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Electron affinity and ionization potential of two-dimensional honeycomb sheets: A first principle study
Chemical Physics Letters 637 (2015) 26–31
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Electron affinity and ionization potential of two-dimensional honeycomb sheets: A first principle study Zexiang Deng, Zhibing Li, Weiliang Wang ∗ State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 16 June 2015 In final form 29 July 2015 Available online 5 August 2015
a b s t r a c t We perform first principle calculations based on density functional theory to study the electron affinity and ionization potential of two-dimensional structures of carbon family, group-III-nitride family and transition-metal dichalcogenide family. We found and explained the atomic number dependence of electron affinity and ionization potential. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Graphene has demonstrated the stability of the novel twodimensional (2D) honeycomb lattice structure [1,2]. However, the gapless energy band near the Fermi level makes it difficult for the applications in devices. Thus, in recent years, many groups pay more attentions to other similar 2D materials [3–7]. Among them, in the case of group IV elements, the graphenelike counterpart of silicon (Si), germanium (Ge) and stannum (Sn) is called silicene, germanene and stanene, respectively. Cahangirov [8] suggested that the low-buckled honeycomb of Si and Ge is stable. The calculations done by Houssa [9] have demonstrated that silicene can behave like graphene. Further experiments have been done by Vogt et al. [10], and Xu [11] who investigated 2D stannum films and found such films are quantum spin Hall (QSH) insulators with sizable bulk gaps of 0.3 eV. Das [12] presented calculations to show that cyclopentadienyl, adsorbed to Si and Ge surfaces, can exhibit spinning motion. The group-III-nitride (boron nitride (BN), aluminum nitride (AlN), gallium nitride (GaN) and Indium nitride (InN)) are very important materials in applications. The lattice mismatch between graphene and honeycomb BN is less than 2%. So the honeycomb BN could be ideal substrate for graphene [13], which can induce band gap in graphene. Many research groups have investigated the defects [14] and transition-metal doped 2D honeycomb AlN sheet or ribbon [15–17], and demonstrated the stability of infinite honeycomb structure of AlN by DFT calculations. Tang [18] have found that the surface effect, edge effects, and quantum size effect are
∗ Corresponding author. E-mail address: [email protected] (W. Wang). http://dx.doi.org/10.1016/j.cplett.2015.07.054 0009-2614/© 2015 Elsevier B.V. All rights reserved.
three important factors that alter the electronic properties of GaN nanoribbons. Another serial of important semiconductor is transition-metal dichalcogenide (TMX2 , TM = Mo, W, etc.; X = S, Se, etc.), which are potential materials for field effect transistor (FET) [19,20]. Although the bulk materials of them are indirect-gap, the monolayers of them are direct-gap [21], which makes them more attractive. Recently, obtaining single-layered MoS2 by mechanical exfoliation of multilayered MoS2 [22], the preparation of large-area graphene/MoS2 heterostructures [23] and the synthesis of a composite-layered MoS2 nanoflakes [24] became possible. It was reported that the FETs based on MoS2 via chemical vapor deposition (CVD) exhibited n-type behaviors with electron mobility up to 6 cm2 V−1 s−1 [20]. The work function (WF), electron affinity (EA) and ionization potential (IP) affect the band lineup at the heterstructures, which is important for device performance, and thus are key parameters in band engineering [25–27]. The work function of graphene is as large as graphite, around 4.56 eV [28,29]. Shi [30] demonstrated that graphene films can be used as thin transparent electrodes with tunable WF via chemical doping. Yu [31] reported tuning the graphene WF by electric field, and other groups have investigated the WF of carbon nanotube [32,33]. There is no complete study of EA and IP of these emerging 2D structures. This Letter reports the EA and IP (for semiconducting materials) of 2D honeycomb structure of carbon family (silicon, germanium and stannum), group-III-nitride family (boron nitride, aluminum nitride, gallium nitride and Indium nitride) and transition-metal dichalcogenide family (molybdenum disulfide, tungsten disulfide, molybdenum diselenide and tungsten diselenide). The WF of graphene is also listed for comparison. We have also calculated the phonon dispersion with linear response method, which demonstrated the stability of monolayer honeycomb structure of group III-nitride.
