Density Functional Theory Study on the Electronic Structure and Optical Properties of SnO2

Rare Metal Materials and Engineering Volume 44, Issue 10, October 2015 Online English edition of the Chinese language journal Cite this article as: Rare Metal Materials and Engineering, 2015, 44(10): 2409-2414.

ARTICLE

Density Functional Theory Study on the Electronic Structure and Optical Properties of SnO2 Shao Tingting,

Zhang Fuchun,

Zhang Weihu

Yan’an University, Yan’an 716000, China

Abstract: The structure electronic and optical properties of rutile-type SnO2 were studied based on plane-wave pseudopotential density functional theory (DFT) adopting GGA, LDA, B3LYP and PBE0, respectively. The computing results show that the properties calculated by GGA and LDA are very close, which correspond to those by ultra-soft pseudopotential and norm conserving pseudopotential, respectively, and the properties calculated by B3LYP are near to those by PBE0. The band gap obtained from B3LYP and PBE0 is much more consistent with the available experimental data than that fr om GGA and LDA, whose band gap calculated by norm conserving pseudopotential is bigger than that by ultra-soft pseudopotential. However, the density of state and optical properties calculated from every type are basically similar in qualitative analysis, and the numerical values have a little difference. From the whole results calculated by the six methods, we can see that the structure, electronic and optical properties of rutile-type SnO2 calculated by B3LYP and PBEO are more near to the available experimental data than those by other methods. Key words: SnO2; density functional theory; electronic structure; electronic property; optical property

Stannic oxide SnO 2, an n-type wide band gap semiconductor, with band gap of 3.6 eV in experiment which is wider than that of ZnO (3.36 eV), has high exciton binding energy (130 meV in experiment) [1], so SnO 2 has attracted increasing interests and presents potential applications such as catalytic support materials, transparent electrodes for liquid crystal displays (LCDs), solar cells, chemical gas sensors, varistors and optoelectronic devices[2,3]. The behaviors of SnO2, such as electronic properties, lattice dynamics and optical properties have attracted sustained investigations both in experiments and theories[4,5]. However, those studies seem just to use one or two methods to calculate the properties of SnO2 that is inadequate to illustrate the different results calculated by different methods and which method is better for SnO2. The more methods to calculate the same SnO2 structure the better to understanding the behavior of the SnO 2. Thus in the present paper, we will investigate the structure, electronic, and optical properties of rutile-type

SnO2 via different types of functional forms and compare the results.

1 Method for calculation In the present letter, we used four types of functional forms to calculate the electronic and optical properties of SnO2. The four types of functional forms were used through the Vienna Ab-initio Simulation Package (VASP) program[6,7], including the generalized gradient approximation (GGA)[8], the local density approximation (LDA)[9], Becke’s Three Parameter Hybrid Functional Using the LYP Correlation Functional (B3LYP), and Perdew-Burke-Ernzerh of based hybrid functional(PBE0). The oxygen 2s2, 2p4 electrons and the stannum 5s2, 5p2 electrons were treated as part of the valence states. The energy cut-off of plane wave, Monkhorst–Pack mesh of Brillouin-zone sampling, and the self-consistent convergence of the total energy for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP

Received date: April 15, 2015 Foundation item: Scientific Research Program of the Educational Committee of Shanxi Province, China (2013JK0917); Scientific Research Program of Yan’an, China (2013-KG03) Corresponding author: Zhang Fuchun, Ph. D., Associate Professor, College of Physics and Electronic Information, Yan’an University, Yan’an 716000, P. R. China, Tel: 0086-911-2332045, E-mail: [email protected] Copyright © 2015, Northwest Institute for Nonferrous Metal Research. Published by Elsevier BV. All rights reserved.

2409

Shao Tingting et al. / Rare Metal Materials and Engineering, 2015, 44(10): 2409-2414

and PBE0 are listed in Table 1.

