Effects of strain on electronic properties of monolayer α-Fe2O3

Accepted Manuscript Effects of strain on electronic properties of monolayer α-Fe2O3 Changmin Shi, Li Chen, Dongchao Wang, Hongmei Liu, Guangliang Cui, Lijie Qiao PII:

S1567-1739(16)30038-4

DOI:

10.1016/j.cap.2016.02.008

Reference:

CAP 4169

To appear in:

Current Applied Physics

Received Date: 19 January 2016 Revised Date:

26 February 2016

Accepted Date: 27 February 2016

Please cite this article as: C. Shi, L. Chen, D. Wang, H. Liu, G. Cui, L. Qiao, Effects of strain on electronic properties of monolayer α-Fe2O3, Current Applied Physics (2016), doi: 10.1016/ j.cap.2016.02.008. 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 proof before it is published in its final 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.

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ACCEPTED MANUSCRIPT

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Effects of strain on electronic properties of monolayer α-Fe2O3 Changmin Shi,a,* Li Chen,a Dongchao Wang,a Hongmei Liu,a Guangliang Cuia and Lijie Qiaob Institute of Condensed Matter Physics, Linyi University, Linyi 276000, China

b

Corrosion and Protection Center, Key Laboratory for Environmental Fracture (MOE), University

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a

of Science and Technology Beijing, Beijing 100083, China

Abstract

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Density functional theory was employed to study the strain-induced modification of

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electronic properties of advanced monolayer α-Fe2O3 for the first time. Theoretical results indicated that there was obvious dependency of band structure on strain. The band gap modulation could reach up to -29.0% for 7% compressive strain and to 10.6% for 7% tensile strain. The analytical results of fat-band structures demonstrated

orbital.

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that the considerable modulation range of band gaps was mainly caused by the Fe-dz2

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Keywords: Monolayer α-Fe2O3; Strain-engineering; Electronic properties

* Corresponding author. E-mail: [email protected]; [email protected]

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ACCEPTED MANUSCRIPT 1. Introduction Hematite α-Fe2O3, is an n-type metal oxide with an accepted experimental band gap of approximately 2.0 eV.[1-3] Considering the advantages of multi-functions, high

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stability, pollution-free and low cost, metal oxide α-Fe2O3 have been extensively investigated for next-generation electronic devices and advanced materials in different kinds of fields, such as lithium batteries, gas sensors, catalysts, magnetic devices and

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pigments.[4-17] In order to improve the performance of α-Fe2O3 materials in

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multi-fields, a number of nanostructure materials based on α-Fe2O3 semiconductor have been designed, including spindle nanoparticles, hollow spheres, nano-rods, nano-wires, nano-tubes, nano-belts, nano-rices, nano-spheres and nano-rings.[18-35] Inspired by graphene,[36, 37] two-dimensional (2D) monolayer nano-materials,

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such as metal oxides, metal sulfides and so on,[38-46] have been the focus of recent research efforts. These monolayer nano-materials provide a new pathway for creating high-performance devices and advanced materials. Reports have proved that the

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electronic and magnetic properties are extremely sensitive to their dimensionality.[47,

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48] Therefore, it is highly desired to prepare monolayer α-Fe2O3 materials with fascinating physical and chemical properties, although it has not yet been synthesized experimentally.

It has been extensively verified that strain is an effective strategy to modify the

band structures of Si-nanowire materials, WSe2-multilayer materials, group-III nitrides materials and silicon materials.[49-52] Therefore, the electronic properties of monolayer α-Fe2O3 materials with and without strain are investigated using density 2

ACCEPTED MANUSCRIPT function theory (DFT) method in this paper. Two optimized structures are contrasted to investigate the stability of monolayer α-Fe2O3 materials. Following this, strain is induced into monolayer α-Fe2O3 nano-materials to modulate its electronic properties.