Z. Deng et al. / Chemical Physics Letters 637 (2015) 26–31
2. Calculation method First principle calculations based on density functional theory were performed with Vienna ab initio simulation package [34], using the projector-augmented-wave (PAW) potential. The exchange-correlation functional was treated using the Perdew–Wang91 (PW91) [35] generalized gradient approximation (GGA), Perdew–Burke–Ernzerhof (PBE) [36] GGA and Ceperly–Alder (CA) [37] local density approximation (LDA) [38], respectively. An energy cutoff of 500 eV was used in all calculations. The structure optimization was carried out until the forces on atoms fell below 0.001 eV/Å. The electronic convergence tolerance was set to10−6 eV. Monkhorst-Pack -centered k grid of 9 × 9 × 1 and 31 × 31 × 1 were used in optimization and static calculations, respectively. Vacuum slabs of 3.5 nm thick are inserted between neighboring 2D atom sheets. The WF, EA and IP are defined as WF = − εF , EA = − εC and IP = − εV , respectively, where is the vacuum level, εF is the Fermi level, εC is the conduction band minimum and εV is the valence band maximum. Usually the Fermi level locates between the valence band and the conduction band depending on the doping and the surface states. The vacuum level is determined from the potential in the vacuum slab where approaches a constant. 3. Monolayers of group IV elements It is reported that a low buckled configuration (Figure 1a) is essential for the stability of silicene (0.44 angstrom buckled displacement) [6,8,39], germanene (0.64 angstrom buckled displacement) [40] and stanene (0.86 angstrom buckled displacement) [41] except for graphene. In our calculations, the buckled displacements are found to be 0.45, 0.68, and 0.85 angstrom for silicene, germanene, and stanene, respectively. The phonon dispersion calculations show such configurations are stable [8,11]. The orbitals of planar graphene are sp2 hybridization with the bond angles exactly 120◦ . The bond angles of silicene, germanene and stanene were found to be between 111.2◦ and 116.4◦ (Figure 1b), which means that they are not pure sp2 hybridization, nor pure sp3 hybridization, but the sp2 /sp3 mixed hybridization. The bond angle of silicene is consistent with Ref. [42]. The bond angle decreases with the atomic number from Si to Sn. The projected
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density of states (PDOS) in Figure 2 indicates that the bands (those states near the Fermi level) of graphene consist of only pz orbitals, while those states near the Fermi level of silicene, germanene and stanene consist of other s and p orbitals which means the sp2 /sp3 mixed hybridization. The sp2 /sp3 mixed hybridization results in the buckled configuration. Table 1 lists the WF, IP and EA we obtained comparing with the results in literature. The IP and EA decreases for larger atoms with the increase of bond length and the decrease of bond angle from silicene to stanene. The system turns from sp2 hybridization into sp2 /sp3 mixed hybridization for larger atoms, which leaves one dangling bond for each atom in a honeycomb structure, which lifts the energy of the whole system, and thus lowers the IP and EA. The band structures of monolayer of group IV elements are shown in Figure 3. The bands near the Fermi level cross linearly at K point if the spin–orbital coupling is turned off. The spin–orbital coupling opens a gap. The gap is largest for stanene which is about 0.1 eV. The gap of stanene is close to Xu’s result [11]. 4. Monolayer honeycomb structure of group III-nitride The group III-nitride semiconductors are important materials [43–45]. AlN (6.2 eV) and GaN (3.4 eV) are wide gap [46,47] semiconductors, which are suitable for high temperature/high power electronic devices [47–50]. Hexagonal BN (h-BN) has the layered structure similar to that of graphene, which makes it a suitable substrate for graphene [13,45]. So the 2D monolayer of group III-nitride materials are worth a detailed study for both theory and practical applications. Figure 4 shows the phonon dispersion of monolayer honeycomb structure of BN, AlN, GaN, and InN. The result of BN agrees with Ref. [71]. There are three acoustical modes and three optical modes. One optical mode separates from the other two optical modes, and the separated gap gets larger for heavier atom mass. It is clear that the lowest-optical mode represents the relative movement of atoms in direction perpendicular to the atom plane. What is important is that there are no imaginary modes in all phonon dispersions, which makes us believe that the monolayer honeycomb structure is stable. A question is that why the monolayer group III-nitride does not have the buckled configuration. It is because that the nitrogen atoms are negatively charged and thus repel each other. The distance is largest in honeycomb
Figure 1. (a) Top view and side view of 2D honeycomb structure of carbon family (left panels), group III-nitride family (middle panels) and the triple layered transition-metal dichalcogenide family (right panels). The atoms in the middle layer in the side view of right panel are Mo or W atoms. (b) Buckled structure of silicene, germanene and stanene. The blue, red and green digits (from top to bottom) are the bond angles obtained with PW91, PBE and CA method respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
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Z. Deng et al. / Chemical Physics Letters 637 (2015) 26–31
Figure 2. The projected density of states (PDOS) of (a) graphene, (b) silicene, (c) germanene, and (d) stanene obtained with PBE including spin–orbital coupling. The red, blue, pink and green lines are the PDOS of pz , py , px , and s orbitals, respectively. The Fermi level is set at zero. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
Table 1 The WF of graphene, EA and IP of other 2D carbon family, of 2D group III-nitride family, and of 2D transition-metal dichalcogenide family (MoS2 , WS2 , MoSe2 and WSe2 ), the data in round brackets was obtained without spin–orbital coupling calculations (unit: eV).
