Studies of the defect structure for V3+ ions in wurtzite structure ZnO

Spectrochimica Acta Part A 82 (2011) 137–139

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Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy journal homepage: www.elsevier.com/locate/saa

Studies of the defect structure for V3+ ions in wurtzite structure ZnO Qun Wei a,∗ , Li-Xin Guo a , Zi-Yuan Yang b , Bing Wei a , Dong-Yun Zhang c a

School of Science, Xidian University, Xi’an 710071, PR China Department of Physics, Baoji University of Arts and Science, Baoji 721007, PR China c School of Chemistry and Chemical Engineering, Guangxi University, Nanning 530004, PR China b

a r t i c l e

i n f o

Article history: Received 12 May 2011 Received in revised form 1 July 2011 Accepted 3 July 2011 Keywords: Defect structure ZnO First-principle calculations Crystal field theory

a b s t r a c t By using crystal field theory, the optical spectra, zero field splitting and g factors have been calculated. The defect structure for V3+ in ZnO crystal has been studied by using crystal field theory and first-principle calculations. The results show that, the V3+ ions do not occupy the exact Zn2+ site, but displaced along C3 axis. © 2011 Elsevier B.V. All rights reserved.

PACS: 76.30Fc 71.70Ch 78.50Ec 71.55Ht

1. Introduction Transition-metal (TM) ions are known as deep centers that strongly influence the electrical and optical properties in most semiconductors. Especially, there has been much attention on the doping ZnO system as a potential dilute magnetic semiconductor to provide efficient injection of spin-polarized carriers for spintronic devices [1]. Doping ZnO with TM elements leads to its many interesting properties. TM ions such as Mn2+ , Fe3+ , Co2+ , and V3+ are active ions in dilute magnetic semiconductors materials [2–5]. These impurity ions in the materials play a major role because they can modify properties of the materials. As known, the spin-Hamiltonian (SH) parameters are sensitive to the local defect structure of an impurity, so we can detect the local structure by fitting the SH parameters. In this work, the SH parameters, including zero-field splitting (ZFS) parameter D and g factors, and the defect structure of a tetrahedral V3+ center in wurtzite ZnO are theoretically studied by the complete diagonalization method (CDM) [6–8]. In our calculations, the distortion parameter Z and optical spectra parameters are obtained by fitting the experimental SH parameters and optical spectra simultaneously. To verify the reliability of

∗ Corresponding author. Tel.: +86 13649273458. E-mail address: [email protected] (Q. Wei). 1386-1425/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2011.07.016

our calculated results, the distortion parameter Z is calculated by using first-principle calculations.

2. Theory 2.1. optical spectra and defect structure of V3+ ions in wurtzite ZnO: crystal-field (CF) method The host ZnO crystal has the wurtzite structure with a space group designated as P63mc and two molecules per unit cell. When V3+ ions are doped into ZnO crystals, V3+ ions will replace Zn2+ ions, and occupy the C3V site. V3+ ion is of 3d2 configuration. The energy matrices for the 3d2 configuration ion with trigonal symmetry have been established based on the following Hamiltonian: H = Hee (B, C) + HCF (Bkq ) + HSO () + HSS (M0 , M2 ) + HSOO (M0 , M2 ) + HOO (M0 , M2 ),

(1)

where Hee , HCF , HSO , HSS , HSOO , and HOO represent, respectively, the electrostatic, the crystal field (CF), the spin–orbit (SO) interaction, the spin–spin (SS) interaction, the spin–other–orbit (SOO) interactions, and the orbit–orbit (OO) interactions. B and C are Racah parameters, Bkq are CF parameters,  is spin-orbit coupling coefficient, M0 and M2 are the Marvin’s radial integrals used for representing the SS, SOO, and OO interactions [9].

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Q. Wei et al. / Spectrochimica Acta Part A 82 (2011) 137–139

The LS-ground term of the 3d2 configuration is 3 F, which is split by tetrahedral CF into 3 A2g , 3 T2g and 3 T2g terms. For 3d2 configuration 3 A2g is the tetrahedral cubic ground state. Due to CF of C3V symmetry, the orbital singlet 3 A2g is split due to the magnetic interactions into a spin doublet |E±1 (3 F ↓ 3 A2g ↓ 3 A2 ) and a spin singlet |A(3 F ↓ 3 A2g ↓ 3 A2 ). Here we use the notation of Ref. [10] to label the final states. The ground state of the 3d2 configuration are obtained by complete diagonalization of the three 15 × 15 matrices in the form of linear combinations of the basis LS states as [8]: +1

=

15 

a+1,j |ϕj ,

(2)

j=1



Fig. 1. The distortion model for ZnO:V3+ crystals.