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The theoretical results demonstrate that there is obvious dependency of band structure on strain. The modulation range of band gaps can reach to -29.0% for 7% compressive strains and to 10.6% for 7% tensile strains. Strain is seen as a practical,

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convenient and economical strategy for modulating monolayer α-Fe2O3 materials’

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band structures in a wide range. The analytical results of fat-band structures demonstrate that the considerable modulation range of band gaps is mainly caused by the Fe-dz2 orbital. Monolayer α-Fe2O3 materials (with and without lattice strain) are found to be significant for creating next-generation high-performance electron devices

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and advanced materials.

2. Theoretical methods and models

The density functional theory (DFT) calculations were performed using the Vienna

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ab initio simulation package (VASP) code,[53, 54] with the projector augmented

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wave (PAW) pseudo-potential. For transition metal or lanthanide compounds with localized d or f electrons, the electron-electron exchange and correlation energies would be described incorrectly by the generalized gradient approximation pseudo-potential with Perdew-Burke-Ernzerhof (GGA-PBE) formulation. The GGA + Ueff methods, adding an on-site coulomb repulsion, could improve the description of localized d or f electrons.[55] The hexagonal structure α-Fe2O3 with space group R-3c was employed for this 3

ACCEPTED MANUSCRIPT research. Its crystal structure parameters derived from experiment,[56] a = b = 5.0351Å, c = 13.7581Å and α = β = 90°, γ = 120°. The atomic fractional coordinates were Fe (0.0000, 0.0000, and 0.3553) and O (0.3062, 0.0000, and 0.2500). Its

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primitive cell was simulated with the cutoff energy of 400eV and k points of 8 × 8 × 4 grid based on Monkhorst-Pack scheme. The convergence criterion energy was 1.0 × 10-5 eV/atom in the process of geometry optimization. Primitive geometry structure of

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hexagonal α-Fe2O3 were optimized with conjugate-gradient algorithm[57]; the

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optimized structure was shown in Fig 1(a). Two different monolayer α-Fe2O3 structures were cleaved from (0 0 1) surface of bulk α-Fe2O3: (1) Fe-O3-Fe monolayer structure labeled M1, as shown in Fig 2(a) and Fig 2(b); (2) Fe-Fe-O3 monolayer structure labeled M2, as shown in Fig 2(c) and Fig 2(d). Then, a 10Å vacuum layer

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was added to the c-parameter of the bulk α-Fe2O3 to simulate the monolayer α-Fe2O3 structure. Following this, the two different monolayer α-Fe2O3 structures were optimized with the cutoff energy of 400eV, convergence criterion energy of 1.0 ×

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10-5eV/atom and k points of 21 × 21 × 1 grid based on Monkhorst-Pack scheme.

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Same criteria were applied when strains were applied to the monolayer α-Fe2O3 structure. The valence-electron distributions of monolayer α-Fe2O3 structures with and without lattice strain were analyzed by the program code of Bader Charge Analysis.[58-60]

3. Results and discussion In this paper, the strain is applied by adjusting its lattice constant. Compressive strain is represented by a decrease of lattice constant, and the tensile strain is 4

ACCEPTED MANUSCRIPT represented by an increase of lattice constant. The strain is described as: δ = (L L0)/L0, where L and L0 represent the lattice constant with and without strain, respectively. With this definition, a positive value indicates a tension strain along the

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axis. G-type anti-ferromagnetic (AFM) ordering have been confirmed as the ground state of bulk α-Fe2O3.[61] Therefore, the band structure of bulk α-Fe2O3 with G-type AFM

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ordering is calculated and shown in Fig 1(b). The band structure prove that bulk

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α-Fe2O3 material’s band gap is 2.017eV (Egap = ECBM - EVBM) in theory, when the on-site effective Ueff = U - J = 4.5eV. This result is consistent with the experimental value.[1-3] The theoretical band structure also reveals that the hexagonal structure of α-Fe2O3 is an indirect band-gap semiconductor.