WF
PW91 PBE LDA PW91 PBE LDA
Graphene
Silicene
Germanene
Stanene
4.61 4.56 4.56 ... ... ...
4.77(4.76) 4.74(4.72) 4.87(4.86) 4.74(4.76) 4.71(4.72) 4.85(4.86)
4.48(4.46) 4.60(4.57) 4.55(4.52) 4.44(4.46) 4.55(4.57) 4.50(4.52)
4.46(4.41) 4.39(4.35) 4.57(4.53) 4.37(4.41) 4.30(4.35) 4.50(4.53)
(WF)4.77(cal) [42] (WF)4.79(cal) [62] (WF)4.8(cal) [63] (WF)4.59(cal) [64]
(WF)3.27–5.12(cal) [65] a
IP
EA
(WF)4.56(exp) [28,29] (WF)4.49(cal) [42] (WF)4.27(cal) [51]
Ref.
BN
AlN
GaN
InN
IP
PW91 PBE LDA
5.89 5.84 5.89
5.40 5.31 5.52
5.37 5.30 5.33
4.93 4.86 4.94
EA
PW91 PBE LDA
1.25 1.12 1.28
2.17 2.24 2.22
3.38 3.34 3.24
4.44 4.43 4.27
(IP)3.45(cal) [51] (IP)4.90(cal) [52] (IP)5.86(cal) [64]
(EA)0.6(exp) [66]
(EA)2.7(exp) [66]
(WF)4.80–5.20(exp) [67]
Ref.
MoS2
WS2
MoSe2
WSe2
IP
PW91 PBE LDA
5.90(6.01) 5.82(5.94) 5.99(6.08)
5.57(5.80) 5.51(5.72) 5.59(5.81)
5.30(5.42) 5.23(5.35) 5.39(5.51)
4.87(5.20) 4.83(5.12) 4.92(5.29)
EA
PW91 PBE LDA
4.33(4.35) 4.23(4.25) 4.19(4.20)
3.95(3.97) 3.87(3.87) 3.76(3.78)
3.96(3.98) 3.88(3.89) 3.87(3.90)
3.64(3.65) 3.52(3.55) 3.60(3.62)
(WF)4.49(exp) [60] (WF)4.36–4.52(exp) [61] (EA)4.33(cal) [68] (IP)6.12 (cal) [68]
(WF)4.9–5.1(exp) [69] (EA)3.98(cal) [68] (IP)5.91(cal) [68]
(IP)5.45(cal) [70]
(EA)4.03(cal) [58] b (IP)5.19(cal) [58] b
Ref.
a b
The value range is the WF of Germanene on which a serial alkali, alkaline-earth, group III and 3d transition metal atom are absorbed. The values were calculated for 8-layers-WSe2 .
Z. Deng et al. / Chemical Physics Letters 637 (2015) 26–31
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Figure 3. Energy band structure of (a) graphene, (b) silicene, (c) germanene, and (d) stanene obtained with PBE method. The curves without (dash lines) and with (solid lines) spin–orbital coupling are magnified near K points. The Fermi level is set at zero.