15

−1

=

a−1,j |ϕj ,

(3)

j=1

0

=

15 

a0,j |ϕj .

(4)

j=1

For V3+ ions at C3V symmetry, the effective spin Hamiltonian, taking into account the ZFS and Zeeman terms [11], can be written as [8]:



HS = D Sz2 −



1 S(S + 1) + B g Bz Sz + B g⊥ (Bx Sx + By Sy ), 3

(5)

with the z-axis along a [1 1 1] direction. The ZFS parameter D is the splitting of spin doublet and spin singlet for C3V symmetry, and is given by D = ε(|E±1 (3 F ↓ 3 A2g ↓ 3 A2 )) − ε(|A(3 F ↓ 3 A2g ↓ 3 A2 )).

(6)

The expressions for the Zeeman g-factors: g|| and g⊥ are given as [8]: g = k g⊥

(1) +1 |L0 |

(1) +1 |S0 |

+1 ,

0 − 

(1) +1 |L+1 |

0 )

0 − 

(1) +1 |S+1 |

0 ),

+1  + ge 

= k(

(1) +1 |L−1 |

+ge (

(1) +1 |S−1 |

(7) (8)

where k is the orbital reduction factor, and ge is the free-spin g value of 2.0023. The rank-one operators are defined in Ref. [8]. On account of the differences between the impurity ions and host ions, the local environment of the paramagnetic ion may be unlike that of the replaced host ion. The EPR results show that, this occupation cannot change the wurtzite structure. In our investigations, we assume that the charge compensation exists somewhere far away from the defect center in the crystal. Thus, we can establish the relationships between the CF parameters and crystal structure parameters by using the superposition model. For a tetrahedron with symmetry C3V , the CF parameters are derived as B20 = 2A¯ 2 B40 = 8A¯ 4

 R 3 0

R1

 R 5 0

R1

+ 3A¯ 2 + 3A¯ 4

 R 3  0 R2

 R 5 0

R2



3 cos2  − 1 ,

(35 cos4  − 30 cos2  + 3),

 R 5 √ 0 B43 = −6 35A¯ 4 sin3  cos , R2

(9) (10) (11)

where R1 is the metal-ligand distance along C3 axis and R2 is the rest three metal-ligand distance,  is the angle between R2 and C3 axis, and R0 is the reference distance. We take R0 as the average value of metal-ligand distances, i.e. R0 = (R1 + 3R2 )/4. A¯ 2 and A¯ 4 are intrinsic parameters, and following the relationship A¯ 4 = − 27Dq/16 and A¯ 2 = 9A¯ 4 [12]. We assume V3+ ion in ZnO does not occupy the exact Zn2+ site, but displays by Z along the C3 axis. The displacement towards

the O2− ion on the R1 bond is defined as the positive displacement direction (see Fig. 1). Considering the displacement, the bond length and bond angle can be expressed as R1 = R10 − Z,

(12) 2 1/2

2

R2 = {[R20 sin( − 0 )] + [R20 cos( − 0 ) + Z] }



 = arctan

R20 sin 0 R20 cos 0 + Z



.

,

(13) (14)

