Ze-Yu
Li
^{a},
Ming-Yang
Liu
^{a},
Yang
Huang
^{a},
Qing-Yuan
Chen
^{a},
Chao
Cao
^{b} and
Yao
He
*^{a}
^{a}Department of Physics, Yunnan University, Kunming, Yunnan 650091, People's Republic of China. E-mail: yhe@ynu.edu.cn
^{b}Department of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, People's Republic of China
First published on 23rd November 2017
As the isoelectronic counterpart of phosphorene, monolayer group IV–VI binary MX (M = Ge, Sn; X = Se, S) compounds have drawn considerable attention in recent years. In this paper, we construct four high-symmetry stacking models for bilayer MX to tune their electronic properties. We systematically explore the dynamical and thermal stabilities of all bilayer MX. It is found that five of them are possible at room temperature. Then, we perform first-principles calculations to study how the bilayer structure affects their electronic properties. The results demonstrate that the electronic properties of MX materials can be modulated by forming bilayer structures. Their bandgap can be tuned over a wide range from 0.789 to 1.617 eV, and an indirect-to-direct transition occurs in three cases. Considering the flexibility of bilayer MX, we utilize in-plane uniaxial tensile strain to adjust their band structures and achieve much more indirect-to-direct bandgap transitions. The realization of direct bandgaps will be helpful for their application in next-generation high-efficiency modern nano-optoelectronic and photovoltaic devices. We also study the responses of different bilayer MX to an external vertical electric field. It is found that their bandgaps decrease rapidly with the increase of the electric field.
Their bulk counterparts crystallize into an orthorhombic structure and the space group is PNMA (No. 62). The vibrational, thermodynamic, electronic and optical properties of bulk MX materials have been studied sufficiently.^{16–18} All these bulk materials have a layered structure and weak van der Waals (vdW) bonds exist between the layers. Naturally, it is possible to obtain ultrathin two-dimensional MX materials via an advanced mechanical exfoliation approach, just like graphene.^{19} Recently, SnS nanosheets have been fabricated through liquid-phase exfoliation of tin(II) sulphide, which claims the advent of two-dimensional MX materials.^{20} For MX monolayers, their hexagonal monolayer structure usually can be assembled in three different geometrical configurations, namely planar, buckled and puckered structures. In these three hexagonal structures, the puckered configuration has been demonstrated to be the most stable structure in the free-standing state by theoretical research.^{2,21} Puckered monolayer MX are constructed from a hinge-like structure where the non-planar structure leads to flexibility and a deformation potential.^{22} In this configuration, each M(X) atom covalently bonds to three nearest neighbor X(M) atoms. Because of their heterogeneous components and puckered configuration, the anisotropy of these materials is conspicuous, endowing two-dimensional MX with excellent piezoelectric performance and thermoelectric effects.^{23,24} Some studies have indicated that their piezoelectric coefficients are 1–2 orders of magnitude higher than the values for h-BN and MoS_{2} sheets due to the scarcity of centrosymmetry in this structure.^{25}
The isoelectronic counterparts of monolayer MX, i.e. black phosphorene and other group-V nanosheet materials, have been investigated systematically.^{26–33} It is well known that these materials exhibit notable thickness-dependent properties. Some studies have illustrated that forming bilayer structures of these materials is an effective way to adjust their electronic properties.^{34,35} Recently, some research studies have demonstrated that the direct bandgap of bilayer phosphorene can be changed from 0.78 to 1.04 eV in three different stacking orders. And different stacking orders influence the response of bilayer phosphorene to an external vertical electric field to different extents.^{36}
Since monolayer MX possess a similar structure to black phosphorus, we try to modulate the properties of nanophase MX materials via a similar approach. Previous research studies have disclosed that monolayer MX materials are all narrow-bandgap semiconductors that cover parts of the visible and infrared spectra.^{37} A series of excellent photovoltaic and optoelectronic applications of nanophase GeSe have been realized owing to its direct bandgap and small carrier effective mass.^{4,19} The utilization of the remaining monolayer MX materials is impeded on account of their indirect bandgaps. It is worth looking for methods to generate direct bandgaps in MX materials. In reality, bilayer SnS nanosheets have been obtained successfully using growth and exfoliation experiments.^{20} It is meaningful to investigate the variation of their electronic structures by forming bilayer MX in different stacking orders. Moreover, previous studies have proved that two monolayer MX, namely SnS and SnSe, transform into direct bandgap semiconductors under a small mechanical strain (−3% ≤ ε ≤ 3%).^{2} Based on their ultrathin and flexible structure, applying uniaxial strain will also be a strategy to tune their electronic structures. In the end, we also investigate the response of bilayer MX to an external vertical electric field.
