Structural and electronic properties of germanene/MoS2 monolayer and silicene/MoS2 monolayer superlattices
© Li et al.; licensee Springer. 2014
Received: 26 January 2014
Accepted: 27 February 2014
Published: 8 March 2014
Superlattice provides a new approach to enrich the class of materials with novel properties. Here, we report the structural and electronic properties of superlattices made with alternate stacking of two-dimensional hexagonal germanene (or silicene) and a MoS2 monolayer using the first principles approach. The results are compared with those of graphene/MoS2 superlattice. The distortions of the geometry of germanene, silicene, and MoS2 layers due to the formation of the superlattices are all relatively small, resulting from the relatively weak interactions between the stacking layers. Our results show that both the germanene/MoS2 and silicene/MoS2 superlattices are manifestly metallic, with the linear bands around the Dirac points of the pristine germanene and silicene seem to be preserved. However, small band gaps are opened up at the Dirac points for both the superlattices due to the symmetry breaking in the germanene and silicene layers caused by the introduction of the MoS2 sheets. Moreover, charge transfer happened mainly within the germanene (or silicene) and the MoS2 layers (intra-layer transfer), as well as some part of the intermediate regions between the germanene (or silicene) and the MoS2 layers (inter-layer transfer), suggesting more than just the van der Waals interactions between the stacking sheets in the superlattices.
In the past decade, the hybrid systems consisting of graphene and various two-dimensional (2D) materials have been studied extensively both experimentally and theoretically [1–6]. It has long been known that the thermal, optical, and electrical transport properties of graphene-based hybrids usually exhibit significant deviations from their bulk counterparts, resulting from the combination of controlled variations in the composition and thickness of the layers [6, 7]. Moreover, the use of 2D materials could be advantageous for a wide range of applications in nanotechnology [8–13] and memory technology [14–16]. Among those hybrid systems, the superlattices are considered as one of the most promising nanoscale engineered material systems for their possible applications in fields such as high figure of merit thermoelectrics, microelectronics, and optoelectronics [17–19]. While the research interest in graphene-based superlattices is growing rapidly, people have started to question whether the graphene could be replaced by its close relatives, such as 2D hexagonal crystals of Si and Ge, so called silicene and germanene, respectively. Silicene and germanene are also zero-gap semiconductors with massless fermion charge carriers since their π and π* bands are also linear at the Fermi level . Systems involving silicene and germanene may also be very important for their possible use in future nanoelectronic devices, since the integration of germanene and silicene into current Si-based nanoelectronics would be more likely favored over graphene, which is vulnerable to perturbations from its supporting substrate, owing to its one-atom thickness.
Germanene (or silicene), the counterpart of graphene, is predicted to have a geometry with low-buckled honeycomb structure for its most stable structures unlike the planar one of graphene [20–22]. The similarity among germanene, silicene, and graphene arises from the fact that Ge, Si, and C belong to the same group in the periodic table of elements, that is, they have similar electronic configurations. However, Ge and Si have larger ionic radius, which promotes sp3 hybridization, while sp2 hybridization is energetically more favorable for C atoms. As a result, in 2D atomic layers of Si and Ge atoms, the bonding is formed by mixed sp2 and sp3 hybridization. Therefore, the stable germanene and silicene are slightly buckled, with one of the two sublattices of the honeycomb lattice being displaced vertically with respect to the other. In fact, interesting studies have already been performed in the superlattices with the involvement of germanium or/and silicon layers recently. For example, the thermal conductivities of Si/SiGe and Si/Ge superlattice systems are studied [23–25], showing that either in the cross- or in-plane directions, the systems exhibit reduced thermal conductivities compared to the bulk phases of the layer constituents, which improved the performance of thermoelectric device. It is also found that in the ZnSe/Si and ZnSe/Ge superlattices , the fundamental energy gaps increase with the decreasing superlattice period and that the silicon or/and germanium layer plays an important role in determining the fundamental energy gap of the superlattices due to the spatial quantum confinement effect. Hence, the studies of these hybrid materials should be important for designing promising nanotechnology devices.