Thus, the relationship between SH parameters and crystal structure has been established. For the host ZnO crystal, R10 = 1.992 Å, R20 = 1.973 Å,  0 = 108.04◦ [13]. Substituting the spectra parameters of ZnO:V3+ crystal into above formulas, the SH parameters can be obtained by daigonalizing the energy matrices. The spectra parameters B = 486 cm−1 , C = 2500 cm−1 , Dq = − 701 cm−1 , = 159 cm−1 , k = 0.75, M0 = 0.1644 cm−1 , M2 = 0.0129 cm−1 are used in calculations. By fitting the optical spectra and ZFS parameter D and g factors, the displacement Z = − 0.005 Åcan be obtained. The comparison between theoretical results and observed values of optical spectra are given in Table 1. From Table 1, one can see that, the calculated optical spectra are in good agreement with experiment values. In Table 2, the calculated SH parameters for Z = 0 Åand Z = − 0.005 Åare listed, respectively. We can see from Table 2 that, when we considered the local distortion, the calculated results are in good agreement with observed ones. 2.2. Local structure of V3+ ions in ZnO: first-principle calculations The first-principle calculations have been done using CASTEP (Cambridge Serial Total Energy Package) developed by Payne et al. [14,15]. Optimization was performed with a convergence threshold for the maximum energy change of 1.0 × 10−6 eV/atom and for the maximum force of 0.01 eV/Å. The Vanderbilt ultrasoft pseudopotential method [16] with a plane wave basis set cut-off energy of 360 eV was used for the geometry optimization calculations. The 3 × 3 × 3 supercells with one Zn ion replaced by one V3+ ion were used for calculations. The Monkhorst-Pack (MP) [17] mesh of 3 × 3 × 2 was used. The effects of exchange and correlation energy were treated within the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof functional [18]. In the first-principle calculations, to compare the results with those in Section 2.1, we adopt the same distortion model as in Section 2.1. The 53 Zn and 54 O atoms are constrained in the 3 × 3 × 3 supercells. The doping V3+ ion is set to move along [0 0 1] (C3 -axis) direction, i.e. the x and y coordinates of V3+ ion are also constrained. After a geometry optimization calculation, the position of V3+ ion can be obtained. The results show that, the V3+ ion move away from the O2− ion on the R1 bond. Using the same definition of Z as shown in Fig. 1, the displacement Z = − 0.006 Åcan be obtained.

Q. Wei et al. / Spectrochimica Acta Part A 82 (2011) 137–139

139

Table 1 Optical spectra of V3+ ions in ZnO crytal (in cm−1 ). Label

Cal.

Exp. [19,20]

Label

Cal.

A2 (A2 , F)A 3 A2 (A2 , F)E 3 E(T2 , F)A 3 E(T2 , F)A 3 E(T2 , F)E 3 E(T2 , F)E 3 A1 (T2 , F)E 3 A1 (T2 , F)A 1 E(E, D)E 3 A2 (T1 , F)A 3 A2 (T1 , F)E 3 E(T1 , F)E 3 E(T1 , F)E 3 E(T1 , F)A 3 E(T1 , F)A

0 0.746 6884 6889 6915 6959 7260 7281 8694 10,502 10,522 11,232 11,300 11,346 11,352

0 0.74 6884 6887

1

A1 (T2 , G)A 1 E(T2 , D)E 1 A1 (T2 , D)A 3 E(T1 , P)A 3 E(T1 , P)E 3 E(T1 , P)A 3 E(T1 , P)E 1 E(T1 , G)E 1 A2 (T1 , G)A 3 A2 (T1 , P)E 3 A2 (T1 , P)A 1 A1 (T2 , G)A 1 E(T1 , G)E 1 E(T2 , G)E 1 A1 (A1 , S)A

14,224 15,333 16,039 16,856 16,871 16,873 16,909 17,721 18,096 18,631 18,632 23,202 23,401 24,482 38,860

3

12,100

Exp. [19,20]

16,930

18,551

Table 2 The SH parameters for V3+ ions in ZnO crystal.

Cal. a Cal. b Cal. c Exp. [13,20] a b c

Z (Å)

R1 (Å)

R2 (Å)

 (◦ )

D (cm−1 )

g||

g⊥

0 −0.005 −0.006

1.992 1.997 1.998

1.973 1.971 1.971

108.04 107.90 107.88

0.642 0.746

1.94396 1.94526

1.93245 1.93189

0.74

1.9451(5)

1.9329(5)

Calculated results with not considering local distortion by CF method. Calculated results with considering local distortion by CF method. Calculated results with considering local distortion by first-principle calculations.

This result is very close to our calculated results obtained in Section 2.1. The related bond lengths and bond angle are listed in Table 2. 3. Conclusions The local lattice structure of V3+ in ZnO crystal has been investigated by means of the theoretical analysis of SH parameters and optical spectra. By diagonalizing the energy matrices the local structure parameters R1 = 1.997 Å, R2 = 1.971 Å,  = 107.90◦ for V3+ in ZnO crystal have been determined. To verify the reliability of our calculated results, the geometry optimization calculations based on first-principle calculations have been done. The calculated results by these two methods agree well with each other. This shows that, the local structure we obtained in this paper is reasonable. Acknowledgments This work was supported by the Fundamental Research Funds for the Central Universities, Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2010JM1015), the Education Committee Natural Science Foundation of Shaanxi Province (Grant No. 2010JK404).

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