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Electronic and optical properties of van der Waals vertical heterostructures based on two-dimensional transition metal dichalcogenides: First-principles calculations
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Electronic and optical properties of van der Waals vertical heterostructures based on two-dimensional transition metal dichalcogenides: First-principles calculations Kai Ren a , Minglei Sun b , Yi Luo c , Sake Wang d , Yujing Xu b , Jin Yu c , Wencheng Tang a,∗ School of Mechanical Engineering, Southeast University, Nanjing, Jiangsu 211189, China b Physical Science and Engineering Division (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia c School of Materials Science and Engineering, Southeast University, Nanjing, Jiangsu 211189, China d College of Science, Jinling Institute of Technology, Nanjing, Jiangsu, 211169, China
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Article history: Received 20 October 2018 Received in revised form 24 January 2019 Accepted 30 January 2019 Available online xxxx Communicated by R. Wu Keywords: Two-dimensional transition metal dichalcogenides First-principles calculations Heterostructures Optical absorption Application
Four vertical heterostructures based on two-dimensional transition-metal dichalcogenides (TMDs) – MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC, were studied by density functional theory calculations to investigate their structure, electronic characteristics, principle of photogenerated electron–hole separation, and optical-absorption capability. The optimized heterostructures were formed by van der Waals (vdW) forces and without covalent bonding. Their most stable geometric configurations and band structures display type-II band alignment, which allows them to spontaneously separate photogenerated electrons and holes. The charge difference and built-in electric field across the interface of these vdW heterostructures also contribute to preventing the photogenerated electron–hole recombination. Finally, the high optical absorption of the four TMD-based vdW heterostructures in the visible and near-infrared regions indicates their suitability for photocatalytic, photovoltaic, and optical devices. © 2019 Published by Elsevier B.V.
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1. Introduction
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Owing to the remarkable structure and physico-chemical performance of graphene (G) [1], other graphene-like two-dimensional (2D) materials have also attracted widespread interest [2–5]. Among the applications of 2D materials, photoelectrophysical catalysis using 2D semiconductor materials is an especially promising technology. In particular, 2D transition-metal dichalcogenides (TMDs) possess excellent mechanical, electronic, and optical properties, which make them promising candidates for a new generation of 2D photovoltaic and photocatalytic materials [6–8]. Some investigations have proved that TMDs can be formed by mechanical exfoliation [9], chemical growth [10], and even protein inducement [11]. In addition, TMDs can also serve as substrates for the construction of other 2D materials [12]. Most interesting of all, many properties of TMDs, such as their electronic structure, magnetic properties, and optical properties, can be tuned by doping [13–16], adsorption [17], chemical treatment [18], electric field [19], and strain application [20–25].
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Corresponding author. E-mail address: [email protected] (W. Tang).
https://doi.org/10.1016/j.physleta.2019.01.060 0375-9601/© 2019 Published by Elsevier B.V.
However, there is a more popular and effective method to tune the properties of 2D materials, namely, the formation of a heterostructure [26] which consists of two or more dissimilar 2D materials held together by van der Waals (vdW) forces. The vdW heterostructure not only tunes the original 2D material’s characteristics, but also further enhances its performance [27–30]. The covalent bonds between atoms ensure the in-plane stability of two-dimensional crystals in a heterostructure, while the vdW interaction combines the different layers. Many G-based vdW heterostructures have been studied because of the outstanding characteristics of G [31–35]. Hence, because TMD is a G-like 2D material, TMD-based heterostructures also have great research value [36–40], and they can be more widely used in nanodevices, optoelectronics, and photocatalysts than monolayered TMD materials [41–45]. Moreover, the formation of TMD-based vdW heterostructures has also been reported [46–48]. At the same time, 2D compounds of group IV elements have also attracted considerable interest because of their direct bandgap, which makes them promising candidates for use in optoelectronics, solar cells, and heterostructures [49–55]. Furthermore, some researchers have proved that 2D GeC has a stable structure [56,57], while the electronic properties [58] and optical properties [56] of GeC have also been studied. An investigation on the mechanical
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Fig. 1. Band structures of GeC and TMDs, obtained by vdW-corrected HSE06 calculations: (a) GeC; (b) MoS2 ; (c) MoSe2 ; (d) WS2 ; (e) WSe2 . The Fermi level is represented by the gray dashed line.