without buckled configuration. It is the same for the group III elements atoms except that they are positively charged. Figure 5 shows that monolayer honeycomb structure of group III-nitride has indirect band gap. The results of BN and GaN agree with Ref. [72,73]. The results are the same when the spin–orbital coupling is turned on. Compared with graphene, the symmetry of the system is reduced due to the chemical inequivalence of the two atoms in the unit cell, and the band structure has a large gap at K point. The IP of monolayer honeycomb structure of group IIInitride decreases with the increasing atomic number of group III element atom (Table 1). The atom with heavier atom mass in the same family has weaker electronegativity, which is related to the IP. The band gap decreases with the increasing atomic number of group III element atom because larger atom is more metallic. The decrease of band gap somehow leads to the increase of EA (Table 1) with the increase of atomic number of group III element atom. The
numerical difference between our results and the experimental EA [66] (also listed in Table 1) may come from the substrates in experiments. The numerical results also can be improved by introducing exchange-correlation energy whose derivative of the density (or density matrix) with respect to the number of electrons is discontinued at integers [53,54]. 5. 2D structure of TMX2 TM stands for transition metal atom (Mo or W in this Letter), and X stands for S or Se in this Letter. The 2D TMX2 is a triple layer structure (right panel of Figure 1a). The bulk structure of TMX2 is a stacking of the 2D structure with van der Waals interactions between neighboring 2D structures [19–22,55]. The bulk TMX2 are indirect band gap semiconductors, while the 2D TMX2 have direct band gap, which is important for device application and makes the
Figure 4. Phonon dispersion of (a) 2D BN, (b) 2D AlN, (c) 2D GaN, and (d) 2D InN obtained with linear response theory. The cyan lines refer to the optical modes, the red, green and blue lines refer to the longitudinal acoustic (LA), transverse acoustic (TA) and z-direction acoustic (ZA) modes, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
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Z. Deng et al. / Chemical Physics Letters 637 (2015) 26–31
Figure 5. Energy band structure of (a) 2D BN, (b) 2D AlN, (c) 2D GaN, and (d) 2D InN obtained with PBE method. The Fermi level is set at zero.
Figure 6. Energy band structure of (a) 2D MoS2 , (b) 2D WS2 , (c) 2D MoSe2 , and (d) 2D WSe2 obtained with PBE method without (dash lines) and with (solid lines) spin–orbital coupling. The Fermi level is set at zero.
2D TMX2 more attractive. Splendiani and Lee have also reported the band gap variation with the number of layers [56,57]. Figure 6 shows that the 2D honeycomb triple layer of TMX2 has the similar band structure with each other. This is because they have the same 2D honeycomb structure and the similar outer electron structure. Another important feature is that they are all direct-gap, which makes them more suitable for microelectronic devices. When spin–orbital coupling is turned on, the top of valence band is raised at K point by 0.1–0.2 eV for MoX2 , and 0.3–0.4 eV for WX2 . The bottom of conduction band is not affected by the spin–orbital coupling. This result agrees with previous investigations of MoS2 done by Padilha who reported spin-orbital coupling mainly leads to a shift of the top of the valence band at K point [74]. Therefore the spin–orbital coupling plays an important role in IP but not in EA. Table 1 shows that the disulfide (TMS2 ) has larger EA and IP than that of diselenide (TMSe2 ), because of the
larger electronegativity of sulfur (S). Molybdenum (Mo) has larger electronegativity than that of tungsten (W), so the molybdenum disulfide (diselenide) has larger EA and IP than that of tungsten disulfide (diselenide). The band gap of TMX2 is sensitive to the number of layers and substrates [56,57]. The band gap of 8-layers-WSe2 is 1.16 eV in Ref. [58], which is much smaller than that (about 1.6 eV in this work, 1.56 eV in Ref. [59]) of single-layer WSe2 . 6. Conclusion We calculated the EA and IP of 2D honeycomb structure of carbon family, group-III-nitride family and transition-metal dichalcogenide family. We explained the reason for the buckled structure of 2D carbon family (silicene, germanene and stanene) and the planar structure of 2D group-III-nitride. The main results are: (1) 2D carbon family: silicene has the largest IP and EA, the IP
Z. Deng et al. / Chemical Physics Letters 637 (2015) 26–31
