Sn1−xTixS2 ternary alloys: A new visible optical material

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ScienceDirect Acta Materialia 72 (2014) 223–228 www.elsevier.com/locate/actamat

Sn1xTixS2 ternary alloys: A new visible optical material Congxin Xia a,b,⇑, Jiao An a, Tianxing Wang a, Shuyi Wei a, Yu Jia b b

a Department of Physics, Henan Normal University, Xinxiang, Henan 453007, People’s Republic of China International Laboratory for Quantum Functional Materials of Henan, Zhengzhou University, Zhengzhou, Henan 450001, People’s Republic of China

Received 5 January 2014; received in revised form 13 March 2014; accepted 17 March 2014

Abstract Based on density functional theory, the electronic structures and optical properties of Sn1xTixS2 ternary alloys are investigated. Numerical results show that the band gap values of Sn1xTixS2 ternary alloys decrease from 1.926 to 1.27 eV with increasing Ti concentration (0 < x 6 0.0625), resulting in an obvious increase in optical absorption in the visible range. Moreover, the static dielectric constant is increased when the Ti concentration is increased in the Sn1xTixS2 ternary alloys. These results indicate that the Sn1xTixS2 ternary alloys with a tunable band gap may serve as a new promising candidate for visible optical absorbers. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Sn1xTixS2; Electronic structures; Optical properties

1. Introduction As the global demand for energy grows inexorably, solar energy is attracting increasing interest due to its abundant, clean and renewable characteristics. Among the present photovoltaic devices, the first-generation crystalline silicon based solar cells have reached an efficiency of more than 23%, but their further development and widespread applications have been limited due to the low optical absorption coefficient and high cost of fabrication [1–3]. Although CdTe and CuInGa(S/Se)2 based solar cells have solar conversion efficiencies of up to 16.5% and 20.3%, respectively [4–6], these materials contain the toxic element Cd, and the expensive, low-abundance heavy elements In and Te [7]. In addition, a high value for solar conversion efficiency devices has been reported by using the multi-junction tandem cell approach in III–V semiconductors [8]. Recent studies also show that GaInNAs quantum well lasers have ⇑ Corresponding author at: Department of Physics, Henan Normal University, Xinxiang, Henan 453007, People’s Republic of China. Tel.: +86 371 67739336. E-mail address: [email protected] (C. Xia).

superior lasing characteristics and low threshold devices [9,10], and this progress has recently resulted in a 43.5% solar conversion efficiency [11]. More recently, abundance and low toxicity have been considered to be major criteria for new photovoltaic absorber materials. Among the studied absorber materials, the quaternary Cu2ZnSnS4 is such a promising material, allowing the fabrication of efficient solar cells [12], but its stability along with the presence of secondary phases is detrimental to solar cells [13–15]. Therefore, simpler binary and ternary abundantly occurring absorbers, such as SnS [16] and FeS2 [17], have attracted renewed interest within the photovoltaic community. In this work, our interest will focus on the abundant and environmentally friendly semiconductor material SnS2, which has attracted intensive interest due to its wide band gap value of 2.0 eV [18,19]. More recently, to investigate the optoelectronic properties of SnS2, different research groups have carried out a great many studies. For example, Chen et al. investigated the optical properties of SnS2 nanostructures [20]. The SnS/SnS2 and SnO2/SnS2 heterostructures were suggested to be good for the visible light

http://dx.doi.org/10.1016/j.actamat.2014.03.042 1359-6454/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