properties of monolayered GeC indicates that 2D GeC has lower stiffness and a higher Poisson’s ratio than G [59]. There are also a number of reports on the tunability of the electrical and magnetic properties of GeC via adsorption [60,61] and the application of biaxial strain [62]. Even though TMD-based vdW heterostructures have been discussed, there has been little research on vdW heterostructures formed by TMDs and GeC. Therefore, in consideration of the outstanding performance of GeC, it is necessary to study TMD/GeC heterostructures in order to obtain theoretical guidelines to further expand the application of TMDs, GeC, and their heterostructures. In this paper, the interlayer interaction were calculated for the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC and WSe2 /GeC heterostructures. We first analyzed the different structures and calculated the most stable stacking configurations. Based on these structures, the electronic properties of the heterostructures were obtained by the DFT method, and the results show that all of the four heterostructures have type-II band alignment, which impart them with the ability to effectively separate the photogenerated hole–electron pairs. The charge difference and potential drop across each interface prove that a large built-in electric field exists in the heterostructures, and the calculated optical absorption in the visible and near-infrared field indicates that the TMD-based vdW heterostructures designed in this paper have considerable prospects for application in photocatalytic, photovoltaic, and optical devices.
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2. Computational details
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In this investigation, all first-principles calculations were based on density functional theory (DFT) and conducted using the Vienna Ab Initio Simulation Package (VASP) [63,64]. The Perdew– Burke–Ernzerhof (PBE) functional with generalized gradient approximation (GGA) was used to describe the exchange correlation functional, and the hybrid Heyd–Scuseria–Eenzerhof (HSE06) functional was also used to obtain more accurate bandgap values from
the DFT calculations [65]. The DFT-D2 method of Grimme64 was considered for the van der Waals interactions in all simulations [31], and the dipole corrected functional was also adopted. The energy cutoff was set to 550 eV for plane-wave expansion, and a 17 × 17 × 1 Monkhorst–Pack k-point grid was used to represent the first Brillouin zone (BZ). Meanwhile, the convergence criterion of energy was controlled within 1 × 10−5 eV, and the residual force on each atom was set to 0.01 eV/Å. To reduce the effect of adjacent atomic layers, all the structures were relaxed in a vacuum with width of 20 Å.
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3. Results and discussion
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First, the structures of pristine monolayers of MoS2 , MoSe2 , WS2 , WSe2 , and GeC were optimized, yielding lattice constants of 3.235, 3.183, 3.303, and 3.302 Å, respectively. Fig. 1 shows that all of these monolayered 2D materials act as semiconductors, and the bandgaps of MoS2 , MoSe2 , WS2 , WSe2 , and GeC are 2.111, 1.927, 2.334, 2.038, and 2.515 eV, respectively. The calculated values of the lattice constant and bandgap all agree well with those in previous reports [36], and their direct bandgap allow them to be widely applied in digital circuits, light-emitting diodes (LEDs), and photovoltaic devices. When GeC is stacked on a TMD, six different geometric structures can be obtained. The most stable stacking configurations are the same for the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures (Fig. 2), and their binding energy (E b ) is defined as E b = E TMDs/GeC − E GeC − E TMDs , where E TMDs/GeC , E TMDs , and E GeC are the total energy of a TMD/GeC heterostructure, energy of the isolated TMD, and energy of GeC, respectively. The following discussions concern only the most stable vdW heterostructures. The calculated binding energies of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC heterostructures are −0.200, −0.189, −0.197, and −0.196 eV/A2 , respectively, which mean that all of these four TMD-based heterostructures are formed by vdW forces instead of covalent bonds. The depth of the interface (di )
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Fig. 4. Migration of photogenerated electrons and holes, as explained by the band alignment schematic of the TMD/GeC vdW heterostructures.