and EA decreases for larger atoms with the increase of bond length and the decrease of bond angle; (2) 2D group III-nitride: the IP (EA) decreases (increases) with the increasing atomic number of group III element atom, all atoms are in a plane; (3) 2D TMX2 : the EA and IP decrease with the increasing atomic number, the band gaps are almost the same. The spin–orbital coupling plays an important role in IP but not in EA. The physical reasons for these observations are discussed. Acknowledgements The project was supported by the National Basic Research Program of China (Grant No. 2013CB933601), National Natural Science Foundation of China (Grant No. 11274393), the Fundamental Research Funds for the Central Universities (No. 13lgpy34) and the high-performance grid computing platform of Sun Yat-sen University. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Electron affinity and ionization potential of two-dimensional honeycomb sheets: A first principle study Zexiang Deng, Zhibing Li, Weiliang Wang ∗ State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 16 June 2015 In final form 29 July 2015 Available online 5 August 2015
a b s t r a c t We perform first principle calculations based on density functional theory to study the electron affinity and ionization potential of two-dimensional structures of carbon family, group-III-nitride family and transition-metal dichalcogenide family. We found and explained the atomic number dependence of electron affinity and ionization potential. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Graphene has demonstrated the stability of the novel twodimensional (2D) honeycomb lattice structure [1,2]. However, the gapless energy band near the Fermi level makes it difficult for the applications in devices. Thus, in recent years, many groups pay more attentions to other similar 2D materials [3–7]. Among them, in the case of group IV elements, the graphenelike counterpart of silicon (Si), germanium (Ge) and stannum (Sn) is called silicene, germanene and stanene, respectively. Cahangirov [8] suggested that the low-buckled honeycomb of Si and Ge is stable. The calculations done by Houssa [9] have demonstrated that silicene can behave like graphene. Further experiments have been done by Vogt et al. [10], and Xu [11] who investigated 2D stannum films and found such films are quantum spin Hall (QSH) insulators with sizable bulk gaps of 0.3 eV. Das [12] presented calculations to show that cyclopentadienyl, adsorbed to Si and Ge surfaces, can exhibit spinning motion. The group-III-nitride (boron nitride (BN), aluminum nitride (AlN), gallium nitride (GaN) and Indium nitride (InN)) are very important materials in applications. The lattice mismatch between graphene and honeycomb BN is less than 2%. So the honeycomb BN could be ideal substrate for graphene [13], which can induce band gap in graphene. Many research groups have investigated the defects [14] and transition-metal doped 2D honeycomb AlN sheet or ribbon [15–17], and demonstrated the stability of infinite honeycomb structure of AlN by DFT calculations. Tang [18] have found that the surface effect, edge effects, and quantum size effect are
∗ Corresponding author. E-mail address: [email protected] (W. Wang). http://dx.doi.org/10.1016/j.cplett.2015.07.054 0009-2614/© 2015 Elsevier B.V. All rights reserved.
three important factors that alter the electronic properties of GaN nanoribbons. Another serial of important semiconductor is transition-metal dichalcogenide (TMX2 , TM = Mo, W, etc.; X = S, Se, etc.), which are potential materials for field effect transistor (FET) [19,20]. Although the bulk materials of them are indirect-gap, the monolayers of them are direct-gap [21], which makes them more attractive. Recently, obtaining single-layered MoS2 by mechanical exfoliation of multilayered MoS2 [22], the preparation of large-area graphene/MoS2 heterostructures [23] and the synthesis of a composite-layered MoS2 nanoflakes [24] became possible. It was reported that the FETs based on MoS2 via chemical vapor deposition (CVD) exhibited n-type behaviors with electron mobility up to 6 cm2 V−1 s−1 [20]. The work function (WF), electron affinity (EA) and ionization potential (IP) affect the band lineup at the heterstructures, which is important for device performance, and thus are key parameters in band engineering [25–27]. The work function of graphene is as large as graphite, around 4.56 eV [28,29]. Shi [30] demonstrated that graphene films can be used as thin transparent electrodes with tunable WF via chemical doping. Yu [31] reported tuning the graphene WF by electric field, and other groups have investigated the WF of carbon nanotube [32,33]. There is no complete study of EA and IP of these emerging 2D structures. This Letter reports the EA and IP (for semiconducting materials) of 2D honeycomb structure of carbon family (silicon, germanium and stannum), group-III-nitride family (boron nitride, aluminum nitride, gallium nitride and Indium nitride) and transition-metal dichalcogenide family (molybdenum disulfide, tungsten disulfide, molybdenum diselenide and tungsten diselenide). The WF of graphene is also listed for comparison. We have also calculated the phonon dispersion with linear response method, which demonstrated the stability of monolayer honeycomb structure of group III-nitride.