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photocatalytic activities [21–23]. In addition, V-doped SnS2 was studied as a new intermediate band material to better exploit the solar spectrum [24]. De et al. also studied the possibilities of high on/off ratio field effect transistors based on SnS2 nanomembranes [25]. These studies show that SnS2 materials will have promising applications in optoelectronics devices. In addition, it is well known that good solar cell absorbers should meet the criteria for solar cell applications: band gaps close to the optimal single-junction value of 1.5 eV and high optical absorption of 1  104 cm1. However, to our knowledge, there are no related published papers in which the optimal band gap value of 1.5 eV is achieved by doping the SnS2 host material. Thus, in order to utilize sunlight effectively, it is imperative to find an efficient way to modify the electronic structures and band gap values of SnS2. Moreover, defect states should also be avoided in SnS2-based semiconductor alloys because defects may become a center of electron–hole recombination, which affects the properties of solar cell devices. Thus, based on the above ideas, the isovalent cationic and anionic dopants should be considered in the SnS2 host material. In the following, we will study for first time the structural, electronic and optical properties of Sn1xTixS2 ternary alloys by using first-principles calculations based on density functional theory (DFT). This is because SnS2 and TiS2 compounds have an isostructural phase with the hexagonal close-packed (hcp) CdI2-type structure and similar lattice constants, and TiS2 has a band gap of 0.30 eV [26]. The obtained results show that the band gap of SnS2 decreases obviously when Ti concentration increases without producing defect states within the band gap, which result in an obvious increase in the optical absorption edge in the visible range. 2. Computational methods All the calculations performed in this work are based on the DFT method as implemented in the Vienna Ab Initio Simulation Package [27]. The exchange-correlation functional is treated within the generalized gradient approximation (GGA) and parameterized by the Perdew– Burke–Ernzerhofer (PBE) formula [28]. A projected augmented wave (PAW) potential [29] is employed to describe the electron–ion potential and a kinetic energy cutoff of 400 eV is selected for the plane wave expansion. The valence electron configurations considered in this study are Sn (4d105s25p2), Ti (3d24s2) and S (3s23p4). In order to compare the band structures with the experimental measurements, we consider more precisely the effect of the on-site Coulomb repulsion of Sn-4d and Ti-3d electrons, and the exchange-correlation energy is treated by the GGA+U approach used by Dudarev et al. [30]. Moreover, U = 9 eV and U = 3.5 eV are chosen for Sn-4d and Ti-3d electrons according to the calculated band gap values for SnS2 and TiS2, respectively. Integrations over the first Brillouin zone are performed using Monkhorst–Pack k-point grid. The lattice vectors and atomic positions for

all considered structures are fully relaxed by minimizing the quantum mechanical stresses and forces. The convergence for energy is chosen as 105 eV between two steps. Structural optimization is obtained when the Hellmann– ˚ –1. Feynman forces acting on each atom are <0.01 eV A In addition, for the characteristic layer-type lattice, the van der Waals interaction is considered by using Grimme’s DFT-D2 method [31]. 3. Results and discussions 3.1. Structural and electronic properties of pure SnS2 To check the applicability and accuracy of the GGA+U method and PAW potentials used in this work, the optimized lattice constants and electronic structures of pure SnS2 are investigated by calculating the total energies, density of states (DOS) and band structures. The modeled structure of pure SnS2 unit cell is an hcp CdI2-type layer structure, and the interlayer is weakly coupled by van der Waals forces. For the GGA+U method, the choice of U = 9 is chosen to optimize the values of the calculated band gap and the lattice con˚, stants. The optimized lattice constants (a = 3.518 A ˚ ) are in excellent agreement with experimental c = 5.844 A ˚ , c = 5.899 A ˚ ) [32]. In addition, Fig. 1 values (a = 3.649 A also shows that the conduction band minimum (CBM) lies at the M point and the valence band maximum (VBM) is very close to the C point, which indicate that pure SnS2 host material is a indirect gap semiconductor with the band gap value of 1.926 eV. Moreover, Fig. 1b also shows that the VBM is composed of S-3p states, while the CBM consists predominantly of the mixtures between S-3p and Sn-5s states. Thus, the above calculated results justify our choice of the GGA+U method and the PAW potentials used throughout the following calculations. 3.2. Structural and electronic properties of Sn1xTixS2 ternary alloys In order to study the influence of Ti concentration on band structures and optical properties of Sn1xTixS2 ternary alloys, we use different SnS2 hosted supercells to simulate different Ti doping concentrations for the Sn1xTixS2 ternary alloys. The case of x = 0.037 can be obtained when one Sn atom is substituted by one Ti atom in the 81-atom 3  3  3 SnS2 supercell. The case x = 0.0556 can be modeled using one Ti atom substituting for one Sn atom in the 54-atom 3  3  2 SnS2 supercell. The case of x = 0.0625 can be modeled when one Sn atom is substituted by one Ti atom in the 48-atom 4  4  1 SnS2 superccell. The case of x = 0.1111 can be modeled using one Ti atom substituting one Sn atom in the 27-atom 3  3  1 SnS2 supercell. In addition, the case of x = 0.25 can also obtained by substituting one Ti atom with Sn in the 12-atom 2  2  1 SnS2 supercell.