In the present work, the structural and electronic properties of superlattices made with alternate stacking of germanene and silicene layers with MoS2 monolayer (labeled as Ger/MoS2 and Sil/MoS2, respectively) are systematically investigated by using a density functional theory calculation with the van der Waals (vdW) correction. In addition, we compare the results of Ger/MoS2 and Sil/MoS2 superlattices with the graphene/MoS2 superlattice  to understand the properties concerning the chemical trend with the group IV atoms C, Si, and Ge in the superlattices. Our results show that Ger/MoS2 and Sil/MoS2 consist of conducting germanene and silicene layers and almost-insulating MoS2 layers. Moreover, small band gaps open up at the K point of the Brillouin zone (BZ), due to the symmetry breaking of the germanene and silicene layers which is caused by the introduction of the MoS2 layers. Localized charge distributions emerged between Ge-Ge or Si-Si atoms and their nearest neighboring S atoms, which is different from the graphene/MoS2 superlattice, where a small amount of charge transfers from the graphene layer to the MoS2 sheet . The contour plots for the charge redistributions suggest that the charge transfer between some parts of the intermediate regions between the germanene/silicene and the MoS2 layers is obvious, suggesting much more than just the van der Waals interactions between the stacking sheets in the superlattices.
The present calculations are based on the density functional theory (DFT) and the projector-augmented wave (PAW) representations  as implemented in the Vienna Ab Initio Simulation Package (VASP) [28, 29]. The exchange-correlation interaction is treated with the generalized gradient approximation (GGA) which is parameterized by Perdew-Burke-Ernzerhof formula (PBE) . The standard DFT, where local or semilocal functionals lack the necessary ingredients to describe the nonlocal effects, has shown to dramatically underestimate the band gaps of various systems. In order to have a better description of the band gap, corrections should be added to the current DFT approximations [31, 32]. On the other hand, as is well known, the popular density functionals are unable to describe correctly the vdW interactions resulting from dynamical correlations between fluctuating charge distributions . Thus, to improve the description of the van der Waals interactions which might play an important role in the present layered superlattices, we included the vdW correction to the GGA calculations by using the PBE-D2 method . The wave functions are expanded in plane waves up to a kinetic energy cutoff of 420 eV. Brillouin zone integrations are approximated by using the special k-point sampling of Monkhorst-Pack scheme  with a Γ-centered 5 × 5 × 3 grid. The cell parameters and the atomic coordinates of the superlattice models are fully relaxed until the force on each atom is less than 0.01 eV/Å.
Results and discussions
Binding energies, geometries, supercell lattice constants, averaged bond lengths, sheet thicknesses, and buckling of superlattices
a = b
2.410 to 2.430
2.420 to 2.440
2.400 to 2.410
2.320 to 2.330
The averaged Mo-S bond lengths of the superlattices are calculated to be all around 2.400 Å (see Table 1). The averaged Ge-Ge/Si-Si bond lengths (dGe-Ge/dSi-Si) in the relaxed superlattices are all around 2.400/2.300 Å, which are close to those in the free-standing germanene/silicene sheets (2.422/2.270 Å). Although the atomic bond lengths in the stacking planes are almost the same for Ger/MoS2 and Sil/MoS2 superlattices, the interlayer distances (d) exhibit relatively larger deviations (but still close to each other; see Table 1). A shorter interlayer distance d is found in the Ger/MoS2 system, indicating that the Ge-MoS2 interaction is stronger than the Si-MoS2 interaction in the Sil/MoS2 system. The Ge-S and Si-S atomic distances in the Ger/MoS2 and Sil/MoS2 superlattices are 2.934 and 3.176 Å, respectively, where both values are shorter than 3.360 Å in the graphene/MoS2 superlattice . Such decreases of interlayer distances indicate the enhancement of interlayer interactions in the Ger/MoS2 and Sil/MoS2 superlattices as compared to the graphene/MoS2 one. This can also explain why the amplitude of buckling (Δ) in the germanene/silicene layers of the superlattices become larger as compared to the free-standing germanene/silicene, i.e., Δ going from 0.706 to 0.782 Å in the germanene layers and from 0.468 to 0.496 Å in the silicene layers. The Ge-S and Si-S atomic distances in the Ger/MoS2 and Sil/MoS2 superlattices (2.934 and 3.176 Å) are much larger than 2.240 and 2.130 Å, the sum of the covalent atomic radius of Ge-S and Si-S atoms (the covalent radius is 1.220/1.110 Å for germanium/silicon and 1.020 Å for sulfur), which suggests that the interlayer bonding in the superlattices is not a covalent one.