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Fig. 2. Top and side views of the optimized and most stable stacking configuration of each TMD/GeC vdW heterostructure. The gray, dark, yellow, and blue spheres represent the Ge, C, S (or Se), and Mo (or W) atoms, respectively. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)
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in the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures was also calculated to be 3.252, 3.374, 3.270, and 3.386 Å, respectively. Because the electronic properties of TMDs are more sensitive to strain [66], we adopted the lattice constants of TMDs as the lattice parameters of the TMD-based heterostructures examined in this study. Fig. 3 shows the projected band structures and density of states of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures in equilibrium; the dotted lines in black and red are attributed to the TMD and GeC layers, respectively. It is obvious that both the TMDs and GeC preserve their direct bandgaps, while the bandgaps of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures are 1.213, 1.674, 1.640, and 1.996 eV, respectively. It is interesting to note that the conduction band minimum (CBM) and the valence band maximum (VBM) of these four vdW heterostructures result from the TMDs and GeC, respectively, and they are located at the K point
in the Brillouin region. Furthermore, the calculated total and partial density of states for TMDs/GeC vdW heterostructures demonstrate that the CBM are mainly resulted from Mo and W atoms for MoS2 /GeC, MoSe2 /GeC and WS2 /GeC, WSe2 /GeC vdW heterostructure, respectively, while the VBM are contributed by C atoms. The band structures of the four vdW heterostructures all share the same rule of VBMTMDs < VBMGeC < CBMTMDs < CBMGeC , which results in a type-II band alignment across their respective interfaces. Hence, the band structures of these TMD-based vdW heterostructures have the ability to spontaneously separate the free holes from the free electrons, which can improve the efficiency of solarenergy conversion and optoelectronic devices. It is well known that band alignment at the vdW heterostructure interface is a significant requirement. The conduction-band offset (CBO) in the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures has values of approximately 1.168, 0.595, 0.904, and 0.389 eV, respectively, while their valence-band offset (VBO) has values of 0.892, 0.248, 0.739 and 0.298 eV, respectively (Fig. 4). Therefore, the CBO of these vdW heterostructures can promote the transfer of photogenerated electrons from the TMD layer to the CB of the GeC layer, while the photogenerated holes in the GeC layer can be reserved for the VB of the TMD layer under the
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Fig. 3. Projected band structures of the TMD/GeC heterostructures, obtained by HSE06 calculations: (a) MoS2 /GeC; (b) MoSe2 /GeC; (c) WS2 /GeC; (d) WSe2 /GeC. The red and black dotted lines indicate the contribution of GeC and the TMDs, respectively; the Fermi level is represented by the gray dashed line.
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Fig. 5. Isosurfaces of charge difference for (a) MoS2 /GeC, (b) MoSe2 /GeC, (c) WS2 /GeC, and (d) WSe2 /GeC. The colors yellow and cyan indicate the gain and loss, respectively, of electrons; the isosurface of charge difference was set to 0.0001 |e|.
light, is 400 to 760 nm, it is necessary to investigate the optical absorption of the TMD/GeC heterostructures in this region. The absorption coefficient, α (ω), is expressed by the equation
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Fig. 6. Potential drop across the interfaces of the TMD/GeC vdW heterostructures.
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assistance of the VBO, thus allowing these TMD/GeC vdW heterostructures to efficiently realize electron–hole separation when they are used as photocatalysts. Another interesting phenomenon is the large built-in electric field that exists across these vdW heterostructures, which can also explain the migration of photogenerated charges [36]. This large built-in electric field mainly stems from the charge difference in the TMD/GeC vdW heterostructures (Fig. 5), and it can be calculated using the following equation:
ρ = ρTMDs/GeC − ρTMDs − ρGeC , where ρTMDs/GeC , ρTMDs , and ρGeC are the total charge density of a heterostructure, charge density of a pristine TMD, and charge density of GeC, respectively. The isosurfaces of charge difference clearly show that GeC always contributes its electrons to the TMDs, and the charge difference of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures are calculated by Bader [67–69] charge analysis to be 0.0263, 0.0180, 0.0221, and 0.0147 |e|, respectively, which are larger than the WS2 /ZnO vdW heterostructures. The transferred charges cause potential drops (Fig. 6) of 9.4021, 9.5362, 8.2251, and 8.4196 eV across the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures, respectively, which are larger than the MoS2 /ZnO and WS2 /ZnO vdW heterostructures. Therefore, it is easy to separate the photogenerated electrons and holes under the assistance of this potential drop of the TMD/GeC vdW heterostructures. Fig. 4 shows that high ability for optical absorption as a photocatalyst is the prerequisite for a TMD/GeC heterostructure to realize the separation of photogenerated electron and holes. Since the wavelength of sunlight arriving at the earth’s surface, i.e. visible
where ε12 (ω) and ε22 (ω) are the real and imaginary parts, respectively, of the dielectric constant [70]. Fig. 7 shows the light absorption capacity of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures, and all of them exhibit excellent light-absorption performance in the visible and near-infrared (NIR) ranges. In the visible-light range, the maximum values of absorption for the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures are 1.902 × 105 , 4.548 × 105 , 2.651 × 105 , and 3.699 × 105 cm, which correspond to wavelengths of 494.383, 407.317, 462.623, and 400.000 nm, respectively. Therefore, it is reasonable to expect the application of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures in various photocatalytic, photovoltaic, and optical devices.