Table 2 Values of optimized structure and experimental structure Structure

a=b/nm

c/nm

c/a

Optimized structure

0.4924

0.3295

0.669

Experimental structure

0.4738

0.3189

0.673

2 Results and Discussion

Table 1

Parameters of energy cut-off, k-point and SCF for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0

Method GGA GGA LDA LDA B3LYP PBE0

Pseudo po-

Energy

tential

cut-off/eV

Ultra-soft

340

5×5×8

1×10-6

750

5×5×8

1×10-6

340

5×5×8

1×10-6

750

5×5×8

1×10-6

750

3×3×4

1×10-6

750

3×3×4

1×10-6

Norm conserving Ultra-soft Norm conserving Norm conserving Norm conserving

k-point set

SCF toler-

Energy/eV

20 15 10 5 0 -5 -10 -15 -20

Energy/eV

Z

20 15 10 5 0 -5 -10 -15 -20

Z 20 15 10 5 0 -5 -10 -15 -20 Z

Energy/eV

2.1 Structural properties The rutile-type SnO2 belongs to the tetragonal system, which contains two Sn atoms and four O atoms in a primitive cell[10]. Two Sn atoms occupy body heart position [0, 0, 0] and vertex position [1/2, 1/2, 1/2] of the tetrahedron, and two O atoms [u, u, 0], [1/2+u, 1/2-u, 1/2] are coplanar with Sn atoms, whose plane is perpendicular to that of the other two O atoms [-u, -u, 0], [1/2-u, 1/2+u, 1/2][11]. The structure of the primitive cell of SnO2 is shown in Fig.1. To minimize the total energy of SnO2 primitive cell, geometry optimization is processed by GGA (PW91), and the values of SnO2 optimized and experimental structure[12] are shown in Table 2. All of the calculations are done to the optimized structure of SnO2. 2.2 Electronic properties The energy band structures of SnO2 for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0 are show in Fig.2. From Fig.2, we can see that rutile-type SnO2 is direct band-gap semiconductor. The Fermi level is chosen to be zero of the energy scale, and the occupied state below the Fermi

0.015 eV

A

M

0.015 eV

A

M

2.581 eV

A

M

Fig.2

20 15 10 5 0 -5 -10 -15 -20

GGA(Norm conserving)

0.602 eV

Z A M 20 LDA(Ultra-soft) 15 10 5 0.619 eV 0 -5 -10 -15 -20 Z R G X G Z A M 20 B3LYP 15 10 5 2.724 eV 0 -5 -10 -15 G Z R X G -20Z A M

G

Z

R

Position

ance/eV·atom-1

Fig.1 Unit cell of SnO2 (black ball is Sn atom and grey ball is O atom)

GGA Ultra-soft

X G

G

Z R

X G

LDA(Norm conserving)

G

Z

R

X G

PBE0

G

Z R

X G

Position

Calculated band structure of SnO2 for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0

energy is valence band, whereas the unoccupied state lying above the Fermi energy is conduction band. The position of bottom of conduction band and top of valence band is G-point of Brillouin zone. The band gaps are 0.015, 0.602, 0.015, 0.619, 2.581, 2.724 eV, respectively, when calculation is done by ultra-soft, norm conserving pseudopotential of GGA and LDA, B3LYP and PBE0. The band gaps calculated by B3LYP and PBE0 are more close to the available experimental data than that by GGA and LDA, which is because GGA and LDA are ground state theory, and the energy-gap belongs to property of excited state[13] . The total density of state (TDOS) and partial density of states (PDOS) of SnO2 calculated for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0 are shown in Fig.3. From Fig.3, we can see that while the energy-gaps of SnO2 calculated by different functional forms are very different from each other, the total density of state (TDOS) and partial density of states (PDOS) have little difference, especially the

2410

Shao Tingting et al. / Rare Metal Materials and Engineering, 2015, 44(10): 2409-2414

ergy gap calculated above. 2.3 Optical properties The complex dielectric function ε(ω)= ε1(ω)+iε2(ω), which can reflect band structure and other spectrum information, is usually used to describe the optical properties of solidity macroscopically[14]. The complex dielectric functions of rutile-type SnO2 from the polarization vectors [0 0 1] calculated for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0 are shown in Fig.4. From Fig.4, we can see that there are some differences in the positions of the peaks in the six conditions, but the curve trend seems to be similar. The real part ε1(ω) is descended as a whole as the energy increases, and the intensity reaches maximum at 2.0, 2.7, 9.0, 9.3 eV, respectively, for GGA/LDA (Utra-soft), GGA/LDA (Norm conserving), B3LYP and PBE0. The probability of photon absorption is directly related to the imaginary part of complex dielectric function ε2(ω). For ε2(ω), the points of curves beginning to rise are very consistent with the calculated energy gaps. In addition, there are three clear peaks, but the positions of the peaks and the peak values are different for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0, and those are listed in Table 3.