C. Xia et al. / Acta Materialia 72 (2014) 223–228

225

6 4 2

Energy(eV)

0 -2

Total S-3s S-3p Sn-5s Sn-5p Sn-4d

-4 -6 -8 -10 -12 -14

Γ

Γ

M K

A

L

H

A

0

1

2

3

4

5

6

Density of states (States/eV) Fig. 1. The calculated band structures and density of states of pure bulk SnS2. The zero of energy is chosen as the highest occupied band.

In order to examine the availability of a Ti atom substituting for an Sn atom in SnS2, the formation enthalpy of Sn1xTixS2 ternary alloys is investigated by means of the equation DH f ¼ EðSn1x Tix S2 Þ  EðSnS2 Þ  nlTi þ nlSn , in which EðSn1x Tix S2 Þ and E(SnS2) are the total energies of Sn1xTixS2 and SnS2 with the same size supercell, respectively. The energies lTi and lSn denote the chemical potentials of bulk Ti and Sn atoms, respectively. The calculated formation enthalpies of Sn1xTixS2 ternary alloys are 2.1 eV for each considered Ti concentration case, which is due to the atomic radius of the Ti atom being very similar to that of the Sn atom. These results suggest that Sn1xTixS2 ternary alloys can be fabricated in experiments. We now turn to investigate the effects of Ti concentration on structural parameters and band structures of SnS2. Firstly, one can see from Fig. 2 that the optimized lattice constants do not change obviously when the Ti

6.0

a c

5.0

4 3

4.5

Energy (eV)

Lattice parameters

5.5

concentration increases in the Sn1xTixS2 ternary alloys. The reason is that the atomic radius of the Ti atom is very close to that of the Sn atom. Then, in order to understand the electronic structures of the Sn1xTixS2 ternary alloys, we present the energy band structures of Sn1xTixS2 (x = 0.1111) as one Ti composition example in Fig. 3. Numerical results show that for the Sn1xTixS2 ternary alloy, the CBM lies at the M point and VBM lies at the G point, which indicate that the Sn1xTixS2 ternary has an indirect band structure. For other Ti composition cases, our band structure calculations also show that the Sn1xTixS2 ternary alloy materials are indirect-band gap materials (not shown in this paper), which can be understood because SnS2 and TiS2 have the same structure types and indirect band structure characteristics. These results mean that in order to obtain optical absorption in Sn1xTixS2 alloys, the alloy must either absorb a phonon in addition to the photon, or emit another phonon after the absorption of the incoming photon. The phononassisted absorption of light is a fundamentally important optical process in the indirect band-gap semiconductors, which is also essential to photovoltaic solar conversion. Thus, the necessity of phonons for indirect interband

4.0

3.5 0.00

2 1 0 -1

0.05

0.10

0.15

0.20

0.25

x Fig. 2. The calculated lattice parameters a and c of the Sn1xTixS2 ternary alloys with different Ti contents.

-2

Γ

M K

Γ

A

L H

A

Fig. 3. The calculated band structures of the Sn1xTixS2 (x = 0.1111) ternary alloys. The zero of energy is chosen as the highest occupied band.

C. Xia et al. / Acta Materialia 72 (2014) 223–228

transitions will impose a significant constraint on the performance of the Sn1xTixS2-based solar cells, such as silicon. In another work, we will work on the optical transitions via phonon assistance to increase the probability of photon–phonon interaction in the indirect band gap Sn1xTixS2 material. In order to search the ideal band gap values for visible optical applications, in Fig. 4, the band gap values were investigated as a function of Ti doping concentration in the Sn1xTixS2 ternary alloys. We would like to point out that these band gap values are indirect band gap values for all Ti doping cases considered. Numerical results show that the band gap value is decreased monotonically when Ti concentration is increased in the Sn1xTixS2 ternary alloys, which indicates that Ti substituting for Sn can narrow effectively the band gap value of SnS2. Moreover, the energy gap values vary from 1.926 to 1.27 eV when the Ti content increases up to x = 0.0625 in the Sn1xTixS2 ternary alloys, which are optimal for the visible optical absorption for solar cells. In addition, we can also see from Fig. 4 that Sn1xTixS2 ternary alloy materials can address the band gap coverage from the visible up to the nearinfrared (NIR) spectral regime. For the studies of optical materials, the significant progress in both visible and NIR photonics materials has been attributed to the advances in both GaN-based [33,34] and InGaAs-based [35,36] material systems, respectively. To gain insight into the origin of the band-gap narrowing of SnS2 due to Ti atom substitution (Fig. 5), the total DOS and projected DOS are calculated as a function of photon energy for the Sn1xTixS2 ternary alloys with x = 0 and 0.0556. The zero of energy is chosen at the top of the occupied bands of the pure SnS2. One can see that after Ti substitution, the top of the valence bands is dominated by S-4p states, while the bottom of the conduction bands consists mainly of the hybridization of the Ti-3d, S-3p and Sn-5s states. Moreover, compared with the pure SnS2 case, the Ti doping can shift down the bottom of the conduction band, while it does not change obviously the valence band of pure SnS2. Thus, we can conclude that the downshift of the conduction band results in a decrease in the band gap of Sn1xTixS2 ternary alloys. As a result, these changes lead to a decrease of the threshold for photon excitation energy 2.0