Z. Deng et al. / Chemical Physics Letters 637 (2015) 26–31
2. Calculation method First principle calculations based on density functional theory were performed with Vienna ab initio simulation package [34], using the projector-augmented-wave (PAW) potential. The exchange-correlation functional was treated using the Perdew–Wang91 (PW91) [35] generalized gradient approximation (GGA), Perdew–Burke–Ernzerhof (PBE) [36] GGA and Ceperly–Alder (CA) [37] local density approximation (LDA) [38], respectively. An energy cutoff of 500 eV was used in all calculations. The structure optimization was carried out until the forces on atoms fell below 0.001 eV/Å. The electronic convergence tolerance was set to10−6 eV. Monkhorst-Pack -centered k grid of 9 × 9 × 1 and 31 × 31 × 1 were used in optimization and static calculations, respectively. Vacuum slabs of 3.5 nm thick are inserted between neighboring 2D atom sheets. The WF, EA and IP are defined as WF = − εF , EA = − εC and IP = − εV , respectively, where is the vacuum level, εF is the Fermi level, εC is the conduction band minimum and εV is the valence band maximum. Usually the Fermi level locates between the valence band and the conduction band depending on the doping and the surface states. The vacuum level is determined from the potential in the vacuum slab where approaches a constant. 3. Monolayers of group IV elements It is reported that a low buckled configuration (Figure 1a) is essential for the stability of silicene (0.44 angstrom buckled displacement) [6,8,39], germanene (0.64 angstrom buckled displacement) [40] and stanene (0.86 angstrom buckled displacement) [41] except for graphene. In our calculations, the buckled displacements are found to be 0.45, 0.68, and 0.85 angstrom for silicene, germanene, and stanene, respectively. The phonon dispersion calculations show such configurations are stable [8,11]. The orbitals of planar graphene are sp2 hybridization with the bond angles exactly 120◦ . The bond angles of silicene, germanene and stanene were found to be between 111.2◦ and 116.4◦ (Figure 1b), which means that they are not pure sp2 hybridization, nor pure sp3 hybridization, but the sp2 /sp3 mixed hybridization. The bond angle of silicene is consistent with Ref. [42]. The bond angle decreases with the atomic number from Si to Sn. The projected
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density of states (PDOS) in Figure 2 indicates that the bands (those states near the Fermi level) of graphene consist of only pz orbitals, while those states near the Fermi level of silicene, germanene and stanene consist of other s and p orbitals which means the sp2 /sp3 mixed hybridization. The sp2 /sp3 mixed hybridization results in the buckled configuration. Table 1 lists the WF, IP and EA we obtained comparing with the results in literature. The IP and EA decreases for larger atoms with the increase of bond length and the decrease of bond angle from silicene to stanene. The system turns from sp2 hybridization into sp2 /sp3 mixed hybridization for larger atoms, which leaves one dangling bond for each atom in a honeycomb structure, which lifts the energy of the whole system, and thus lowers the IP and EA. The band structures of monolayer of group IV elements are shown in Figure 3. The bands near the Fermi level cross linearly at K point if the spin–orbital coupling is turned off. The spin–orbital coupling opens a gap. The gap is largest for stanene which is about 0.1 eV. The gap of stanene is close to Xu’s result [11]. 4. Monolayer honeycomb structure of group III-nitride The group III-nitride semiconductors are important materials [43–45]. AlN (6.2 eV) and GaN (3.4 eV) are wide gap [46,47] semiconductors, which are suitable for high temperature/high power electronic devices [47–50]. Hexagonal BN (h-BN) has the layered structure similar to that of graphene, which makes it a suitable substrate for graphene [13,45]. So the 2D monolayer of group III-nitride materials are worth a detailed study for both theory and practical applications. Figure 4 shows the phonon dispersion of monolayer honeycomb structure of BN, AlN, GaN, and InN. The result of BN agrees with Ref. [71]. There are three acoustical modes and three optical modes. One optical mode separates from the other two optical modes, and the separated gap gets larger for heavier atom mass. It is clear that the lowest-optical mode represents the relative movement of atoms in direction perpendicular to the atom plane. What is important is that there are no imaginary modes in all phonon dispersions, which makes us believe that the monolayer honeycomb structure is stable. A question is that why the monolayer group III-nitride does not have the buckled configuration. It is because that the nitrogen atoms are negatively charged and thus repel each other. The distance is largest in honeycomb
Figure 1. (a) Top view and side view of 2D honeycomb structure of carbon family (left panels), group III-nitride family (middle panels) and the triple layered transition-metal dichalcogenide family (right panels). The atoms in the middle layer in the side view of right panel are Mo or W atoms. (b) Buckled structure of silicene, germanene and stanene. The blue, red and green digits (from top to bottom) are the bond angles obtained with PW91, PBE and CA method respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
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Figure 2. The projected density of states (PDOS) of (a) graphene, (b) silicene, (c) germanene, and (d) stanene obtained with PBE including spin–orbital coupling. The red, blue, pink and green lines are the PDOS of pz , py , px , and s orbitals, respectively. The Fermi level is set at zero. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
Table 1 The WF of graphene, EA and IP of other 2D carbon family, of 2D group III-nitride family, and of 2D transition-metal dichalcogenide family (MoS2 , WS2 , MoSe2 and WSe2 ), the data in round brackets was obtained without spin–orbital coupling calculations (unit: eV).