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After optimization, the monolayer α-Fe2O3 structure with Fe-Fe-O3 (M2 mode) reconstructs and transforms to monolayer α-Fe2O3 structure with Fe-O3-Fe (M1 mode, see Fig 2) for strains δ = -7%, 0% and 7%. The results demonstrate that monolayer

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α-Fe2O3 structure with Fe-Fe-O3 is extremely unstable and hence difficult to

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synthesize. Without strain, the calculated total energy of monolayer α-Fe2O3 structure in M1 mode with AFM ordering is lower than that of with FM ordering, about 0.818eV, while the total energy of monolayer α-Fe2O3 in M1 mode with AFM ordering is about 1.192eV (0.789eV) lower than that of with FM ordering for 7% compressive (tensile) strain. The results demonstrate that the ground state of monolayer α-Fe2O3 remains Fe-O3-Fe structure with AFM ordering for 7% compressive (tension) strain. Therefore, the optimized Fe-O3-Fe monolayer α-Fe2O3 5

ACCEPTED MANUSCRIPT with AFM ordering is employed for further research or investigation with and without strains. After relaxation of monolayer α-Fe2O3 structure, the intra-layer distance (D) is

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0.830Å, smaller than that of in bulk (1.688Å). Fig 2(e) depicts the variation of intra-layer distance with lattice strains from -7% to 7% for monolayer α-Fe2O3 structure. Simulated sample structures of monolayer α-Fe2O3 structures with different

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lattice strains are also inserted into Fig 2(e), such as (f) -6%, (g) -3%, (h) 0%, (i) 3%

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and (j) 6%. As shown in Table1 and Fig 2(e), the intra-layer distance increases with an increase of compressive strain, while the intra-layer distance decreases with the increasing tensile strain. The modulation range of intra-layer distance D can reach to 58.2% and -94.1% for 7% compressive strains and 7% tensile strains, respectively.

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(Modulation range is described as: (D-D0)/D0, where D and D0 represents the intra-layer distance with and without lattice strain). Fig 3(a) shows the unrelaxed and relaxed Fe-O bond lengths of monolayer α-Fe2O3

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structures with lattice strains from -7% to 7%. The optimized bond lengths of Fe-O

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bond decrease with the increasing compressive strain and increase with the increasing tensile strain. As shown in Table 1, the optimized bond lengths of Fe-O bond with compressive strain are obviously larger than unrelaxed bond lengths of Fe-O bond, with a very minor modulation range about -0.7% for 7% compressive strains. However, the optimized Fe-O bond lengths with tensile strains are smaller than those of without relaxation. It also had a very minor modulation range about 0.5% for 7% tensile strains. The variation of Fe-O bond lengths with strains from -7% to 7% can be 6

ACCEPTED MANUSCRIPT described as: dFe-O = -0.523 δ2 + 0.158 δ + 1.775

(1)

Program code of Bader Charge Analysis is employed to analyze the magnetic

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moments and valence-electrons distributions of monolayer α-Fe2O3 structures with different lattice strains from -7% to 7%. The number of valence-electrons on each atom labeled as Fig. 3(b) is listed in Table 2. The valence-electrons distributed on Fe1

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and Fe2 ions are equal with same lattice strain. However, the valence-electrons

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distributed on O1, O2 and O3 ions exhibit an unequal state with same lattice strain. Fig. 3(b) shows the dependences of average number of valence-electrons on Fe and O ions with lattice strains for monolayer α-Fe2O3 structures. The modulation of the average number of valence-electrons on one Fe ion for 7% compressive (tensile)

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strain was only 1.1% (0.7%), while for one O ion the corresponding modulation was 0.6% (0.4%) for 7% compressive (tensile) strain. The variation of average number of valence-electrons on Fe ions with strains from -7% to 7% can be described as: CFe = -1.231 δ2 + 0.528 δ + 7.152

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(2)

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while for O ions with strains from -7% to 7%, the polynomial can be rewritten as: CO = 1.862 δ2 – 0.792 δ + 6.272