PDOS/electron·eV-1 TDOS/electron·eV-1

PDOS/electron·eV-1 TDOS/electron·eV-1

positions of peak values are mainly identical except the results calculated by B3LYP and PBE0 that have some translation motion. From the figure of density of state calculated by GGA and LDA, we can find that the valence band includes two parts: (1) the low valence band, –15.5~–18.5 eV region, which are dominated by O 2s2 states, with a minor-presence of Sn 5s2 and Sn 5p2 states, can be ignored because it is far from Fermi level that has little influence on it; (2) the high valence band, –8.5 ~ 0 eV region, which is dominated by O 2p4 states, with a few contributions of Sn 5s2 and Sn 5p2 states to the valence band, is close to Fermi level, and illustrates that O atom can absorb electrons strongly and O 2p4 orbits are almost filled. The conduction band is mainly dominated by Sn 5p2 and Sn 5s2, and O 2p4 have a few contributions. There are some hybridizations of atomic orbits, such as hybridization between Sn 5s2 and Sn 5p2 ranging from –15.5 eV to –18.5 eV, hybridizations between Sn 5s2 and Sn 5p2 as well as between Sn 5s2 and O 2p4 ranging from –8.5 eV to Fermi energy, and hybridizations between O 2p4 and Sn 5s2 as well as between Sn 5s 2 and Sn 2p2 in conduction band. From the TDOS and PDOS, we can see that the electronic state contributions of Sn and O atoms are obvious, and there is a strong interaction between them. The densities of states calculated by B3LYP and PBE0 are similar, but the low valence bands shift left a little, and the conduction bands shift right a little, which is consistent with the result of en-

Energy/eV Fig.3

Calculated TDOS and PDOS of SnO2 for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0

2411

Shao Tingting et al. / Rare Metal Materials and Engineering, 2015, 44(10): 2409-2414

the electron transition from the top of valence band to the bottom of conduction band, and the second peak results from the electron transition from O 2p4 orbits to Sn 5s2 orbits. The highest peak appears because of electrons transition from O 2p4 orbits to Sn 5p2 orbits. The codex refractive index is an important optical constant of absorbing medium. The real part n is refractive index, and imaginary part k is extinction coefficient. The refractive index and extinction coefficient of rutile-type SnO2 from the polarization vectors [001] calculated for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0 are shown in Fig.5. From Fig.5, we can see that the curves tends seem to be similar calculated by different functional forms but there are also some differences. The n and k calculated for GGA/LDA (Ultra-soft), GGA/LDA (Norm conserving), respectively, are very close, and the results calculated by

Refractive Index

Complex Dielectric Function

Complex Dielectric Function

Complex Dielectric Function

The peaks appear because of the electrons transition from valence band to conduction band. The first peak arises from

Fig.4

Refractive Index

Photon Energy/eV Calculated complex dielectric function of SnO2 for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0 (Note: Re and Im denote real part and imaginary part, respectively) Table 3

Peak positions and values of ε2(ω) for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm

Method GGA GGA LDA LDA B3LYP PBE0

Pseudo potential Ultra-soft Norm conserving Ultra-soft Norm conserving Norm conserving Norm conserving

Position of peaks/eV

Peak values/unit

2.71 4.96 8.08

2.37 3.41 7.16

3.32 5.34 7.98

1.81 3.02 7.25

2.75 4.94 7.96

2.52 3.57 7.43

3.44 5.43 7.90

1.88 3.16 7.31

5.03 7.44 10.05

0.70 1.61 4.18

Refractive Index

conserving), B3LYP and PBE0

Energy/eV

Fig.5 5.15 7.69 10.27

0.62 1.48 3.86

Calculated codex refractive index of SnO2 for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0

2412

Shao Tingting et al. / Rare Metal Materials and Engineering, 2015, 44(10): 2409-2414

