hole coupling. This gives rise to interesting properties, such as the increase of charge carriers. On the other hand, the ferromagnetism is rarely observed 1. corresponding author. E-mail address : [email protected]
in semiconductors due to of the low density of carriers. Also, because of the ascendancy of the superexchange between local magnetic moments. In addition, the magnetic semiconductors have low Curie temperature values. The diluted magnetic semiconductors (DMSs) are the basis of new materials for spintronic devices. This is due to their magnetic and electronic properties. The ferromagnetism in the DMSs was first observed in Mn-doped GaAs [2], but not at room temperature. These materials exhibit also half-metalic behavior. This half metalic behavior stands for metalic behavior in one spin direction, but shows an insulator behavior in the other spin direction. Some recent studies, of diluted magnetic semiconductors (DMSs), have shown interesting results for new generation of spintronics. These compounds showed high Curie temperatures TC and half-metalic behaviors. Many efforts have been devoted to investigate to study different semicondutors (III-V , II-VI , IV-VI and IV). The results found for these compounds are based on the DMSs properties. The specific compounds, DMS II- VI are the most intensively studied materials after Dietl’s work [3]. They are known by their magnetic properties which are dominated by the super-exchange antiferromagnetic interactions between the localized spins. This induces a paramagnetic character, or antiferromagnetic spin glass depending on the concentration of incorporated magnetic ions. On the other hand, recent results have shown a specific ferromagnetic phase induced by carriers (holes) [4]. Among the II-VI semiconductors, showing ferromagnetism at room temperature, the elements : Zn1−x Cox O and Zn1−x Crx O [5] exhibit Curie temperature values higher than room temperature. Recently, the Cadmium Telluride (CdTe), which stands for a semiconductor belonging to the II-VI group, has attracted much attention. Due to its potential application in the spintronic [6] and also in the photovoltaic devices [7]. This compound is used in many fields such as Infra-Red detectors, solar cells, visible, Infra-Red lasers, and in the electro-optic modulators [8]. The world record efficiency for the CdTe solar cell has been dramatically increased from 16.5 % to 21.5 % during the last four-years [9]. The CdTe compound has a direct energy band gap between the visible and the ultraviolet regions. This compound is a ferromagnetic material at room temperature. Its high thermal equilibrium stability is motivating a lot of work in the solar cell application. It is known that the CdTe doped by vanadium (V) has a high sensibility and attractive photorefractive (PR) gain [10, 11]. This compound is also becoming a real promising material for applications in optical telecommunication. In this work, we present results of magnetic properties of the material CdTe doped by Vanadium. We investigated the effect of doping on this material, for the doping concentrations : Cd1−x Vx T e (x=0.02, 0.06, 0.09, 0.12, 0.15, 0.20). 2. Crystal structure and calculation method In this paper, we perform calculations based on the Density Functional Theory (DFT), using the Korringa-Kohn-Rostoker (KKR) method combined with the coherent potential approximation (CPA)[12, 13]. This method has been developed by Akai and Dederichs in treating transition metal alloys [14], with the parameterization of Vosko, Wilk and Nusair (VWN) [15]. We used the program package MACHIKANEYAMA2002V09 produced by Akai of Osaka University, Japan [16]. In their calculations only the valence electrons were considered. The Local Density Approximation (LDA) is the most widely used approximation in the density functional theory (DFT). The LDA is based on the parameterization given by Moruzzi, Janak and Williams (MJW) [17]. Our calculations depend on the concetrations of the dopants. The pure compound CdTe Cd(Z=48) Te(Z=52) presents the zinc-blend crystal
structure. The lattice constant is a=6.4805 ˚ A. To improve the quality of our calculations, we added empty spheres (ES) with Z=0 at inter-sites, see Figure 1. The compound CdTe belongs to the F 43m space group, with eight atoms per unit cell : four Cadmium (Cd) taking the positions : (0 0 0) ; (0 12 21 ) ; ( 12 0 12 ) ;( 12 21 0) and four Tellurure (Te) placed at positions : ( 14 41 41 ) ; ( 14 43 43 ) ; ( 14 43 43 ) ; ( 34 43 41 ). Two empty-spheres ES are localised at the positions : ( 14 1 1 ) ; ( 12 21 21 ) as indicated in Figure 1. The electronic configurations considered are : 4 4 Cd : (1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 ) Te : (1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p4 ) V : (1s2 2s2 2p6 3s2 3p6 4s2 3d3).