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4. Conclusion Four TMD-based vertical heterostructures were designed to extend the application of monolayered TMDs and GeC as 2D materials with novel properties. First-principles calculations generated optimized MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC heterostructures that were constructed by vdW interaction, and all of them are semiconductors with bandgaps of 1.213, 1.674, 1.640, and 1.996 eV, respectively. Their band energies indicate that they are type-II heterostructures, which means that they can be used in photocatalytic and photovoltaic devices because their VBO and CBO can promote spontaneous separation of the photogenerated electrons and holes. The large built-in electric field induced by charge difference further explains the migrational force driving the photogenerated electrons and holes across the interface of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures. Together with their high ability for light absorption in the visible and NIR ranges, we conclude that the TMD-based vdW heterostructures examined in this work are qualified for application in photocatalytic, photovoltaic, and optical devices.
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This work was supported by the Transformation project of scientific and technological achievements of JiangSu (BA2015077), National Natural Science Foundation of China (51675100), National Science and Technology Major Projects of Numerical control equipment (2016ZX04004008), the Innovation Project Foundation
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Fig. 7. Optical absorption by MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures, calculated using the HSE06 functional.
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Electronic and optical properties of van der Waals vertical heterostructures based on two-dimensional transition metal dichalcogenides: First-principles calculations Kai Ren a , Minglei Sun b , Yi Luo c , Sake Wang d , Yujing Xu b , Jin Yu c , Wencheng Tang a,∗ School of Mechanical Engineering, Southeast University, Nanjing, Jiangsu 211189, China b Physical Science and Engineering Division (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia c School of Materials Science and Engineering, Southeast University, Nanjing, Jiangsu 211189, China d College of Science, Jinling Institute of Technology, Nanjing, Jiangsu, 211169, China
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Article history: Received 20 October 2018 Received in revised form 24 January 2019 Accepted 30 January 2019 Available online xxxx Communicated by R. Wu Keywords: Two-dimensional transition metal dichalcogenides First-principles calculations Heterostructures Optical absorption Application
Four vertical heterostructures based on two-dimensional transition-metal dichalcogenides (TMDs) – MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC, were studied by density functional theory calculations to investigate their structure, electronic characteristics, principle of photogenerated electron–hole separation, and optical-absorption capability. The optimized heterostructures were formed by van der Waals (vdW) forces and without covalent bonding. Their most stable geometric configurations and band structures display type-II band alignment, which allows them to spontaneously separate photogenerated electrons and holes. The charge difference and built-in electric field across the interface of these vdW heterostructures also contribute to preventing the photogenerated electron–hole recombination. Finally, the high optical absorption of the four TMD-based vdW heterostructures in the visible and near-infrared regions indicates their suitability for photocatalytic, photovoltaic, and optical devices. © 2019 Published by Elsevier B.V.