B3LYP and PBE0 are very similar but different from the former. The values of refractive indexes in low energy are 2.29, 2.11, 2.34, 2.12, 1.63, 1.59 for GGA/LDA (Ultra-soft), GGA/LDA (Norm conserving), B3LYP and PBE0, respectively. Comparing 1.997 and 2 for the bulk and the values 1.8~1.9 for MLD (molecular layer deposition) films [15], the values calculated by norm conserving pseudopotential of GGA and LDA are close. The absorption and loss function of SnO 2 from the polarization vectors [001] calculated for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0 are shown in Fig.6. From Fig.6a, we can see that the absorption edge energies are 1.20, 1.81, 1.13, 1.83, 3.38, 3.52 eV, calculated for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0, respectively which are bigger than the corresponding calculated energy gaps, because of the need of electron transition between occupied state to unoccupied state. The strongest absorption peak is at about 16.0 eV calculated by the six methods, which is formed by direct transition of electrons from valence band to conduction band. Loss function indicates the energy loss when electrons rush through solid materials. From Fig.6b, we can see that the loss peak positions and the peaks values are different for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0, and they those are listed in Table 4.

Absorption/×104

30

a

25

GGA(Ultra-soft) GGA(Norm) LDA(Ultra-soft) LDA(Norm) B3LYP PBE0

20 15 10

0

5

30

Loss Function

Peak position and value of loss function for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0 Peak

The Peak values

positions/eV

/unit

Ultra-soft

20.57

16.78

GGA

Norm conserving

20.11

25.74

LDA

Ultra-soft

20.45

18.25

LDA

Norm conserving

19.98

32.11

B3LYP

Norm conserving

20.76

5.22

PBE0

Norm conserving

20.97

4.83

Method

Pseudo potential

GGA

3 Conclusions 1) The band gaps getting from PBE0 and B3LYP are much more consistent with the available experimental data, while those getting from GGA and LDA are much smaller. 2) The density of state, dielectric function, codex refractive index, absorption and loss function calculating from every type basically have the same trend in qualitative analysis but different from each other. The results calculated by ultra-soft pseudopotential of GGA and LDA are very close, and those getting from norm conserving pseudopotential of GGA and LDA are very consistent, while the results calculated by B3LYP fit well with those acquire from PBE0. 3) Although there are differences in calculating behaviors of rutile-type SnO2 using different methods, the results calculated by every method are very consistent. The structural electronic and optical properties of SnO2 calculated by B3LYP and PBED are more near to the available experimental data than those by other methods.

References

5 0 10

15

20

25

b

GGA(Ultra-soft) GGA(Norm) LDA(Ultra-soft) LDA(Norm) B3LYP PBE0

25 20 15

30

165414 2 Bataill M, Diebold U. Prog Surf Sci[J], 2005, 79: 47 2011, 50: 1571 4

He Y, Liu J F, Chen W et al. Phys Rev B[J], 2005, 72: 212 102

10 0 0

1 Batzill M, Katsiev K, James M et al. Phys Rev B[J], 2005, 72:

3 Liu Chunmei, Chen Xiangrong, Ji Guangfu. Comp Mater Sci [J],

5 Shieh S R, Kubo A, Duffy T S et al. Phys Rev B[J], 2006, 73:

5 5

10

15

20

25

30

Energy/eV Fig.6

Table 4

Calculated absorption (a) and loss function (b) of SnO 2 for GGA (Ultra-soft), GGA (Norm conserving), LDA (Ultra-soft), LDA (Norm conserving), B3LYP and PBE0

014 105 6 Milman V, Winkler B, White J A et al. Quantum Chem[J], 2000, 77: 895 7 Kresse G, Furthmüller J. Phys Rev B[J], 1996, 54, 011 169 8 Perdew J P, Burke K, Ernzerhof M. Phys Rev[J], 1996, 77: 3865 9 Vosko S H, Wilk L, Nusair M et al. Phys[J], 1980, 58: 1200 10 Hassan F El Haj, Moussawi S, Noun W et al. Comp Mater Sci [J],

2413

Shao Tingting et al. / Rare Metal Materials and Engineering, 2015, 44(10): 2409-2414

2013, 72: 86 11 Bouhemadou A. Braz J Phys[J], 2010, 40: 52 12 Hadia N M A, Ryabtsev S V, Domashevskaya E P et al. Eur Phys J AP[J], 2009, 48: 10 603

14 Yu Feng, Wang Peiji, Zhang Changwen. Acta Physica Sinica[J], 2010, 59: 7285 15 Chatelon J P, Terrier C, Roger J A. Semiconduct Sci[J], 1999, 14: 642

13 Rahman G, Victor M, Garcia S. APPL [J], 2010, 96: 052 508

2414