Figure 1 – The unit cell of CdTe, with the Cd (purple), Te (green) and the empty spheres with x (white) between Cd atoms. 3. Results and discussion We begin our calculations by determining the electronic structure. Then we study the magnetic propreties of CdTe doped by Vanadium. We calculete two different energies : the Disordered Local Moment energy (EDLM ) and the Ferromagnetic energy (EF erro ). The DLM configuration can be defined as a random arrangement of two distinct magnetic states of the same atomic species in a metallic system. More precisely, half of the impurity ion spins point in the upward direction and the other spins point in the opposite direction. We also estimate the corresponding Curie temperature Tc . Besides, total, d and p projected densities of states (DOS) of the compound (Cd,V)Te for different doping concentrations are studied. First calculations were performed for the pure CdTe. It is known that all semiconductors of group II-VI present two structures : Wurtzite and Sphalerite. The properties of these two structures are different. Due to its stability, we chose the Sphalerite structure of CdTe without doping as illustrated in Figure 1. We found a direct band gap of Eg = 1.15eV , which is approximately equal to the value found in literature [18, 19], which is Eg = 1.2eV and
Eg = 1.45eV . The intrinsic CdTe is a N-type semiconductor. However when this compound is doped by Vanadium, it becomes of P-type with a typical concentration of holes. This behavior is caused by a deficit of electrons at the level of the peripheral layer. This lack of peripheral electrons does not allow us to restore all the initial covalent connections. This deficit is due to the appearance of a pseudo energy level situated above the valence band. The energy needed so that a valence electron cross this acceptor level is low. The migration of the electrons causes the appearance of holes in the valence band. The DOS of minority and majority spin states is equal because CdTe is not magnetic, hence the sum of the spin moments is zero (see Figure 2). To become magnetic, one must dope with magnetic impurities. Figure 2 reveals that the valence band (VB) contains two parts : the high VB band (in the energy range from -6 to -4.3 eV) and the short VB band (ranging from -4.3 to -1.15 eV). The conduction band (CB) contains many parts which come from the interactions between the Cd-d and Te-p electrons.
Figure 2 – The total DOS of the pure compound CdTe and the partial DOS from Cd(d) and Te(p) states Doping CdTe with Vanadium (with a concentration of 2 %), leads to a spin polarization in the total density of states (T-DOS) and the partial Vanadium density of states (V-DOS) of the doped compound, see Figures 3.a and b. The doped CdTe becomes magnetic, because at the Fermi level EF new peaks appear but only for spins ”Up” electrons. For all concentrations of the magnetic impurities, the system exhibits a Ferromagnetic behavior (see figures 3 : a, b, c, d, e, and f ). The peaks in the T-DOS near EF are caused by the Vanadium spins up electrons. This reveals that this compound is half-metal (see figure 3). The total density of states (T-DOS) at EF increases with the Vanadium doping. However, the partial V-DOS (see figures 3 : b, d and f ) broadens and decreases due to an increased hybridization with the other valence states.
By comparing figures 3 (a, c and e) and figures 3 (b, d and f ), one can realize that there is a hybridization between the ”p” layer of Telluride (Te) and ”3d” layer of Vanadium (V). This result can be interpreted by a coupling of exchange responsible for the magnetism appearing in the doped compound Cd(V)Te, called double exchange interaction. This interaction is a short-range and can appear only when the carriers are induced.
Figure 3 – The influence of different V concentrations on Total DOS of our compound CdTe, and the partial DOS from Cd(d), Te(p) and V(d) states
Figure 4 shows how the density of states originating from the Vanadium 3d states vary with the concentration. The magnetic impurity (V) induces a peak in the band gap. This figure confirms the prediction of the double exchange mechanism , which can be explained by the fact that the density of states decreases while the peak widens when one increases the concentrations of vanadium. This is caused by the hybridization between d states. The impurity band is partially occupied due to this band broadening so stabilizing the the ferromagnetic configuration. The peaks in figure 4 from the atomic orbitals with eg and t2g symmetry are well separated. Hence, one can conclude that there is a crystal field. Furthermore, one finds that the atomic orbital peak eg is completely filled whereas the atomic orbital peak t2g is only partially filled.