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1. Introduction
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Owing to the remarkable structure and physico-chemical performance of graphene (G) [1], other graphene-like two-dimensional (2D) materials have also attracted widespread interest [2–5]. Among the applications of 2D materials, photoelectrophysical catalysis using 2D semiconductor materials is an especially promising technology. In particular, 2D transition-metal dichalcogenides (TMDs) possess excellent mechanical, electronic, and optical properties, which make them promising candidates for a new generation of 2D photovoltaic and photocatalytic materials [6–8]. Some investigations have proved that TMDs can be formed by mechanical exfoliation [9], chemical growth [10], and even protein inducement [11]. In addition, TMDs can also serve as substrates for the construction of other 2D materials [12]. Most interesting of all, many properties of TMDs, such as their electronic structure, magnetic properties, and optical properties, can be tuned by doping [13–16], adsorption [17], chemical treatment [18], electric field [19], and strain application [20–25].
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Corresponding author. E-mail address: [email protected] (W. Tang).
https://doi.org/10.1016/j.physleta.2019.01.060 0375-9601/© 2019 Published by Elsevier B.V.
However, there is a more popular and effective method to tune the properties of 2D materials, namely, the formation of a heterostructure [26] which consists of two or more dissimilar 2D materials held together by van der Waals (vdW) forces. The vdW heterostructure not only tunes the original 2D material’s characteristics, but also further enhances its performance [27–30]. The covalent bonds between atoms ensure the in-plane stability of two-dimensional crystals in a heterostructure, while the vdW interaction combines the different layers. Many G-based vdW heterostructures have been studied because of the outstanding characteristics of G [31–35]. Hence, because TMD is a G-like 2D material, TMD-based heterostructures also have great research value [36–40], and they can be more widely used in nanodevices, optoelectronics, and photocatalysts than monolayered TMD materials [41–45]. Moreover, the formation of TMD-based vdW heterostructures has also been reported [46–48]. At the same time, 2D compounds of group IV elements have also attracted considerable interest because of their direct bandgap, which makes them promising candidates for use in optoelectronics, solar cells, and heterostructures [49–55]. Furthermore, some researchers have proved that 2D GeC has a stable structure [56,57], while the electronic properties [58] and optical properties [56] of GeC have also been studied. An investigation on the mechanical
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Fig. 1. Band structures of GeC and TMDs, obtained by vdW-corrected HSE06 calculations: (a) GeC; (b) MoS2 ; (c) MoSe2 ; (d) WS2 ; (e) WSe2 . The Fermi level is represented by the gray dashed line.
properties of monolayered GeC indicates that 2D GeC has lower stiffness and a higher Poisson’s ratio than G [59]. There are also a number of reports on the tunability of the electrical and magnetic properties of GeC via adsorption [60,61] and the application of biaxial strain [62]. Even though TMD-based vdW heterostructures have been discussed, there has been little research on vdW heterostructures formed by TMDs and GeC. Therefore, in consideration of the outstanding performance of GeC, it is necessary to study TMD/GeC heterostructures in order to obtain theoretical guidelines to further expand the application of TMDs, GeC, and their heterostructures. In this paper, the interlayer interaction were calculated for the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC and WSe2 /GeC heterostructures. We first analyzed the different structures and calculated the most stable stacking configurations. Based on these structures, the electronic properties of the heterostructures were obtained by the DFT method, and the results show that all of the four heterostructures have type-II band alignment, which impart them with the ability to effectively separate the photogenerated hole–electron pairs. The charge difference and potential drop across each interface prove that a large built-in electric field exists in the heterostructures, and the calculated optical absorption in the visible and near-infrared field indicates that the TMD-based vdW heterostructures designed in this paper have considerable prospects for application in photocatalytic, photovoltaic, and optical devices.
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In this investigation, all first-principles calculations were based on density functional theory (DFT) and conducted using the Vienna Ab Initio Simulation Package (VASP) [63,64]. The Perdew– Burke–Ernzerhof (PBE) functional with generalized gradient approximation (GGA) was used to describe the exchange correlation functional, and the hybrid Heyd–Scuseria–Eenzerhof (HSE06) functional was also used to obtain more accurate bandgap values from
the DFT calculations [65]. The DFT-D2 method of Grimme64 was considered for the van der Waals interactions in all simulations [31], and the dipole corrected functional was also adopted. The energy cutoff was set to 550 eV for plane-wave expansion, and a 17 × 17 × 1 Monkhorst–Pack k-point grid was used to represent the first Brillouin zone (BZ). Meanwhile, the convergence criterion of energy was controlled within 1 × 10−5 eV, and the residual force on each atom was set to 0.01 eV/Å. To reduce the effect of adjacent atomic layers, all the structures were relaxed in a vacuum with width of 20 Å.