To discuss the relative stabilities of the superlattices, the binding energy between the stacking sheets in the superlattice is defined as , where Esupercell is the total energy of the supercell, and and EGer/Sil are the total energies of a free-standing MoS2 monolayer and an isolated germanene/silicene sheet, respectively. When N = N(Ge/Si) = 32, the number of Ge/Si atoms in the supercell, Eb is then the interlayer binding energy per Ge/Si atom. When N = N(MoS2) = 25, the number of sulfur atoms in the supercell, then, Eb is the interlayer binding energy per MoS2. The interlayer binding energies per Ge/Si atom and those per MoS2 are presented in Table 1. is calculated by using a 5 × 5 unit cell of the MoS2 monolayer, and EGer/Sil is calculated by using a 4 × 4 unit cell of the germanene/silicene. The binding energies between the stacking layers of the superlattices, calculated by the PBE-D2 method, are both relatively small, i.e., 0.277 eV/Ge and 0.195 eV/Si for the Ger/MoS2 and Sil/MoS2 superlattices, respectively (see Table 1). The small interlayer binding energies suggest weak interactions between the germanene/silicene and the MoS2 layers. The binding energy also suggests that the interlayer interaction in Ger/MoS2 superlattice is slightly stronger than that in the Sil/MoS2 one. The interlayer binding energies are 0.354 eV/MoS2 and 0.250 eV/MoS2 for the Ger/MoS2 and Sil/MoS2 superlattices, respectively, both are larger than 0.158 eV/MoS2 in the graphene/MoS2 superlattice . This is an indication that the mixed sp2-sp3 hybridization in the buckled germanene and silicene leads to stronger bindings of germanene/silicene with their neighboring MoS2 atomic layers, when compared with the pure planar sp2 bonding in the graphene/MoS2 superlattice. In addition, the interlayer bindings become stronger and stronger in the superlattices of graphene/MoS2 to silicene/MoS2 and then to germanene/MoS2 monolayer.
In summary, the first principles calculations based on density functional theory including van der Waals corrections have been carried out to study the structural and electronic properties of superlattices composed of germanene/silicene and MoS2 monolayer. Due to the relatively weak interactions between the stacking layers, the distortions of the geometry of germanene, silicene and MoS2 layers in the superlattices are all relatively small. Unlike the free-standing germanene or silicene which is a semimetal and the MoS2 monolayer which is a semiconductor, both the Ger/MoS2 and Sil/MoS2 superlattices exhibit metallic electronic properties. Due to symmetry breaking, small band gaps are opened up at the K point of the BZ for both the superlattices. Charge transfer happened mainly within the germanene/silicene and the MoS2 layers (intra-layer charge transfer), as well as in some parts of the intermediate regions between the germanene/silicene and MoS2 layers (inter-layer charge transfer). Such charge redistributions indicate that the interactions between some parts of the stacking layers are relatively strong, suggesting more than just the van der Waals interactions between the stacking sheets.
This work is supported by the National 973 Program of China (Grant No. 2011CB935903) and the National Natural Science Foundation of China under Grant No. 11104229, 21233004.
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