Figure 4 – Partial DOS (from V-d states) as a function of V concentration
In order to compute the stability of magnetic fields we calculate the energy of the ferromagnetic and the DLM state (or spin-glass state) by the Akai-KKR code (see Table 1). We remark that they increase according to the concentrations. Then we estimate the total energy difference ΔE, between the DLM and ferromagnetic energy, according to : ΔE = EDLM − EF erro
(1)
This quantity describes the stability of the magnetic phase in the studied diluted magnetic semiconductor (CdTe). The variation of the total energy difference ΔE as a function of the concentration of V doped CdTe, is given in Table 1 and Figure 5. We found that ΔE is positive and increases with the concentration of V (see Figure 5). Thus the most stable phase of CdTe doped by Vanadium is the ferromagnetic one because its energy is lower.
V (%) 6 9 12 15 20
EF erro (µB ) (Ry) -24199.3413380 -23920.8095395 -23642.2777400 -23363.7459666 -22899.5264266
EDLM (Ry) -24199.3409988 -23920.8090227 -23642.2770162 -23363.7450132 -22899.5250459
ΔE (ev) 0.004624 0.006936 0.009928 0.012920 0.018768
Stability phase Ferro Ferro Ferro Ferro Ferro
Table 1 – Ferro energy, DLM energy, the total energy difference and stability phase for the compound Cd1−x Vx T e with different concentrations of V
By using the Mean Field Approximation (MFA), the transition from the ferromagnetic phase to DLM phase is given by the Curie temperature (Tc ). Which can be estimated from the total energy difference ΔE using the following equation :
Tc =
2 ΔE . 3KB C
(2)
where C is the doping concentration and KB is the Boltzmann constant. For a detailed formulation, we refer Refs. [20, 21]. According to our calculations we obtained the results represented in the Figure 5, which can shows that the Curie temperature increases with the doping concentration of Vanadium. The MFA overestimate Tc of DMS systems in particular for low concentrations.
Figure 5 – The energy difference between the disordered local moment (DLM) and ferromagnetic state and the Curie temperature as function of V concentrations A Vanadium atom (with its 3d-orbitals) are surrounded by the tetrahedral environment. Due to the crystal field splitting ΔCR : 0.408 eV (see Table 2), the orbitals are divided into ”eg ” and ”t2g ” ones (see Figure 4). The impurity states show a variation of exchange splitting ΔEx from 1.496 to 1.906 eV (see Table 2), which leads to the high-spin configuration of d-electrons. The exchange splitting is defined as the separation between the corresponding spin-up and spin-down peaks due to the effective V-3d states [22]. Considering the local symmetry of the Cd-substitutional site, it is concluded that 3dα orbitals, which have the same symmetry as the functions xy, yz and zx, hybridize well with the p orbitals of the valence bands. On the other hand, 3dβ orbital’s, which have the same symmetry as the functions x2 − y 2 and 3z 2 − r 2 ; point to the interstitial region making nonbonding states (eg ). It was already proposed that the origin of the ferromagnetism in DMSs was the double exchange mechanism [23].
V (%) 2 6 9 12 15 20
M V (µB ) -2.56844 -2.57227 -2.57420 -2.57601 -2.57946 -2.58011
ΔEx (eV ) 1.496 1.632 1.632 1.768 1.768 1.906
ΔCR (eV ) 0.408 0.408 0.408 0.408 0.408 0.408
Table 2 – The magnetic moment, the exchange splitting and crystal-field splitting calculations for different concentration of Vanadium
4. Conclusion In this work, we have investigated the magnetism of Vanadium doped CdTe. This coumpond is found to show a half-metal behavior. It is worth mentioning that the Curie temperature Tc increases is proportional to the energy difference divided by concentration. By doping more and more the ferromagnetic phase stabilises. The energy difference between the ferromagnetic and the disorder local moment states increases more than the concentration. As a result, the Curie temperature Tc increases. Furthermore, the mechanism of the double exchange interaction is also investigated.