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First, the structures of pristine monolayers of MoS2 , MoSe2 , WS2 , WSe2 , and GeC were optimized, yielding lattice constants of 3.235, 3.183, 3.303, and 3.302 Å, respectively. Fig. 1 shows that all of these monolayered 2D materials act as semiconductors, and the bandgaps of MoS2 , MoSe2 , WS2 , WSe2 , and GeC are 2.111, 1.927, 2.334, 2.038, and 2.515 eV, respectively. The calculated values of the lattice constant and bandgap all agree well with those in previous reports [36], and their direct bandgap allow them to be widely applied in digital circuits, light-emitting diodes (LEDs), and photovoltaic devices. When GeC is stacked on a TMD, six different geometric structures can be obtained. The most stable stacking configurations are the same for the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures (Fig. 2), and their binding energy (E b ) is defined as E b = E TMDs/GeC − E GeC − E TMDs , where E TMDs/GeC , E TMDs , and E GeC are the total energy of a TMD/GeC heterostructure, energy of the isolated TMD, and energy of GeC, respectively. The following discussions concern only the most stable vdW heterostructures. The calculated binding energies of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC heterostructures are −0.200, −0.189, −0.197, and −0.196 eV/A2 , respectively, which mean that all of these four TMD-based heterostructures are formed by vdW forces instead of covalent bonds. The depth of the interface (di )
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Fig. 4. Migration of photogenerated electrons and holes, as explained by the band alignment schematic of the TMD/GeC vdW heterostructures.
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Fig. 2. Top and side views of the optimized and most stable stacking configuration of each TMD/GeC vdW heterostructure. The gray, dark, yellow, and blue spheres represent the Ge, C, S (or Se), and Mo (or W) atoms, respectively. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)
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in the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures was also calculated to be 3.252, 3.374, 3.270, and 3.386 Å, respectively. Because the electronic properties of TMDs are more sensitive to strain [66], we adopted the lattice constants of TMDs as the lattice parameters of the TMD-based heterostructures examined in this study. Fig. 3 shows the projected band structures and density of states of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures in equilibrium; the dotted lines in black and red are attributed to the TMD and GeC layers, respectively. It is obvious that both the TMDs and GeC preserve their direct bandgaps, while the bandgaps of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures are 1.213, 1.674, 1.640, and 1.996 eV, respectively. It is interesting to note that the conduction band minimum (CBM) and the valence band maximum (VBM) of these four vdW heterostructures result from the TMDs and GeC, respectively, and they are located at the K point
in the Brillouin region. Furthermore, the calculated total and partial density of states for TMDs/GeC vdW heterostructures demonstrate that the CBM are mainly resulted from Mo and W atoms for MoS2 /GeC, MoSe2 /GeC and WS2 /GeC, WSe2 /GeC vdW heterostructure, respectively, while the VBM are contributed by C atoms. The band structures of the four vdW heterostructures all share the same rule of VBMTMDs < VBMGeC < CBMTMDs < CBMGeC , which results in a type-II band alignment across their respective interfaces. Hence, the band structures of these TMD-based vdW heterostructures have the ability to spontaneously separate the free holes from the free electrons, which can improve the efficiency of solarenergy conversion and optoelectronic devices. It is well known that band alignment at the vdW heterostructure interface is a significant requirement. The conduction-band offset (CBO) in the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures has values of approximately 1.168, 0.595, 0.904, and 0.389 eV, respectively, while their valence-band offset (VBO) has values of 0.892, 0.248, 0.739 and 0.298 eV, respectively (Fig. 4). Therefore, the CBO of these vdW heterostructures can promote the transfer of photogenerated electrons from the TMD layer to the CB of the GeC layer, while the photogenerated holes in the GeC layer can be reserved for the VB of the TMD layer under the
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Fig. 3. Projected band structures of the TMD/GeC heterostructures, obtained by HSE06 calculations: (a) MoS2 /GeC; (b) MoSe2 /GeC; (c) WS2 /GeC; (d) WSe2 /GeC. The red and black dotted lines indicate the contribution of GeC and the TMDs, respectively; the Fermi level is represented by the gray dashed line.