(3)

However, the valence ratios of Fe ion to O ion in monolayer α-Fe2O3 structures was identically equal to 3/2 with different lattice strains from -7% to7%. According

to

Pauling’s

electronegativity

scale,[62]

the

difference

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electronegativity between oxygen and iron is equal to 1.61, closing to 1.7. Therefore, the Fe-O bonds in hematite α-Fe2O3 semiconductor exhibit minor ionic character and 7

ACCEPTED MANUSCRIPT major covalent character. With an increase of tensile strain, the increasing Fe-O bond lengths (see Fig. 3(a)) lead to an increasing ionicity of Fe-O bond. Owing to the stronger attraction of oxygen than iron, more electrons shared by Fe and O ions will

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be pulled to O ion. Therefore, the average number of valence-electrons on one Fe ion decreases and the average number of valence-electrons on one O ion increases with the increasing tensile strain. However, the decreasing Fe-O bond lengths caused by

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compressive strains (see Fig. 3(a)) lead to a decreasing ionicity of Fe-O bond. Then,

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fewer electrons will be attracted by O ion. The results lead to the average number of valence-electrons on one Fe ion increases and the average number of valence-electrons on one O ion decreases with the increasing compressive strain. In addition, the magnetic moments on Fe1 and Fe2 ions are also calculated in

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monolayer α-Fe2O3 structures with AFM ordering for lattice strains from -7% to 7%. The absolute values of magnetic moments on Fe1 and Fe2 ions are equal, as listed in Table 1 and shown in Fig 3(c). The variation of magnetic moments on Fe ions with

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strains from -7% to 7% can be described as: (4)

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M = 1.429×101 δ3 – 2.228 δ2 + 0.709 δ + 3.972

From the results of charge analysis, we know that the number of valence-electrons distributed on one Fe ion is greater than five. Five electrons are in spin-up states and others are in spin-down states, according to Hund’s rule. With an increase of compressive strain, few valence-electrons transfers to Fe ion (see Fig.3 (b)) and fills in the d orbit with spin-down states. Therefore, the absolute values of magnetic moments on Fe ion decrease slightly. With an increase of tensile strain, some 8

ACCEPTED MANUSCRIPT valence-electrons with spin-down states deviate from d orbit of Fe ion to O ion (see Fig.3 (b)). The results imply that the absolute values of magnetic moments on Fe ion increase slightly. However, the modulation range of magnetic moments on one Fe ion

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is only -1.6% and 1.1% for 7% compressive strains and 7% tensile strains, respectively.

The band gap of optimized monolayer α-Fe2O3 structure without lattice strain is

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1.828eV, which is about 0.189eV lesser than that of bulk α-Fe2O3 structure. As shown

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in Fig. 3 (d), the band gaps are 1.297eV, 1.420eV, 1.526eV, 1.606eV, 1.676eV, 1.735eV, 1.784eV, 1.828eV, 1.865eV, 1.897eV, 1.916eV, 1.954eV, 1.978eV, 1.998eV and 2.022eV for lattice strains from -7% to 7%, respectively. With an increase of compressive strain, the band gaps decrease. However, the band gaps of monolayer

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α-Fe2O3 structure increase with the increasing tensile strain, as shown in Fig. 3 (d). The variation of band gaps with strains from -7% to 7% can be described as: Egap = 2.665×102 δ3 – 3.380×101 δ2 + 3.867 δ + 1.830

(5)

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The modulation range of band gaps can reach to -29.0% and 10.6% for 7%

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compressive strains and 7% tensile strains, respectively. The obvious variation caused by strain proves that it is an effective strategy to modulate the band gaps of monolayer α-Fe2O3 structures. It provides theoretical guidance for creating high-performance electron devices and advanced materials. Fig. 4 shows the band structures of monolayer α-Fe2O3 with different lattice strains, such as (a) -6%, (b) -3%, (c) 0%, (d) 3% and (e) 6%. The theoretical band structures imply that the monolayer α-Fe2O3 structures with lattice strains within the range (-7% to 7%) are still an indirect 9