Band gap (eV)

1.8 1.6 1.4 1.2 1.0 0.8 0.00

0.05

0.10

x

0.15

0.20

0.25

Fig. 4. The calculated band gap values as a function of Ti concentration x in the Sn1xTixS2 ternary alloys.

100 80 60 40 20 0 40

Density of states (States/eV)

226

pure SnS2

(a)

Sn1-xTixS2

pure SnS2 S-3p (b) Sn1-xTixS2 S-3p

20 0 15 10

Sn1-xTixS2

Ti-4s Ti-3d

(c)

Sn1-xTixS2

Sn-5s Sn-5p Sn-4d

(d)

Sn 5s Sn 5p Sn 4d

(e)

5 0 21 14 7 0 21

SnS2

14 7 0

-8

-6

-4

-2

0

2

4

6

8

Energy (eV) Fig. 5. The total and partial DOS of the pure SnS2 and Sn1xTixS2 (x = 0.0556) ternary alloys. The energy zero is set to the valence-band maximum of pure SnS2.

and induce more significant red shift of optical absorption in the visible light optics, which are beneficial to visible light optoelectronic devices applications. 3.3. Optical properties of Sn1xTixS2 ternary alloy It is well known that the optical absorption properties of solar cell absorbers are very important for photovoltaic devices. Thus, in this section, we will investigate the imaginary part e2(x) and real part e1(x) of the dielectric function eðxÞ ¼ e1 ðxÞ þ ie2 ðxÞ of Sn1xTixS2 ternary alloys, and then calculate its optical absorption coefficients considering different Ti concentrations x. The imaginary part e2 ðxÞ of the dielectric function could be calculated from the momentum matrix elements between the occupied and unoccupied wave functions with the selection rules, and the real part e1 ðxÞ of the dielectric function can be evaluated from the imaginary part by the Kramer–Kronig relationship: Z 4p2 e2 X dS k 2 ð1Þ e2 ðwÞ ¼ 2 2 jP nn0 ðkÞj m w nn0 rwnn0 ðkÞ Z 2 X w0 e2 ðw0 Þ 0 e1 ðwÞ ¼ 1 þ p dw ð2Þ p nn0 w02  w2 where P nn0 ðkÞ denotes the dipole matrix element, xnn0 ðkÞ is the energy difference between initial and final states, Sk is a constant of the surface energy and p represents the principal part of the integral. In addition, the optical absorption coefficient aðxÞ can be further obtained by using the above parameters as follows:

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aðxÞ ¼

 12 pffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2x e21 ðxÞ þ e22 ðxÞ  e1 ðxÞ