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Fig. 5. Isosurfaces of charge difference for (a) MoS2 /GeC, (b) MoSe2 /GeC, (c) WS2 /GeC, and (d) WSe2 /GeC. The colors yellow and cyan indicate the gain and loss, respectively, of electrons; the isosurface of charge difference was set to 0.0001 |e|.
light, is 400 to 760 nm, it is necessary to investigate the optical absorption of the TMD/GeC heterostructures in this region. The absorption coefficient, α (ω), is expressed by the equation
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Fig. 6. Potential drop across the interfaces of the TMD/GeC vdW heterostructures.
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assistance of the VBO, thus allowing these TMD/GeC vdW heterostructures to efficiently realize electron–hole separation when they are used as photocatalysts. Another interesting phenomenon is the large built-in electric field that exists across these vdW heterostructures, which can also explain the migration of photogenerated charges [36]. This large built-in electric field mainly stems from the charge difference in the TMD/GeC vdW heterostructures (Fig. 5), and it can be calculated using the following equation:
ρ = ρTMDs/GeC − ρTMDs − ρGeC , where ρTMDs/GeC , ρTMDs , and ρGeC are the total charge density of a heterostructure, charge density of a pristine TMD, and charge density of GeC, respectively. The isosurfaces of charge difference clearly show that GeC always contributes its electrons to the TMDs, and the charge difference of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures are calculated by Bader [67–69] charge analysis to be 0.0263, 0.0180, 0.0221, and 0.0147 |e|, respectively, which are larger than the WS2 /ZnO vdW heterostructures. The transferred charges cause potential drops (Fig. 6) of 9.4021, 9.5362, 8.2251, and 8.4196 eV across the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures, respectively, which are larger than the MoS2 /ZnO and WS2 /ZnO vdW heterostructures. Therefore, it is easy to separate the photogenerated electrons and holes under the assistance of this potential drop of the TMD/GeC vdW heterostructures. Fig. 4 shows that high ability for optical absorption as a photocatalyst is the prerequisite for a TMD/GeC heterostructure to realize the separation of photogenerated electron and holes. Since the wavelength of sunlight arriving at the earth’s surface, i.e. visible
where ε12 (ω) and ε22 (ω) are the real and imaginary parts, respectively, of the dielectric constant [70]. Fig. 7 shows the light absorption capacity of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures, and all of them exhibit excellent light-absorption performance in the visible and near-infrared (NIR) ranges. In the visible-light range, the maximum values of absorption for the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures are 1.902 × 105 , 4.548 × 105 , 2.651 × 105 , and 3.699 × 105 cm, which correspond to wavelengths of 494.383, 407.317, 462.623, and 400.000 nm, respectively. Therefore, it is reasonable to expect the application of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures in various photocatalytic, photovoltaic, and optical devices.
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4. Conclusion Four TMD-based vertical heterostructures were designed to extend the application of monolayered TMDs and GeC as 2D materials with novel properties. First-principles calculations generated optimized MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC heterostructures that were constructed by vdW interaction, and all of them are semiconductors with bandgaps of 1.213, 1.674, 1.640, and 1.996 eV, respectively. Their band energies indicate that they are type-II heterostructures, which means that they can be used in photocatalytic and photovoltaic devices because their VBO and CBO can promote spontaneous separation of the photogenerated electrons and holes. The large built-in electric field induced by charge difference further explains the migrational force driving the photogenerated electrons and holes across the interface of the MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures. Together with their high ability for light absorption in the visible and NIR ranges, we conclude that the TMD-based vdW heterostructures examined in this work are qualified for application in photocatalytic, photovoltaic, and optical devices.
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This work was supported by the Transformation project of scientific and technological achievements of JiangSu (BA2015077), National Natural Science Foundation of China (51675100), National Science and Technology Major Projects of Numerical control equipment (2016ZX04004008), the Innovation Project Foundation
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Fig. 7. Optical absorption by MoS2 /GeC, MoSe2 /GeC, WS2 /GeC, and WSe2 /GeC vdW heterostructures, calculated using the HSE06 functional.
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