ACCEPTED MANUSCRIPT band-gap semiconductor like bulk α-Fe2O3 structures. Fig. 5 shows the fat-band structures of monolayer α-Fe2O3 structure without lattice strain.[63, 64] Different sized symbols are given to represent the weights of

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corresponding atomic partial orbitals: (a) shows the O-px orbital; (b) shows the O-py orbital; (c) shows the O-pz orbital; (d) shows the Fe-dz2 orbital; (e) shows the Fe-dx2-y2 orbital; (f) shows the Fe-dxy orbital; (g) shows the Fe-dxz orbital; (h) shows

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the Fe-dyz orbital. As shown in Fig. 5, the conduction band is occupied by Fe-dz2

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orbital. While the valence band is occupied by majority of O-px, O-py orbitals and minority of Fe-dx2-y2 orbital (see Fig. 5 (a), (b) and (e)). The theoretical results imply that there is strong interaction and hybridization between Fe ion and O ion in monolayer α-Fe2O3 structure. The interaction and hybridization mainly come from: (1)

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O-px orbital and Fe-dx2-y2 orbital; (2) O-py orbital and Fe-dx2-y2 orbital. The valence-electrons distributed on the Fe-dz2 orbital become more localized with an increase of tensile strain, as shown in Fig. 4 and Fig. 5. The variation range of

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Fe-dz2 orbital is only about 0.063eV for 7% tensile strain. The localized Fe-dz2 orbital

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in the LUMO shifted to high energy resulting in a larger band gap. In addition, the valence-electrons distributed on the Fe-dz2 orbital become more far-ranging with an increase of compressive strain. Its variation range for Fe-dz2 orbital could reach to 0.773eV for 7% compressive strains. The far-ranging Fe-dz2 orbital lead to the LUMO shifted to low energy and, then a smaller band gap. The localized level of Fe-dz2 orbital (conduction band) has a crucial influence on the LUMO and band gaps of monolayer α-Fe2O3 structures with and without lattice strains. 10

ACCEPTED MANUSCRIPT 4. Conclusions In this paper, we employed density functional theory method to investigate the modification of electronic properties in advanced monolayer α-Fe2O3 materials for the

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first time. Theoretical results proved that there was strong dependence of band structures of monolayer α-Fe2O3 on strain. The intra-layer distance and average number of valence-electrons on Fe ion decreased with the strains from -7% to 7%.

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While the optimized Fe-O bond lengths, average number of valence-electrons on O

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ion, magnetic moments on Fe ion and optimized band gaps increased with the strains from -7% to 7%. The analytical results of fat-band structures demonstrated that the variation of band gaps was mainly caused by the Fe-dz2 orbital. The localized level of Fe-dz2 orbital (conduction band) decided the α-Fe2O3 monolayer’s LUMO and band

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gaps. Theoretical results proved strain was a practical, economical and effective strategy for modulating the α-Fe2O3 monolayer’s band gaps. The modulation range of band gaps for monolayer α-Fe2O3 materials could reach to -29.0% for 7%

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compressive strains and to 10.6% for 7% tensile strains.

Acknowledgments

This work was supported by National Natural Science Foundation of China (Nos. 51431004, 11274151, 11204120 and 11404158) and Key Disciplines of Condensed Matter Physics of Linyi University.

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[63] O. Jepsen, O. Andersen, Z. Phys. B 97 (1995) 35-47. [64] J. Rondinelli, N. Spaldin, Phys. Rev. B 81 (2010) 085109.

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Figure captions Fig 1 The optimized (a) geometry structure and (b) band structure of bulk α-Fe2O3.