WF
PW91 PBE LDA PW91 PBE LDA
Graphene
Silicene
Germanene
Stanene
4.61 4.56 4.56 ... ... ...
4.77(4.76) 4.74(4.72) 4.87(4.86) 4.74(4.76) 4.71(4.72) 4.85(4.86)
4.48(4.46) 4.60(4.57) 4.55(4.52) 4.44(4.46) 4.55(4.57) 4.50(4.52)
4.46(4.41) 4.39(4.35) 4.57(4.53) 4.37(4.41) 4.30(4.35) 4.50(4.53)
(WF)4.77(cal) [42] (WF)4.79(cal) [62] (WF)4.8(cal) [63] (WF)4.59(cal) [64]
(WF)3.27–5.12(cal) [65] a
IP
EA
(WF)4.56(exp) [28,29] (WF)4.49(cal) [42] (WF)4.27(cal) [51]
Ref.
BN
AlN
GaN
InN
IP
PW91 PBE LDA
5.89 5.84 5.89
5.40 5.31 5.52
5.37 5.30 5.33
4.93 4.86 4.94
EA
PW91 PBE LDA
1.25 1.12 1.28
2.17 2.24 2.22
3.38 3.34 3.24
4.44 4.43 4.27
(IP)3.45(cal) [51] (IP)4.90(cal) [52] (IP)5.86(cal) [64]
(EA)0.6(exp) [66]
(EA)2.7(exp) [66]
(WF)4.80–5.20(exp) [67]
Ref.
MoS2
WS2
MoSe2
WSe2
IP
PW91 PBE LDA
5.90(6.01) 5.82(5.94) 5.99(6.08)
5.57(5.80) 5.51(5.72) 5.59(5.81)
5.30(5.42) 5.23(5.35) 5.39(5.51)
4.87(5.20) 4.83(5.12) 4.92(5.29)
EA
PW91 PBE LDA
4.33(4.35) 4.23(4.25) 4.19(4.20)
3.95(3.97) 3.87(3.87) 3.76(3.78)
3.96(3.98) 3.88(3.89) 3.87(3.90)
3.64(3.65) 3.52(3.55) 3.60(3.62)
(WF)4.49(exp) [60] (WF)4.36–4.52(exp) [61] (EA)4.33(cal) [68] (IP)6.12 (cal) [68]
(WF)4.9–5.1(exp) [69] (EA)3.98(cal) [68] (IP)5.91(cal) [68]
(IP)5.45(cal) [70]
(EA)4.03(cal) [58] b (IP)5.19(cal) [58] b
Ref.
a b
The value range is the WF of Germanene on which a serial alkali, alkaline-earth, group III and 3d transition metal atom are absorbed. The values were calculated for 8-layers-WSe2 .
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Figure 3. Energy band structure of (a) graphene, (b) silicene, (c) germanene, and (d) stanene obtained with PBE method. The curves without (dash lines) and with (solid lines) spin–orbital coupling are magnified near K points. The Fermi level is set at zero.