Bibliographie [1] V.K. Sharma, R. Xalxo, G.D. Varma, Structural and magnetic studies of Mn-doped ZnO, Cryst. Q6 Res. Technol. 42 (2007) 34. [2] H. Ohno, A. Shen, F. Matsukura, A. Oiwa, A. Endo, S. Katsumoto and Y. Iye, (Ga,Mn)As : A new diluted magnetic semiconductor based on GaAs, Appl. Phys. Lett. 69, 363 (1996). [3] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Zener Model Description of Ferromagnetism in Zinc-Blende Magnetic Semiconductors, Science 287,1019,(2000). [4] K. H. J. Buschow, Handbook of Magnetic Materials, Volume 14, (2002). [5] K. Sato, et al., Stabilization of ferromagnetic states by electron doping in Fe-, Co- or Ni-doped ZnO, Jpn. J. Appl. Phys. Part 2-Lett. 40 (4A) (2001) L334–L336, APR 1. [6] K. Sato, et al., First-principles theory of dilute magnetic semiconductors, Rev.Modern Phys. 82 (2010) 1633–1690, MAY 20. [7] T. Myers, S. Edwards, J. Schetzina, Optical properties of polycrystalline CdTe films, J. Appl. Phys. 52 (1981) 4231-4237. [8] J.K. Furdyna, Diluted magnetic semiconductors, J. Appl. Phys. 64 (1988) 29. [9] M.Green, K. Emery, Y.Hishikawa, W. Warta, E. Dunlop, Solar cell efficiency tables (Version 46), Prog , Photovolt. : Res. Appl. 23 (2015) 805-812. [10] M. Ziari, W. H. Steier, P . Ranon, M. B. Klein, S. Trivedi, Enhancement of the photorefractive gain at 1.3–1.5 micro-metre in CdTe using alternating electric fields, Opt. Soc. Am. b 9 (1992) 1461. [11] J. Y. Moisan, N. Wolffer, O. Moine, P. Gravey, G. Martel, A. Aoudia, E. Repka , Y. Marfaing, R. Triboulet, Characterization of photorefractive CdTe :V : high two-wave mixing gain with an optimum low-frequency periodic external electric field, J. Opt. Soc. Am. B 11 (1994) 1655. ´ Nagy, Density functional. Theory and application to atoms and molecules, Physics Reports [12] A. 298(1998)1–79. [13] H. Akai, Fast Korringa-Kohn-Rostoker coherent potential approximation and its application to FCC Ni-Fe systems, J. Phys. Condens. Matter 1 (1989) 8045. [14] A.D. Becke, Phys. Rev. A , 38 (1988) 3098. [15] S.H. Vosko, L. Wilk, M. Nusair, Accurate spin-dependent electron liquid correlation energies for local spin density calculations : a critical analysis, Can. J. Phys. 58 (1980) 1200. [16] MACHIKANEYAMA2002v08 : H. Akai, Departement of Physics, Graduate School of Science, Osaka University, Machikaneyama 1-1,Toyonaka 560-0043, Japan, [email protected]. [17] V. L. Mouruzzi, J. F. Janak, A. R. Williams, Properties of Metals, Pergramon. New york, 1998. [18] A. Ait Raiss, Y. Sbai, L. Bahmad, A. Benyoussef, Magnetic and magneto-optical properties of doped and co-doped CdTe with (Mn, Fe) : Ab-initio study, J. Magn. Magn. Mater. Volume 385 (1 July 2015) 295–301. 11
[19] K. Durose, P.R. Edwards, D.P. Halliday, Materials aspects of CdTe/CdS solar cells, J.Crys.Growth197(1999)733–742. [20] K. Sato, H. Katayama-Yoshida, Electronic structure and magnetism of IV–VI compound based magnetic semiconductors, J.Non-Cry.Sol, 358 (2012) 2377–2380. [21] K. Sato, P. H. Dederics,H. Katayama-Yoshida, Curie temperatures of III–V diluted magnetic semiconductors calculated from first principles, Europhys. Lett.,61,(2003)403–408. [22] U.P. Verma, , Sonu Sharma, Nisha Devi, P.S. Bisht, P. Rajaram, Spin polarized structural, electronic and magnetic properties of diluted magnetic semiconductors (Cd,Mn)Te in zinc blende phase, J. Magn. Magn. Mater. Volume 323, March 2011, Pages 394–399. [23] H. Akai, Phys. Rev. Lett. 81 (1998) 3002.