ð3Þ

In Fig. 6, we present the imaginary part e2 ðxÞ dispersions of Sn1xTixS2 ternary alloys with different Ti concentrations, considering different optical incident light polarization directions. Numerical results show that the imaginary parts e2 ðxÞ are anisotropic in the Sn1xTixS2 ternary alloys, as expected. The reason is that the hexagonal structure of Sn1xTixS2 ternary alloys leads to a difference in the dielectric responses between the x–y plane and the zdirection. It can also be seen from Fig. 6 that for the imaginary part of the spectra of pure SnS2, the threshold energy value occurs at 2.6 eV, which corresponds to the direct optical transition between the upper of the valence band and the lowest conduction band level at the M point. This is because the CBM lies at the M point; moreover, the top valence band energy level of the M point is slightly lower than that of VBM. Moreover, Fig. 6 also shows that the threshold energy values decrease with increasing Ti concentrations in the Sn1xTixS2 ternary alloys, which is due to the results of the decrease of the band gap of Sn1xTixS2 ternary alloys. In addition, one can also see from Fig. 6 that with increasing Ti concentration, the x–y plane imaginary part of the spectra of Sn1xTixS2 ternary alloys shows many more peaks than that of pure SnS2 in the 1.5–3.5 eV energy range, while the z-direction imaginary part structures exhibit little change. These results indicate Ti doping has much more obvious influences on the x–y plane optical properties of Sn1xTixS2 ternary alloys. As is also well known, the static dielectric constant e1 ð0Þ is the most important parameter of the real part e1 ðxÞ of the dielectric function, which may be related to the reflective index measured at a frequency above the lattice vibration frequencies. Thus, in order to understand well the real part e1 ðxÞ of the dielectric function of Sn1xTixS2 ternary alloys, in Fig. 7, the real part e1 ðxÞ of the dielectric function is investigated as a function of photon energy in the

Fig. 6. The imaginary part e2 ðxÞ of the dielectric function of the Sn1xTixS2 ternary alloys along the x–y plane and z-direction, considering different Ti concentrations.

227

Sn1xTixS2 ternary alloys, considering different Ti doping concentrations. Numerical results show that the real part e1 ðxÞ of the dielectric constants also presents anisotropy along the x–y plane and parallel to the z-axis directions. It is also clear from Fig. 7 that the real parts e1 ðxÞ of the dielectric function are zero at certain photon energies, and then they decrease to negative values. In addition, Fig. 7 also shows that the values of the static dielectric constants e1(0) are increased when the Ti concentration is increased in Sn1xTixS2 ternary alloys. Thus, we can conclude from Figs. 6 and 7 that the effects of a Ti atom substituting for an Sn atom are obvious on the dielectric function of Sn1xTixS2 ternary alloys. In order to further understand the optical absorption properties of Sn1xTixS2 ternary alloys, in Fig. 8, the optical absorption coefficients are investigated as a function of photon energy in the Sn1xTixS2 ternary alloys, considering different Ti doping concentrations. It can be seen from

Fig. 7. The real part e1 ðxÞ of the dielectric function of the Sn1xTixS2 ternary alloys along the x–y plane and z-direction, considering different Ti concentrations.

Fig. 8. The optical absorption coefficients as a function of photon energy along the x–y plane and z-directions of the Sn1xTixS2 ternary alloys, considering different Ti concentrations.

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Fig. 8 that the characteristics of the x–y plane and the z-direction optical absorption coefficients are different for each doping case considered, which further indicates that the optical absorptions are anisotropic in the Sn1xTixS2 ternary alloys. In addition, Fig. 8 also shows that after a Ti atom substitutes for an Sn atom in the SnS2 host, the red shift of the absorption edge occurs along both the x–y plane and the z-direction. Moreover, the decreases in band gap induce the increases in optical absorption strength (of 105 cm1) in the visible light activity range. These results are beneficial to solar energy applications, and indicate that Ti doping is an efficient way to tune the band gap to the visible optical application for abundantly occurring SnS2 materials. 4. Conclusion In conclusion, we have investigated in detail the electronic structures and optical properties of Sn1xTixS2 ternary alloys by means of first-principles calculations based on DFT. Our results show that the substitution of Ti atoms can cause a significant change in the band gap and optical absorption of SnS2. The band gap values of Sn1xTixS2 ternary alloys can be decreased from 1.926 to 1.27 eV when the Ti content increases up to x = 0.0625 in the Sn1xTixS2 ternary alloys, which results in an obvious increase of the visible optical absorption. Moreover, the influences of Ti content are much more obvious on optical properties along the x–y plane than that along the z-direction in the Sn1xTixS2 ternary alloys. In addition, the static dielectric constants are also increased when the Ti concentration is increased. These results are interesting and useful to understand the electronic structures and optical properties of Sn1xTixS2 ternary alloys. However, experimental studies for the Sn1xTixS2 ternary alloys are still lacking at present. We hope that these theoretical results may shed light on further experimental investigations of the Sn1xTixS2 ternary alloys as a low-cost optical material. Acknowledgments This research was supported by the National Natural Science Foundation of China under Grant No. U1304518 and National Basic Research Program of China under Grant No. 2012C13921300.

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