without buckled configuration. It is the same for the group III elements atoms except that they are positively charged. Figure 5 shows that monolayer honeycomb structure of group III-nitride has indirect band gap. The results of BN and GaN agree with Ref. [72,73]. The results are the same when the spin–orbital coupling is turned on. Compared with graphene, the symmetry of the system is reduced due to the chemical inequivalence of the two atoms in the unit cell, and the band structure has a large gap at K point. The IP of monolayer honeycomb structure of group IIInitride decreases with the increasing atomic number of group III element atom (Table 1). The atom with heavier atom mass in the same family has weaker electronegativity, which is related to the IP. The band gap decreases with the increasing atomic number of group III element atom because larger atom is more metallic. The decrease of band gap somehow leads to the increase of EA (Table 1) with the increase of atomic number of group III element atom. The
numerical difference between our results and the experimental EA [66] (also listed in Table 1) may come from the substrates in experiments. The numerical results also can be improved by introducing exchange-correlation energy whose derivative of the density (or density matrix) with respect to the number of electrons is discontinued at integers [53,54]. 5. 2D structure of TMX2 TM stands for transition metal atom (Mo or W in this Letter), and X stands for S or Se in this Letter. The 2D TMX2 is a triple layer structure (right panel of Figure 1a). The bulk structure of TMX2 is a stacking of the 2D structure with van der Waals interactions between neighboring 2D structures [19–22,55]. The bulk TMX2 are indirect band gap semiconductors, while the 2D TMX2 have direct band gap, which is important for device application and makes the
Figure 4. Phonon dispersion of (a) 2D BN, (b) 2D AlN, (c) 2D GaN, and (d) 2D InN obtained with linear response theory. The cyan lines refer to the optical modes, the red, green and blue lines refer to the longitudinal acoustic (LA), transverse acoustic (TA) and z-direction acoustic (ZA) modes, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
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Z. Deng et al. / Chemical Physics Letters 637 (2015) 26–31
Figure 5. Energy band structure of (a) 2D BN, (b) 2D AlN, (c) 2D GaN, and (d) 2D InN obtained with PBE method. The Fermi level is set at zero.
Figure 6. Energy band structure of (a) 2D MoS2 , (b) 2D WS2 , (c) 2D MoSe2 , and (d) 2D WSe2 obtained with PBE method without (dash lines) and with (solid lines) spin–orbital coupling. The Fermi level is set at zero.
2D TMX2 more attractive. Splendiani and Lee have also reported the band gap variation with the number of layers [56,57]. Figure 6 shows that the 2D honeycomb triple layer of TMX2 has the similar band structure with each other. This is because they have the same 2D honeycomb structure and the similar outer electron structure. Another important feature is that they are all direct-gap, which makes them more suitable for microelectronic devices. When spin–orbital coupling is turned on, the top of valence band is raised at K point by 0.1–0.2 eV for MoX2 , and 0.3–0.4 eV for WX2 . The bottom of conduction band is not affected by the spin–orbital coupling. This result agrees with previous investigations of MoS2 done by Padilha who reported spin-orbital coupling mainly leads to a shift of the top of the valence band at K point [74]. Therefore the spin–orbital coupling plays an important role in IP but not in EA. Table 1 shows that the disulfide (TMS2 ) has larger EA and IP than that of diselenide (TMSe2 ), because of the
larger electronegativity of sulfur (S). Molybdenum (Mo) has larger electronegativity than that of tungsten (W), so the molybdenum disulfide (diselenide) has larger EA and IP than that of tungsten disulfide (diselenide). The band gap of TMX2 is sensitive to the number of layers and substrates [56,57]. The band gap of 8-layers-WSe2 is 1.16 eV in Ref. [58], which is much smaller than that (about 1.6 eV in this work, 1.56 eV in Ref. [59]) of single-layer WSe2 . 6. Conclusion We calculated the EA and IP of 2D honeycomb structure of carbon family, group-III-nitride family and transition-metal dichalcogenide family. We explained the reason for the buckled structure of 2D carbon family (silicene, germanene and stanene) and the planar structure of 2D group-III-nitride. The main results are: (1) 2D carbon family: silicene has the largest IP and EA, the IP
Z. Deng et al. / Chemical Physics Letters 637 (2015) 26–31
and EA decreases for larger atoms with the increase of bond length and the decrease of bond angle; (2) 2D group III-nitride: the IP (EA) decreases (increases) with the increasing atomic number of group III element atom, all atoms are in a plane; (3) 2D TMX2 : the EA and IP decrease with the increasing atomic number, the band gaps are almost the same. The spin–orbital coupling plays an important role in IP but not in EA. The physical reasons for these observations are discussed. Acknowledgements The project was supported by the National Basic Research Program of China (Grant No. 2013CB933601), National Natural Science Foundation of China (Grant No. 11274393), the Fundamental Research Funds for the Central Universities (No. 13lgpy34) and the high-performance grid computing platform of Sun Yat-sen University. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
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