In this paper, our results indicate that forming bilayer MX is an effective method to tune the electronic properties of nanophase MX materials. When we apply uniaxial tensile strain to bilayer MX, many direct bandgaps emerge. Different stacking bilayer MX almost exhibit a strong response to an external vertical electric field. Their tunable bandgaps distribute over a relatively wide range on this occasion.
α (Å) | β (Å) | Bandgap (eV) | ||
---|---|---|---|---|
PBE | HSE06 | |||
GeSe |
3.985
3.965^{2} |
4.273
4.302^{2} |
1.146
1.160^{2} |
1.587
1.71^{45} |
GeS |
3.681
3.642^{2} |
4.425
4.492^{2} |
1.678
1.757^{2} |
2.344
2.43^{45} |
SnSe |
4.246
4.260^{2} |
4.316
4.453^{2} |
0.916
0.929^{2} |
1.468
1.44^{45} |
SnS |
4.056
4.047^{2} |
4.224
4.347^{2} |
1.460
1.447^{2} |
2.058
2.03^{45} |
Secondly, after the optimization, we turn to construct models of bilayer MX for further study. Through sufficient analysis, we choose four different high-symmetry stacking orders of bilayer MX. These four models are named after AA, AB, AC and AD, respectively, as depicted in Fig. 2. In the AA stacking order, without any change, the upper layer just stacks over the under layer directly. In the AB and AC stacking orders, the upper layer shifts along either the α or β direction by a half lattice constant, respectively. In the AD stacking order, the upper and under layers are the mirror images of each other, shifting one of them along both the α and β directions successively by a half lattice constant to build it. After full optimization, we calculated the relaxed lattice constants and nearest distances between the upper and under layers (d_{int}) of these four structures, listed in Table 2 in order. It is obvious that the changes in lattice constants are mostly small compared with monolayer MX. And d_{int} is larger than that of bulk MX, which can be ascribed to the change in interaction between interlayers. In the same stacking order, the different elementary compositions of MX induce relatively small differences of d_{int}. However, in the same MX material, the differences of d_{int} in the four stacking orders are remarkable.
Fig. 2 (a) The unit cell of bilayer MX. (b–e) Top and side views of the four possible stacking orders (AA, AB, AC, and AD) of bilayer MX. |
AA | AB | AC | AD | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
α (Å) | β (Å) | d _{int} (Å) | α (Å) | β (Å) | d _{int} (Å) | α (Å) | β (Å) | d _{int} (Å) | α (Å) | β (Å) | d _{int} (Å) | |
GeSe | 3.932 | 4.138 | 3.004 | 3.894 | 4.339 | 3.019 | 3.946 | 4.201 | 3.091 | 3.943 | 4.202 | 3.524 |
GeS | 3.681 | 4.291 | 3.227 | 3.666 | 4.363 | 2.793 | 3.713 | 4.234 | 2.963 | 3.675 | 4.330 | 3.458 |
SnSe | 4.226 | 4.254 | 3.227 | 4.211 | 4.348 | 3.016 | 4.252 | 4.236 | 3.060 | 4.241 | 4.250 | 3.626 |
SnS | 4.051 | 4.132 | 3.187 | 4.029 | 4.132 | 2.906 | 4.078 | 4.079 | 3.025 | 4.064 | 4.113 | 3.599 |
For example, d_{int} ranges from 3.626 to 3.016 Å in the SnSe subsystem. It is clear that the d_{int} is affected strongly by different interactions of stacking orders. In these four stacking orders, the dislocation of the upper and under layers in the AB and AC stacking orders gives more space to accommodate the host atoms. In contrast, the mirror images of each other in the AD stacking order mean the mutual competition of the same atoms having a relatively large incompatibility. Hence, in all structures, the biggest d_{int} of these four MX materials is in AD stacking order without exception. At the same time, the smallest d_{int} is almost in AB stacking order that has the strongest compatibility.