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The blue (big) and red (small) balls represented Fe and O atoms, respectively. Fig 2 The (a)/(c) top view and (b)/(d) side view of monolayer α-Fe2O3 with Fe-O3-Fe/Fe-Fe-O3 structures. (e) The intra-layer distance dependence of lattice

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strains from -7% to 7% and parts of monolayer α-Fe2O3 structures with different

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strains: (f) -6%, (g) -3%, (h) 0%, (i) 3% and 6%. The blue (big) and red (small) balls represented Fe and O atoms, respectively.

Fig 3 The dependences of (a) Fe-O bond lengths, (b) average numbers of valence-electrons on Fe and O ions, (c) magnetic moments on one Fe ion and (d) band

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gaps on strains from -7% to 7%. The blue (big) and (small) red balls represented Fe and O atoms, respectively.

Fig. 4 The band structures of monolayer α-Fe2O3 with (a) -6%, (b) -3%, (c) 0%, (d)

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3% and (e) 6% strains.

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Fig. 5 The partial orbitals of Fe ions and O ions: (a) O-px orbital; (b) O-py orbital; (c) O-pz orbital; (d) Fe-dz2 orbital; (e) Fe-dx2-y2 orbital; (f) Fe-dxy orbital; (g) Fe-dxz orbital; (h) Fe-dyz orbital.

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ACCEPTED MANUSCRIPT Table 1. The calculated results of monolayer α-Fe2O3 structures with lattice strains from -7% to 7%: D was the intra-layer distance, d0 was the unrelaxed Fe-O bond lengths, d was the relaxed Fe-O bond lengths and M was magnetic moments on Fe ion. D (Å)

d0 (Å)

d (Å)

M (µ B)

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

1.313 1.252 1.177 1.120 1.054 0.981 0.911 0.830 0.752 0.669 0.592 0.492 0.405 0.230 0.049

1.658 1.675 1.691 1.708 1.725 1.742 1.758 1.775 1.792 1.809 1.826 1.842 1.859 1.876 1.893

1.762 1.764 1.766 1.768 1.770 1.773 1.774 1.775 1.777 1.778 1.780 1.781 1.782 1.783 1.784

3.907 3.919 3.929 3.939 3.949 3.958 3.965 3.972 3.979 3.986 3.992 3.998 4.004 4.010 4.016

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ACCEPTED MANUSCRIPT Table 2. The calculated numbers of valence-electrons distributed on each ion for monolayer α-Fe2O3 structures with different lattice strains from -7% to 7%. Oavg was the average valence-electrons on one O ion. Fe1 (e)

Fe2 (e)

O1 (e)

O2 (e)

O3 (e)

Oavg (e)

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

6.3377 6.3257 6.3142 6.3040 6.2980 6.2934 6.2778 6.2715 6.2662 6.2576 6.2470 6.2424 6.2357 6.2323 6.2260

6.3377 6.3257 6.3142 6.3040 6.2980 6.2934 6.2778 6.2715 6.2662 6.2576 6.2470 6.2424 6.2357 6.2323 6.2260

7.1168 7.1146 7.1228 7.1306 7.1356 7.1386 7.1535 7.1529 7.1559 7.1616 7.1734 7.1717 7.1792 7.1763 7.1816

7.1091 7.1076 7.1162 7.1238 7.1297 7.1325 7.1488 7.1489 7.1523 7.1580 7.1698 7.1683 7.1764 7.1745 7.1777

7.0987 7.1264 7.1327 7.1376 7.1387 7.1420 7.1420 7.1553 7.1594 7.1651 7.1627 7.1752 7.1730 7.1846 7.1887

7.1082 7.1162 7.1239 7.1307 7.1347 7.1377 7.1481 7.1524 7.1559 7.1616 7.1683 7.1717 7.1762 7.1785 7.1827

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ACCEPTED MANUSCRIPT ► Band gaps of monolayer α-Fe2O3 can be effectively modulated by strain ►The localized level of Fe-dz2 orbital decides the band gap of monolayer α-Fe2O3

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►Fat-band proved hybridization come from O-px/O-py orbital and Fe-dx2-y2 orbital