To evaluate the stability of bilayer MX, we calculate the binding energy (E_{b}), phonon dispersion spectrum, and AIMD to ensure their dynamical stability and thermal stabilities. We obtain the E_{b} according to the formula which is defined as
E_{b} = E_{bilayer} − 2E_{monolayer}, | (1) |
AA | AB | AC | AD | |
---|---|---|---|---|
GeSe | −27.534 | −27.935 | −28.473 | −17.081 |
GeS | −18.867 | −29.385 | −25.508 | −14.705 |
SnSe | −30.594 | −40.526 | −40.696 | −23.413 |
SnS | −26.884 | −39.525 | 25.790 | −20.401 |
To check the practical possibility of these structures, we perform phonon dispersion and AIMD simulations. However, a further calculation of their phonon structures indicates that there are only nine structures existing at 0 K. None of them belongs to the GeSe subsystem. The phonon dispersion spectra based on PBE structural parameters are shown in Fig. 4. Furthermore, it is essential to ensure the stability of bilayer MX at finite temperature for their practical application. So the stability of these structures is further investigated by AIMD simulations at finite temperature (300 K) in 3 ps. The results elucidate that bilayer GeS structures are unstable at room temperature, which means that bilayer GeS material may not be synthesized. The AD stacking bilayer SnSe evolves into a new structure that is formed by shifting the upper layer along the α and β directions by a quarter lattice constant successively, as in Fig. 5. After the AIMD simulations, the AD stacking bilayer SnS is also transformed into an unstable structure. Thus, we confirm that five presupposed bilayer MX structures are stable for practical applications.
Fig. 5 (a and b) The oblique, top and side views of a new bilayer SnSe structure after the AIMD simulations. |
In these five stable structures, for the same MX material, a smaller binding energy tends to be related to a smaller d_{int} illustrated by Tables 2 and 3. The magnitude of binding energy does not show an apparent sequence. Correspondingly, the most stable structure of bilayer MX appears alternately in AB or AC stacking order mainly because of the differences in the electronegativities and atomic radii of anions. The result implies that the staggered structure facilitates the buildup of bilayer MX. Therefore, these two stacking orders are the most reasonable constructions of bilayer MX.
AA (%) | AB (%) | AC (%) | |
---|---|---|---|
SnSe | −46.253 | −23.569 | −34.469 |
SnS | −24.733 | −21.429 | — |
There is another important result that the band structures of bilayer MX possess many conduction-band minima and valence-band maxima. We note that the energy difference between the indirect and direct band gaps is small in several bilayer MX. The values of direct and indirect bandgaps and their absolute differences are given in Table 5. It will be meaningful to accomplish an indirect to direct bandgap transition in these bilayer MX by appropriate external influences.
AA | AB | AC | |||||||
---|---|---|---|---|---|---|---|---|---|
Bandgap | Indirect (eV) | Direct (eV) | Diff (eV) | Indirect (eV) | Direct (eV) | Diff (eV) | Indirect (eV) | Direct (eV) | Diff (eV) |
SnSe | 0.789 | 0.814 | 0.025 | 1.232 | 1.122 | 0.110 | 1.101 | 0.962 | 0.139 |
SnS | 1.549 | 1.620 | 0.071 | 1.659 | 1.617 | 0.042 | — | — | — |
In consideration of the flexibility of bilayer MX, like other two-dimensional materials, we achieve indirect-to-direct bandgap transitions by applying a small in-plane uniaxial tensile strain (−3% ≤ ε ≤ 3%) to bilayer MX. For example, 2% or 3% tensile strain along the α direction converts AA and AB stacking bilayer SnS into direct bandgap semiconductors. In the SnSe system, the uniaxial tensile strain is also able to convert indirect into direct bandgaps as illustrated in Fig. 7. From Fig. 7, we find that all direct bandgaps lie in the region between Y and Γ points because of the shift of the CBM.
Fig. 7 Under in-plane uniaxial tensile strain, the direct bandgaps of bilayer MX are all highlighted by green arrows. |
These results suggest that the direct bandgap tends to emerge from the configurations possessing approximate lattice constants, i.e. α ≈ β. According to the definition of the structure anisotropy factor κ,
κ = (α − β)/(α + β) | (2) |
The electronic structures display a wide bandgap range which is from 0.789 to 1.617 eV for different stacking bilayer MX. The bandgap covers more regions of the visible and infrared spectra. At the same time, an effective approach is proposed to achieve an indirect-to-direct bandgap transition by applying an in-plane uniaxial strain (−3% ≤ ε ≤ 3%). These direct bandgaps are also located over a wide range from 0.902 to 1.624 eV. This result will be beneficial to fabricate high-efficiency modern nano-optoelectronic and photovoltaic devices.
When an external vertical electric field is applied to bilayer MX, the bandgap can be tuned effectively like bilayer phosphorene. The responses of most bilayer MX show poor endurance against the external electric field. Their bandgaps decrease quickly and vanish at some electric field value. This result suggests that both stacking orders and electric field can help in promoting their potential application in nanoelectronics. Combined with the breakthrough in experiment, it is expected that bilayer MX may become promising 2D materials for high-efficiency modern electronic devices in the future.
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